Spin-Resolved Valence Photoemission … · 1D One dimensional 2D Two dimensional 2PPE Two-photon...

Spin-Resolved Valence Photoemission

Elaine A. SeddonThe Photon Science Institute, The University of Manchester, Manchester, UKThe Cockcroft Institute, Sci-Tech Daresbury, Daresbury, Warrington, UK

Abstract

Spin-resolved valence photoemission has recently seen a resurgence of interest fostered by excitingresults in a range of interesting materials. Reviewed here are the basics of, the instrumentation for, andtechniques useful in spin-resolved photoemission, together with illustrative examples of its utilization formaterials of general importance and of particular relevance to spintronics applications. The examplematerials are broadly classified into nonmagnetic and magnetic systems. The former covers Rashbasystems and topological insulators. The latter includes thin films, half-metals, adsorbates and inducedmoments, and, finally, a short section on imaging. The review is not intended to be comprehensive in itscoverage but rather to provide an introduction to hardware and techniques together with an overview ofselected results and state-of-the-art developments.

List of Abbreviations

1D One dimensional2D Two dimensional2PPE Two-photon photoemission3BS Three-body scatteringARPES Angle-resolved photoemission spectroscopyBCB Bulk conduction bandbcc Body-centered cubicBISS Bulk-induced spinterface stateBVB Bulk valence bandBZ Brillouin zoneDFT Density functional theoryDOS Density of statesEF Fermi energyFM FerromagnetFOM Figure of meritFS Fermi surfaceHA Hemispherical analyzerH2Pc PhthalocyanineHHG High harmonic generationHIS Hybrid interface stateHOMO Highest occupied molecular orbitalLDC Lower Dirac coneLEED Low-energy electron diffractionMCP Multichannel plateMDC Momentum distribution curve

Handbook of SpintronicsDOI 10.1007/978-94-007-7604-3_32-1# Springer Science+Business Media Dordrecht 2014

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ML MonolayerMPc Metal-phthalocyanineOEP OctaethylporphyrinOSC Organic semiconductorPEEM Photoelectron emission microscopeQL Quintuple layerRT Room temperatureSBZ Surface Brillouin zoneSEMPA Scanning electron microscopy with polarization analysisSISS Surface-induced spintronic stateSO Spin-orbitSPLEED Spin-polarized low-energy electron diffractionSR-2PPE Spin-resolved two-photon photoemissionSRARPES Spin-resolved and angle-resolved photoemission spectroscopySRPE Spin-resolved photoemissionSRPEEM Spin-resolved photoelectron emission microscopeSRPES Spin-resolved photoemission spectroscopySR-STS Spin-resolved scanning tunneling spectroscopySS Surface stateTI Topological insulatorTOF Time-of-flightTR Time-resolvedTSS Topological surface stateUDC Upper Dirac coneUV UltravioletXMCD X-ray magnetic circular dichroism

Introduction

Spintronics devices are typically built from complex ferromagnetic/nonmagnetic multilayers, the overallperformance of which are determined both by the characteristics of the individual layers and theirinterfaces. The relevant fundamental properties of these layers and interfaces are often studied by spin-resolved photoemission spectroscopy (SRPES) which is a very powerful and well-proven probe of spin-dependent electronic structure and which gives insight into, for example, band structure, exchange, andSO effects.

This review presents the basics of, and instrumentation for, valence SRPES together with illustrativeexamples of its utilization for materials of relevance to spintronics applications. The review is notintended to be comprehensive in its coverage rather to provide an introduction to the techniques togetherwith an overview of selected results and state-of-the-art developments. The aim has been for clarity and toprovide sufficient pointers for those who intend to dig deeper into specific areas. Advances in theory arenot explicitly covered.

The essentials of spin-resolved photoemission (SRPE) are presented in “Spin-ResolvedPhotoemission” which also includes material on photon sources and 2-2PPE. Statistical errors relevantfor measured spectra are discussed within “Instrumentation.” This section starts with an introduction tospin polarimetry and then presents a number of illustrative examples of some of the latest developmentsand trends. Also included are subsections on polarimeter calibration (see “Polarimeter Calibration”),


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instrumental asymmetry (see “Instrumental Asymmetry and its Elimination”), errors (see “PolarimeterErrors”), and peak fitting (see “Peak Fitting”).

The remainder of the review is concerned with examples and is split into nonmagnetic(see “Non-magnetic Surfaces and Thin Films”) and magnetic (see “Magnetic Systems”) systems. Asthe Rashba effect can be used to manipulate spin-polarized currents in semiconductor heterojunctions, itsimpact on spin-resolved band structures is presented in detail in “The Rashba Effect.” The classicShockley SSs of Au(111),

ffiffiffi3

p � ffiffiffi3

p� �-Au/Ge(111), and W(110)-(1 � 1)H are the three principal

examples in the following subsections.Topologically ordered phases of matter display collective quantum motion of electrons that give rise to

unconventional spin physics at sample surfaces and have considerable technological potential. Bi2Se3 andBi2Te3 exhibit a rich variety of effects and have been studied extensively both from theoretical andexperimental viewpoints. Spin-resolved and angle-resolved photoemission (SRARPES) on these andrelated systems has revealed a wealth of information that is covered in “Topological Insulators.”

The “Magnetic Systems” section presents a cross section of results on magnetic materials. SRPE, in itsvarious guises, has played a major role in the direct exploration of phenomena that occur as parameterssuch as film thickness, temperature, composition, etc. are varied. This section aims to highlight somecurrent developments involving ferromagnetic thin films (see sections “Surface and Bulk ElectronicStructure,” “Temperature Dependence and the Persistence of Short Range Order above TC,” “Spin AxisReorientation”) and half-metals (see section “Half-Metals”) that have general relevance to spintronics.Half-metallic behavior has been proposed for a range of oxides such as CrO2, Fe3O4, and variousmanganites, various sulfides, and many Heusler alloys. However, as discussed in “Half-Metals,” thearea is fraught with controversy.

As electrons in organometallic semiconductors typically have long spin relaxation times and becausethe interfaces between them and ferromagnetic metals have attracted considerable interest due to theirflexibility and potential for chemical “tailoring,” the results of recent studies on model systems such asCo/CuPc and Co/Al(OP)3 are discussed in “Ferromagnet/Adsorbate Interfaces.” This section focusesparticularly on the wealth of information concerning hybrid interface states (HISs) that can be gleanedfrom SRPES together with theory – information that is important for understanding and thereforemanipulating the magnetoresistance of, for example, organic spin valves.

“Spin-Resolved Imaging” covers spin-resolved imaging and in particular the recently developed, muchimproved, spin-resolved photoelectron emission microscope (SRPEEM) utilizing multichannel spinpolarimetry principles. A flavor of recent contributions made by SRPE techniques to magnetodynamicsin itinerant ferromagnets is presented in “Dynamics.” Confined systems such as thin films often exhibitunique electronic and magnetic characteristics and information on the temporal behavior of their spin-dependent electronic structure is essential for understanding the fundamental physics behind theirproperties. Hot electrons also play an important role in the transport of spin-dependent currents.

Spin-Resolved Photoemission

The basics of photoemission are detailed in a number of books and reviews [e.g., 1–4]; those of SRPESare covered in works by Johnson [5], Osterwalder [6], and Suga and Sekiyama [7].

Though SRPES is muchmore exacting than spin-integrated photoemission and technical developmentsin the field have been sporadic, recently there has been a significant rise in the number of spin-resolvedreports on materials of technological relevance and on instrumental developments that promise torevolutionize the technique.


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The process of spin-resolved photoemission is a very direct way to obtain electronic structureinformation. At its most basic, it involves allowing a monochromatic photon beam, of energy ħo, toimpinge upon a material and then a measurement of the total number of emitted photoelectrons and theirpolarization – regardless of their direction of emission or energy. Many of the early spin-resolvedphotoemission experiments from solids yielded plots of spin polarization versus photon energy andinvolved ionization with photons from monochromated discharge or arc sources (e.g., [8–10]). Thephotoelectrons were accelerated, without prior energy selection, to 100 keV for spin analysis by Mottscattering (of which more later). However, very soon after these pioneering works, it was recognized thatthe extra information attainable by employing photoelectron energy selection prior to spin analysisjustified the extra experimental effort.

The initial states in a material may or may not exhibit energy differences dependent upon their spincharacter, but if they are spin-split, then, as photoemission is to good approximation a spin conservingprocess, this will generally be apparent in the measured spectra.

Given a known photon energy,ħo; and work function, f, the photoelectron kinetic energies, EK, revealinformation about electron binding energies, EB, and can be compared to calculated spin-specific electrondensities of state using

EB ¼ ħo� EK � f (1)

Many basic SRPES measurements are of this type; see Fig. 1 in which the initial states are exchange split.

Fig. 1 Schematic of the link between spin-resolved density of states information and photoemission from solids withphotoelectron energy resolution. The dashed red (dark blue) line represents negative (positive) spin


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However, it is possible to go further, assuming the electron momentum parallel to the surface is conservedon photoemission (but see below); by measuring both the kinetic energy, EK, and emission angle, y, of theemitted electrons, it is possible to obtain directly the binding energy, EB, and the in-plane momentum, kk,values for the electron states within a crystal:

kk ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi2meEK

ħ2

rsin y (2)

¼ 0:5123ffiffiffiffiffiffiEK

psin y (3)

where me is the electron mass, kk is expressed in Å�1, and EK is in eV. Due to the abrupt potential change,

V0, perpendicular to the surface the out-of-plane momentum, k⊥ is not conserved on photoemission.However, making certain assumptions concerning the dispersion of final electron states, it is possible toarrive at a value for k⊥ [3]. A single plot of k versus binding energy is referred to as a momentumdistribution curve (MDC); a plot of a series of MDCs is a momentum distribution map (e.g., Fig. 14).

In many cases, angle-resolved photoemission has been described by the so-called “three-step model” inwhich step 1 is a direct transition to a nearly free final state (similar to a free-electron state) within the solid,step 2 involves transmission to the surface, and step 3 covers emission from the surface. When this approachhas been adopted, peaks in the experimental spectrum are assigned by matching the points where thefree-electron parabola, displaced by the photon energy, and the calculated band structure overlap; see Fig. 2.

This approach has particular limitations for initial states for which electron correlation is important asthese states behave as though the electron mass is larger than the true electron mass. This effective electronmass, denoted by m*, varies with the degree of correlation (i.e., photoemission peaks similar in bindingenergy may have different effective masses) and is very important for many systems not least the first rowtransition metals Fe, Co, and Ni (see “Surface and Bulk Electronic Structure”).

Fig. 2 Left panel, band structure calculation for Fe along GH; solid red (dashed blue) lines represent majority (minority) spinbands, and the solid black line is a free-electron final state with V0 set to 10 eV. Right panel, spin-polarized photoemissionspectrum taken at normal emission with hƲ = 128 eV [235] (Reproduced with permission from Physical Review B, Copyright2007 American Physical Society)


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Complications to this simple picture of photoemission also occur when SO coupling is significant (i.e.,when heavy atoms are present) and when final state effects come into play.

More precisely, photoemission involves promoting a solid (ofN electrons within the interaction region)from an initial state Ci (N) to a (N � 1) photoexcited electron state Ci (N � 1, ki) with a hole in state kiand an electron in a free-electron state that propagates in the vacuum. The photoemission intensity in aparticular direction (y, ’) can be written as

I ϵf , k� � � Mi, f

�� 2 � A ki ,Eð Þ � d ki � kf þ G� �� d ϵf þ E0

f þ E � Ei � hu� �

(4)

whereMi,f is a one-electron matrix element, A(ki, E) is a spectral function of the system, E is the excitationenergy of the many-body system, and the two delta functions represent energy and momentum conser-vation [6]. In the one-electron picture, E ¼ 0, and the difference in the total energy between the final andthe initial states, E0

f � Ei, corresponds to the binding energy EB of the one-electron wave function.The spectral function yields energy and momentum space information on the occupied and unoccupied

single-particle states. It is frequently expressed in terms of a “self-energy” which describes how particlesare “dressed” by their interactions with the remainder of the system. The real part of the self-energy isrelated to binding energy renormalization (i.e., binding energy shift), and the imaginary part of the self-energy is related to peak width (i.e., the decay rate of the photohole).

As described above, it is frequently asserted that electron spin is a conserved quantity in photoemission,thus allowing a direct link back to the electronic structure of the material under investigation. However,while this is a valid assumption in many cases, recent studies have clearly shown that it is not always thecase. Admittedly, the incident photons do not couple directly to the electron spin, but indirect couplingdoes occur due to spin-dependent effects in the (N � 1) electron system, due to SO coupling and spin-dependent elastic exchange scattering in the photoelectron final state, or due to spin-dependent inelasticscattering during electron transport to the surface [6, 11].

The matrix elements link the initial and the final states. In the nonrelativistic limit, transitions betweenone-electron states excited with linearly polarized photons are limited to transitions with Dl ¼ �1 andDml ¼ 0. With circularly polarized photons, the transitions are limited to Dl ¼ �1 and Dml ¼ �1 – thelatter depending on the handedness of the radiation. When SO coupling is significant, the total angularmomentum must be used and the appropriate selection rules are Dj ¼ 0, �1 and Dmj ¼ �1.

For standard angle-resolved photoemission spectroscopy (ARPES), the energy and angular resolutionsare routinely 3–5 meVand 0.1�, respectively (and sub-meV resolution has been achieved); however, theadditional experimental burden of spin resolution means that in general these parameters are relaxed to afew tens of meV and 1–3 % of the SBZ (surface Brillouin zone).

The identification of surface as opposed to bulk features can be achieved using ARPES by measuringmomentum distribution curves over a range of photon energies and angles that are chosen to access thesamekk but differentk⊥. Peaks that do not disperse withk⊥ are indicative of SSs. Broad bands with strongdispersion are indicative of emission from bulk bands.

After selecting photoelectrons on the basis of their energy and angle of emission (or integrating over alarge emission angle), their spin is determined by one of the techniques outlined in the following section.These measurements permit a so-called complete experiment as all of the quantum numbers of thephotoelectrons are known.

The polarization, P, of a free-electron beam with respect to a particular axis may be determinedexperimentally by a range of spin-sensitive techniques that primarily involve scattering measurementsfrom metals with strong SO coupling or long-range ferromagnetic order.

For the strong SO coupling case, a measured, normalized, asymmetry, Ameas,


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Ameas ¼ NL � NR

NL þ NR(5)

is then related to the polarization by

P ¼ Ameas

Seff(6)

where Seff, the effective Sherman function, represents the analyzing power or spin sensitivity of thepolarimeter and NL and NR are the number of electrons counted in the left and right backscatteringdetectors. By measuring the polarization and the spin-integrated intensity, IT = NL + NR, the spin-resolved intensities can be recovered using

I" ¼ 1þ Pð ÞIT2

(7)

I# ¼ 1� Pð ÞIT2

(8)

For magnetic scattering measurements, see “Exchange Scattering Polarimetry.” In many cases, boththe polarization and the spin-resolved intensities are reported in papers; see, for example, Fig. 3.The statistical errors for measured polarizations are discussed in “Polarimeter Errors.”

Fig. 3 A particularly clear example of (a) spin-resolved photoemission bands and (b) the measured polarization (Data forBi2Se3 adapted from Pan et al. [137]) (Reproduced with permission from Physical Review Letters, Copyright 2011 AmericanPhysical Society)


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In the above explanation, only one component of the polarization is measured. In manyinstances nowadays, the two transverse components of P are measured in one polarimeter, and byhaving two polarimeters at right angles, all three components are measured with some redundancy;see “Mott Scattering.”

Avariety of laboratory sources have been used for SRPES; these include DC discharge sources for UVradiation below 50 eV and laser sources. Most laser-based work has been undertaken using Ti-sapphirelasers. Current high harmonic generation (HHG) laser sources, though capable of generating up to around140 eV, do not deliver photon fluxes sufficient for SRPES with standard retarding Mott polarimeters. Yethigher energies are available from the free-electron laser sources that have been, or are currently being,developed worldwide. Though these sources have been used for some time for gas-phase spin-polarizedphotoelectron spectroscopy, the first spin-resolved publication for surfaces has only recently emerged[12]. Synchrotron radiation has on the other hand been very widely used for SRPES, and facilities exist at,for example, the Advanced Photon Source (APS), the Advanced Light Source (ALS), the Swiss LightSource (SLS), the European Synchrotron Radiation Facility (ESRF), Soleil, BESSY, DELTA, the PhotonFactory KEK, the Hiroshima Synchrotron Radiation Centre (HSRC), MAX-Lab, and the SynchrotronRadiation Research Centre (Hsinchu, Taiwan) [13–22]. This is a direct consequence of the photon energyreach, the intensity, the tunability, and the polarization characteristics of synchrotron radiation. Inphotoemission from alloys or adsorbate systems, the use of synchrotron radiation of more than onephoton energy is frequently employed so that cross-section effects enable the atomic origin of states to beidentified. The tabulated atomic cross-section information of Yeh and Lindau are often cited [23].

The incorporation of time resolution into SRPES undoubtedly adds a level of complexity, but it has thepotential to allow detection of transient changes in electronic structure and has been used to revealnonequilibrium processes in materials. Advances in laser and synchrotron radiation technology haveensured that this area of research has undergone major development over the last decade. Picosecondpulses of synchrotron radiation are naturally generated in single or few-bunch mode, and pulse slicing hasenabled pulses in the femtosecond regime but with, typically, only 106 photons per pulse.

Modern laser sources have been employed to good effect for linear TR-ARPES (right – hand process inFig. 4) and, in particular, nonlinear two-photon photoemission (2PPE) (left-hand process in Fig. 4). In a

Fig. 4 Schematic of the basis of 2PPE from a metal surface [26] (Reproduced with permission from CHIMIA, Copyright 2011CHIMIA)


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typical SR-2PPE setup, the linearly polarized beam from a Ti-sapphire laser is frequency doubled to yieldca. 2 nJ pulses with a photon energy of 3.1 eVand a repetition rate of 80 MHz. This beam is then split intotwo equally intense, orthogonally polarized beams frequently termed the pump and the probe the latter ofwhich follows a path with a variable delay stage. Two-colour 2PPE with a fraction of the 800 nm beamused as the pump beam is also often utilised. As indicated in Fig. 4 the pump photons excite electrons fromtheir ground state to an intermediate unoccupied state below the vacuum level. The probe photons thenexcite these electrons to above the vacuum level. By varying the time delay between pump and probephotons and analyzing the spin, kinetic energy, and parallel momentum of the photoelectrons, thetemporal evolution of the excited state can be followed with fs resolution [24–27].

Photoemission spin polarization of transition metals measured by 2PPE is typically enhanced by afactor of two compared with direct single-photon photoemission [24, 25]. While the polarization resultingfrom single-photon photoemission is, in principle, a direct measure of the occupied DOS, that resultingfrom 2PPE also depends on the spin-dependent lifetimes of the intermediate states. For ferromagnetic Feand Co, there is greater opportunity for the excited minority spin electrons to decay than for thecorresponding majority spin electrons; the lifetimes of the latter are therefore significantly longer thanthe former [28]. The spin-dependent lifetimes of both majority and minority spin electrons are ofparticular relevance to transport measurements.

Instrumentation

Instrumentation suitable for SRPES has been presented a number of times over the years [13, 14, 16,29–33]; hence, this review will focus on the essential basics and give a few illustrative examples of someof the latest developments and trends.

Given the relative inefficiency of spin polarimetry, the importance of a whole system approach, leadingto a total spectrometer efficiency, cannot be overemphasized. While the most common systems are, due totheir relative simplicity and reliability, undoubtedly hemispherical analyzer plus some variant of Mottpolarimeter (see “Mott Scattering”), several groups have taken advantage of the parallel energy detectioncharacteristics of TOF energy analyzers and combined themwith polarimeters. For example, instrumentaldevelopments at the ALS have resulted in a system employing a TOF electron energy analyzertogether with a high-efficiency low-energy exchange scattering polarimeter; see “Exchange ScatteringPolarimetry.” Finally, an exciting though experimentally demanding recent breakthrough has been thedevelopment of a multichannel spin polarimeter based on spin-polarized low-energy diffraction. This isdiscussed in “Spin-Polarized Low-Energy Electron Diffraction (SPLEED) Polarimetry.”

Spin Polarimetry Techniques and Data HandlingA variety of techniques, based primarily on the SO or the exchange interaction, has been developed toallow determination of the polarization state of the free electrons generated in SRPES. Mott polarimetrytechniques have been reviewed a number of times (see, e.g., [34–39]) as having the essential performancecharacteristics of different polarimeters (see [40–42]). Here the focus is on polarimetry for photoemissionincluding a number of important recent advances.

Mott ScatteringFollowing theoretical work by Nevill Mott in the 1930s [43, 44], electron scattering by a high Z targetmaterial, such as gold, was the first technique to be employed for the determination of the polarization of afree-electron beam. The early polarimeters, now generally referred to as “classical” Mott polarimeters,were bulky (typically several cubic meters) as electron energies of around 100 keVwere involved for both


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scattering and detection. A modern classical Mott polarimeter has been developed and fully characterizedby Petrov [45, 46]. This instrument (which is commercially available; see “Commercially AvailablePolarimeters”) has a spherical geometry and is used, inter alia, for photoemission studies on the SwissLight Source where it has proved to be very reliable. Though still widely used in accelerator environmentsfor high-energy beam characterization [47], classical Mott polarimeters have for photoemissionapplications largely, though by no means entirely, given way to so-called retarding Mott polarimeters,in which the scattering occurs at around 20 keV and the electron detection at low energy. Following asuggestion by Farago, pioneering work on this approach was performed by Campbell in the earlyeighties [48].

The polarization measurement involves interacting the electron beam with, for example, gold orthorium and measuring the normalized intensity difference in two symmetrically placed backscatteringdetectors situated in the scattering plane; see Fig. 5. Assuming ideal conditions, asymmetry measured inthe scattering plane (defined by the incoming and outgoing detected electrons) gives information on thepolarization component of the incoming beam perpendicular to the scattering plane.

The asymmetry is defined as:

A ¼ NL Tð Þ � NR Bð ÞNL Tð Þ þ NR Bð Þ

(9)

where NL(T), NR(B) are the number of electrons counted in the detectors placed to the left (top), right(bottom) in the horizontal (vertical) scattering plane (top, bottom, left, right are numbered 1–4, respec-tively, in Fig. 5). The polarization, P, is then determined using Eq. 6. In situations where multiple orinelastic scattering is minimized (e.g., in extremely thin target foils), Sherman functions approaching�0.5 are possible, but in general values are of the order of �0.2 and depend on experimental factors.(Note: Though the Sherman function value for high-energy scattering at angles around 120� is negative, inthe literature its magnitude is often quoted without attention to its sign. Spin sensitivity, which is theequivalent of the effective Sherman function for polarimeters other than the high-energy scattering type, isgenerally quoted as a positive quantity.) The spin sensitivity is then referred to as the effective Shermanfunction and is denoted by Seff. The polarization taken together with the total intensity, IT = NL + NR,gives the spin-resolved intensities; see Eqs. 7 and 8).

The figure of merit (FOM) by which scattering polarimeters may be compared is derived by aconsideration of statistical errors in polarization measurement [49] and is given by

Fig. 5 Detector arrangement for determining electron beam polarization by scattering


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F ¼ S2effI

I0(10)

where I is the detected beam intensity and I0 is the incoming beam intensity. Typically, for a high-energy(classical) Mott polarimeter, F is circa 10�4.

Since their introduction in the late 1980s [50], compact retarding Mott polarimeters have proved apopular choice for integration with electron energy analyzers for photoemission. In particular, the periodfrom 2000 to 2010witnessedmany examples of the incorporation of this simple robust type of polarimeterinto instrumentation in both university and synchrotron radiation laboratories [14, 16, 17, 22, 30, 32, 33,51–56].

A compact example is illustrated in Fig. 6. Electrons entering the polarimeter at the top are scatteredfrom a target foil (maintained in this case at 25 kV) towards detectors in the backscattering direction.Rejection of inelastically scattered electrons is controlled by adjusting the voltage on retarding grids. TheSherman function and FOM of the polarimeter are �0.374 and ~1.3 � 10�4, respectively. The errorsassociated with spin polarization measurement by Mott scattering are generally dominated by thestatistical error of counting the detected electrons (see [57]; see “Polarimeter Errors”).

Routinely, the two transverse components of the polarization are determined in which case Ax and Ayare given by

Ax ¼ N1 � N2

N1 þ N2(11)

and

Ay ¼ N3 � N4

N3 þ N4(12)

Fig. 6 A compact retarding Mott polarimeter [51] (Reproduced with permission from Reviews of Scientific Instruments,Copyright 2007 AIP Publishing LLC)


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where the detector numbering is given in Fig. 5. Increasingly, full polarization measurements are required.In this case, two orthogonal polarimeters can be used to obtain all three polarization components. Thisapproach has been taken in the COPHEE apparatus on the Swiss Light Source; see Fig. 7. Photoelectronsfrom the sample are energy and angle selected by a combination of an input electron lens and hemispher-ical analyzer; they are then electrostatically deflected into one or other of the two high-energy (60 keV)spherical polarimeters to obtain Py, Pz (from polarimeter 1) and Px, Pz (from polarimeter 2) [15]. The factthat Pz is obtained twice is useful as a cross-check during data acquisition.

Exchange Scattering PolarimetryExchange scattering polarimeters utilize scattering from a magnetic target. The electron beam whosepolarization is to be determined has a very low energy (typically less than 20 eV) and impinges on thetarget with an angle close to the surface normal. A single “scattering” detector is used to determine thescattered electron current. The intensity of the reflected electron beam depends on the relative orientationsof the electron spins and the target magnetization direction.

The normalized intensity asymmetry A in this case is given by

A ¼ N⇉ � N⇄

N⇉ þ N⇄(13)

whereN⇉ andN⇄ are the number of electrons counted in the detector with the target filmmagnetized eitherparallel (⇉) or antiparallel (⇄) to the spin quantization axis of interest in the sample, i.e., two successivemeasurements using the same detector have to be carried out for each asymmetry measurement. Though

Fig. 7 The two polarimeter arrangement of the COPHEE apparatus [15] (Reproduced with permission from Journal ofElectron Spectroscopy and Related Phenomenon, Copyright 2002 Elsevier B.V.)


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potentially leading to systematic errors due to film degradation, this approach avoids false asymmetriesarising due to different detector responses.

The polarization, P, is then given by

P ¼ A

S(14)

where S is the spin sensitivity, which is the equivalent of Seff for Mott scattering. S is obtained bymeasuring the reflectivity of an electron beam of known polarization:

AS ¼ 1

P

N⇉ � N⇄

N⇉ þ N⇄� Seff (15)

Electrons at particular energies and momenta can be reflected with high intensity and, if the energy is lowenough, most of the intensity is found in the specular beam. The intensity of the incoming beam isdetermined with a detector that can be inserted temporarily before the magnetic film or, in the case of aremovable target, placed behind the magnetic film. At the very low electron energies involved, the valuesof both I/I0 and S are very surface sensitive. In fact both the exchange interaction and SO coupling cancontribute to the measured asymmetry, but for iron the exchange term is by far the larger of the two [58].

The FOM is given by

F ¼ A2S

I

I0(16)

Although the first exchange scattering polarimeter was developed in the late 1980s [59] using Fe thin filmsas the scattering target, attention soon turned to oxygen-passivated iron surfaces [60]. Films of Fe(001)-p(1 � 1)O have proved an ideal target material with enhanced spin sensitivity compared to iron films andgood long-term (weeks) stability. As a consequence, a number of polarimeters utilizing it as the targetmaterial have been reported [19, 20, 61–66].

Exchange scattering polarimeters typically have values for I/I0 in the range between 0.05 and 0.10,clearly orders of magnitude larger than that found for Mott scattering. The reported spin sensitivities arealso good at up to 0.48 [19, 60, 65, 67]. Combined, these result in figures of merit of up to 10�2 two ordersof magnitude better than those typically observed for Mott polarimeters.

Okuda et al. working at the Hiroshima Synchrotron Radiation Centre [66] have combined an exchangescattering polarimeter with a large hemispherical analyzer; see Fig. 8. Photoemitted electrons enter thehemispherical analyzer via an entrance slit S and are then either directed to a multichannel plate (MCP)detector M for spin-integrated measurements or they pass through an aperture A and then via a 90�

electrostatic deflector into the polarimeter. Though not shown in Fig. 8, the target can be magnetized alongthe z- or the x- axes. Very good spin sensitivity (Seff between 0.2 and 0.4), energy, and angular resolution(DE ~7.5 meV and Dy ~ �0.18�, respectively) have been achieved. A FOM of 1.9 � 0.2 � 10�2 wasreported [65].

Exchange Scattering Polarimetry and Time-of-Flight Energy Analysis Hussein and coworkers havereported the development of a high-efficiency spin-resolving photoemission spectrometer that combines alow energy (ca. 10 eV) exchange scattering polarimeter with a TOF electron energy analyzer for use witha pulsed light source; see Fig. 9 [20].

The photoemitted electrons enter the polarimeter from the left within a tube that passes through thecenter of a rear-facing MCP detector assembly. The electrons impinge on the target at near-normal


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incidence and the specularly reflected beam is collected by the front face of the MCP detector. Themagnetization direction of the target is switched along the yt-axis by the inner set of Helmholtz coils. Theassembly is sensitive to polarization along any axis within a plane perpendicular to the incoming electronbeam axis by virtue of the fact that both the target assembly and the magnetization coils are mounted on adifferentially pumped rotary stage that rotates about this axis. As shown in the insert in Fig. 9, either“planar” or “perpendicular” scattering geometry may be utilized though the adoption of the “planar”geometry more completely isolates the exchange and SO interactions.

Ultrathin films of Co(0001) grown on W(110) were used as scattering targets. Initial work focused onfilms 5 ML thick as they offer potentially the largest Seff and FOM (0.40 and 2 � 10�2 respectively [68]).However, films of around 50 ML were found to be more reliable and more forgiving in terms of growthprocedures. While the Seff of the thick films (at 0.12–0.23) is comparable to that of Mott polarimeters, theincreased electron reflectivity results in a FOM of ca. 10�3, an order of magnitude better than thosetypically observed for Mott polarimeters. The measured instrumental asymmetry of <0.04 % is alsoparticularly impressive. The TOF approach enables parallel acquisition of a range of electron energiesfurther enhancing the overall efficiency of the apparatus. The scattering target preparation and character-ization are however more onerous than those required for Mott polarimeters.

Spin-Polarized Low-Energy Electron Diffraction (SPLEED) PolarimetryThe physical principle behind SPLEED polarimetry is that the intensity of the electron diffractionscattering into certain LEED spots of a single crystal, heavy-element material is spin dependent.

A polarimeter based upon SPLEED using a single crystal of tungsten as a target was first developed byKirschner and Feder more than 30 years ago [69] and is one of the few polarimeters commercially

Fig. 8 High performance exchange scattering polarimeter and hemispherical analyzer combination [66] (Reproduced withpermission from Reviews of Scientific Instruments, Copyright 2011 AIP Publishing LLC)


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available; see “Commercially Available Polarimeters.” Although the spin sensitivity (0.28 � 0.05) isgood, this approach has not been widely adopted (but see, e.g., [70–73]). Rapid deterioration of thetungsten target surface, with concomitant loss of spin sensitivity, is probably the main reason for this eventhough a new surface can be prepared quite quickly.

Multi-Channel Spin Polarimetry Based on SPLEED Recognizing that a major bottleneck in polari-zation determination has been its single-channel nature, groups based at Halle and Mainz in Germanyhave developed a multichannel spin polarimeter based on SPLEED from a W(100) single crystal. Byadopting specular geometry, the lateral energy and angular information at the exit to a hemisphericalanalyzer is encoded in the scattering coordinates and angles at a 2D delay line detector with a lateralresolution of around 50 mm [74]. This setup is shown schematically in Fig. 10. By operating at a scatteringenergy of 26 eV, a large reflectivity (0.012) and spin sensitivity (Sherman function 0.43) were obtained.A two-dimensional FOM (F2D) was defined as

F2D ¼ N Fsingle

� ¼ N S2ijI ijI ij, 0

�(17)

where N is the number of resolved data points, F is the single-channel FOM averaged over thesimultaneously acquired energy interval, and indices i and j identify the individual data points. With anenergy interval of 3 eV, values of <Iij/Iij,0> = 1.2 %, <Sij> =0.38, and F2D = 1.8 were obtained. Thislast FOM is some 104 times that of a single-channel polarimeter operating at a similar resolution – adevelopment that will undoubtedly have a large impact. In the apparatus described above, 1,044 datapoints were acquired simultaneously. In a more recent spin filter experiment adopting the same scatteringprinciples, 3,500 data points were resolved [75]. Alternatives to scattering from tungsten are also being

Planar geometry Perpendicular geometry

nt ntn n

Psignal out

e−

grid

MCPs

M

target

target / cartridgetransfer

anode / cap. coup.output

opposed double-Helmholtz pair

cartridge

P

Zt

Xt

θθ

θθ

M

M

Yt[110]

[110][001]

ωt

θ = 5°

Fig. 9 Schematic diagram of the LEX polarimeter developed for use on the ALS, Berkeley [20] (Reproduced with permissionfrom Reviews of Scientific Instruments, Copyright 2010 AIP Publishing LLC)


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explored and the 5 � 1 reconstructed surface of Ir(001) is particularly promising [76]. Spin-resolvedimaging results using spin filtering are described in “Spin-Resolved Imaging.”

Absorbed Current Polarimetry and Spin-Polarized Low-Energy Diffuse ScatteringA number of groups have promoted polarimeters based on the differential absorption of polarizedelectrons by magnetic target materials (see, e.g., [77–79]). However, the fact that it is not possible tosingle-electron count and the technique’s modest advantages compared to other approaches have meantthat it has found little favor with the SRPES community.

Spin polarimeters based on low-energy diffuse scattering (see, e.g., [80–83]), though compatible withthe experimental requirements of photoemission from surfaces, have spin sensitivities and efficiencies(e.g., 0.15 and 2.3 � 10�4, respectively [81]) that make them unattractive compared with other modernpolarimeters.

Commercially Available PolarimetersFor those who do not wish to embark on the design of a complete spin-polarized photoemission (SPPE)apparatus, a number of polarimeters are available commercially. These include:

• The FOCUS SPLEED polarimeter available from Omicron GmbH (http://www.omicron.de/en/products/csa-300-spleed/instrument-concept). The characterization of this instrument has been reported byYu et al. [73].

• A retarding Mott polarimeter system from SPECS Scientific Instruments (see http://www.specs.de/cms/front_content.php?idcat=183).

• A compact classical Mott polarimeter available from the Surface Magnetism Group of St. PetersburgState Polytechnical University (http://www.surfmgroup.com).

Though the polarimeter FOM is an important factor when choosing a polarimeter, other features such aslong-term stability, reliability, and compatibility with the user environment are also importantconsiderations.

Fig. 10 Schematic diagram of the first multichannel spin polarimeter mounted at the exit to a hemispherical analyzer [74](Reproduced with permission from Physical Review Letters, Copyright 2011 American Physical Society)


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http://www.omicron.de/en/products/csa-300-spleed/instrument-concept

http://www.omicron.de/en/products/csa-300-spleed/instrument-concept

http://www.specs.de/cms/front_content.php?idcat=183

http://www.specs.de/cms/front_content.php?idcat=183

http://www.surfmgroup.com

Whole SystemsAn important consideration for spin-polarized electron spectroscopic experimental systems is thematching and efficiencies of the instrumentation for electron spin polarimetry and electron energyanalysis. This requires a detailed understanding of the electron optics of both components, togetherwith the associated linking electron optics. With care, start-to-end modeling of electron trajectories can beundertaken using commercial electron optics packages, e.g., SIMION.

Leaving aside the multichannel spin polarimeter, the big advantages of which are discussed above, it isuseful to make some qualitative observations concerning the relative merits of various energy analyzer-plus-polarimeter systems. The widely used (e.g., [13, 14, 21, 22, 30, 32, 33, 53]) hemispherical analyzerplus retardingMott polarimeter combination (HA + retarding-Mott) has a long history, is well understood,and is an appropriate benchmark for discussion.

One approach to reduce overall data acquisition times is to stick with the retarding Mott polarimeter butto replace the hemispherical energy analyzer with a TOF energy analyzer. This allows parallel electronenergy detection, and Moreschini et al. [16] have shown experimentally that compared with the bench-mark, the TOF + retarding-Mott combination results in an intensity gain of approximately one order ofmagnitude for a 20 eVenergy window. A constraint of this approach is that the TOF technique requires apulsed photon source. The spin sensitivty of this combination is, of course, the same as the benchmark.For spintronics-related studies, where the interest is generally in a spin imbalance over a very small energywindow (e.g., a few hundreds of meV close to the Fermi level), the TOF + retarding-Mott combinationloses out to the HA + retarding-Mott on resolution grounds [16].

An alternative approach is to retain the hemispherical analyzer but to change the basis of thepolarimetry. In particular, there are a number of reports of hemispherical analyzers pluspolarimeters based on specular reflection from ferromagnetic surfaces (i.e., HA + exchange polr)(e.g., [19, 62, 63, 65–67]). As the figure of merit for exchange polarimeters is ~100× better than thatfor retarding-potential Mott polarimeters, this means that compared with the HA + retarding-Mottbenchmark, the HA + exchange polarimeter systems exhibit higher spin sensitivity and much higherdetected electron counts. High throughput is, of course, very desirable, but other factors, such as the desirefor a “stiff” beam in a “workhorse” polarimeter that shows insignificant temporal variation over the typicallifetime of a variety of samples, may drive instrumentation decisions in other directions.

By choosing a TOF energy analyzer combined with an exchange polarimeter (TOF + exchange polr), itis possible to gain both in terms of spin analyzer FOM and energy analyzer parallel detection efficiency.This approach has been adopted by the group of Hussain at the ALS [20], where the combined gains haveresulted in an instrument with a similar spin sensitivity to a retarding Mott polarimeter but a 1,000-foldincrease in overall electron detection efficiency. Further increases in spin sensitivity are clearly stillpossible for this instrument.

It should be noted that Mott polarimetry, in particular, is very sensitive to the detrimental effects ofbeam trajectory offsets and off-normal-incidence angles. For this reason, Petrov and coworkers have beenactive in combining various electron energy analyzers with compact spherical high-energy Mott polar-imeters [15, 31, 45, 46]; they have also performed comparative tests of this type of polarimeter with theretarding-potential Mott polarimeter [41].

The above discussion focuses on the technical advantages of various approaches; however, the finaldecision is affected by a wide range of other factors, such as user experience, science to be performed,environment for the equipment, etc. For these reasons, a detailed analysis of all the various factorsinfluencing the choice of a particular electron energy and spin analyzer is beyond the scope of this review.However, particularly useful discussions of the issues involved can be found in the following references[20, 30, 35, 42, 62].


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A unique whole-system approach that allows simultaneous acquisition of a 1D spin-resolved EDC anda 2D spin-integrated band map has been adopted by Plucinski et al. [84]. At the exit plane of ahemispherical analyzer, these authors commissioned a rectangular (27.5 × 30 mm) delay line detectorwith a small aperture in one corner. The majority of the electrons are detected (without spin resolution) bythe delay line detector; those passing through the aperture have their spin determined with a SPLEEDpolarimeter based on W(100) [84].

Polarimeter CalibrationAs detailed above, polarimeter calibration requires determination of the spin sensitivity, S or Seff, andvarious approaches have been used to determine this experimentally. The calibration techniques possiblein Mott polarimetry have been appraised critically by Gay and Dunning [36, 39, 85]. They includeextrapolation of measured polarimeter asymmetries to zero foil thickness or zero inelastic energy loss,followed by normalization to the calculated Sherman function for single atom scattering, undertakingdouble scattering, or using electrons of known polarization. The double scattering approach has also beenemployed in conjunction with SPLEED polarimetry; see, for example, [69].

High-energy Mott polarimetry, though not the easiest or most convenient to establish in a university-type laboratory, has the advantage that the physical processes inherent in the polarimeter are wellunderstood, well described, and thoroughly studied. Though much of the polarimeter characterizationwork was carried out up to the mid 1990s, it is still valid today. In early work on retarding Mottpolarimeters, Dunning and Walters used polarized electrons produced, for example, by chemi-ionizationreactions [86] and by surface Penning ionization [87]. However, for surface photoemission studies, apolarized source derived from a solid sample is more compatible with the UHV conditions universallyemployed.

Using a source of known polarization is very attractive, but care must be taken to establish the absoluteaccuracy to which its polarization has been determined, together with its sensitivity to ambient conditionsand its long-term reliability. A selection of sources of polarized electrons from solids that could beimplemented with relative ease are given in Table 1. Additional possibilities include photoemission fromFe(110) on W(110) over 1.5–3 eV binding energy where the polarization is steady at a value ofapproximately 80 % [88] and ARPES from Au(111) SSs [89]. Other approaches and materials havebeen, used but the degree of complexity or lack of detail, for example, of the polarization figure used or ofthe energy, precludes their inclusion here.

Instrumental Asymmetry and Its EliminationThough in principle a measured asymmetry in Mott scattering leads directly to the polarization of interest,this is not actually the case as, experimentally, the measured asymmetry contains instrumental contribu-tions that arise due to factors such as misalignment of the electron beam and differing detector efficiencies[90]. Minimal instrumental asymmetry is clearly the primary aim in polarimetry, but as long as anyinstrumental asymmetry does not vary with time, it may be removed by processes that reverse only thespin component of the scattering intensity.

Traditional approaches to removing instrumental asymmetries involve flipping the spins of theelectrons to be analyzed either by flipping the helicity of the radiation used to generate them or byflipping the magnetization direction of the sample from which they originate (both these approaches willideally reverse only the spin scattering). In these cases, the polarization is given by:

P ¼ 1

Seff

X � 1

X þ 1

� (18)


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where

X � Lþ

RþR�

L�

� �1=2

(19)

and L(R) indicates the detector and +(�) indicates the helicity/magnetization direction respectively.In situations where an unpolarized beam can be generated, then the instrumental asymmetry A0 can be

established and P can be given in terms of the measured asymmetry A (which contains both the spin andinstrumental components) and the instrumental asymmetry A0:

P ¼ 1

Seff

A� A0

1� AA0

� (20)

Further, if the instrumental asymmetry is a well-behaved linear function, Yu et al. have shown that it canbe largely removed by subtraction from asymmetry measurements made with unpolarized or linearlypolarized radiation on nonmagnetic materials [91].

It is important to note that eliminating instrumental asymmetries by taking multiple measurements withopposing sample magnetizations, by flipping the helicity of the ionizing radiation, or (in the case ofexchange scattering polarimetry) by flipping the magnetization direction of the polarimeter target [62] isonly valid if the reversal itself does not introduce a change in trajectory of the electron beam andconsequently an instrumental asymmetry [92]. In principle, reversing the magnetization of the sampleunder study is equivalent to reversing that of the polarimeter. However, the systematic errors caused bystray fields mean that for exchange scattering polarimeters, it is generally preferable to reorient themagnetization of the polarimeter scattering surface.

Table 1 Some examples of sources that have been used for polarimeter calibration.

Polarization/% Source details Comments Reference

25 � 2 NEA GaAs Absolute calibration of source by Mott scattering Bertacco et al. [61]

84 � 2 (�1 for bothstatistical andsystematic errors)

Strained superlattice GaAs(14 GaAs/GaAsP layers)

Measured with JLAB 5 MeV Mott polarimeter, Seff�0.4008, which was calibrated by thicknessextrapolation to zero foil thickness Grameset al. [47]

McCarter et al. [55]

42.69 � 0.92 100 nm film of GaAs(110)in purpose built polarizedelectron source

Measured using a 120 kV Mott polarimeter Mulhollanet al. [293]

�83 � 5 Photoemission from Fe(110) on W(110) at EF

P value refers back to Dedkov et al. [194] andKurazawa et al. [88], which both then refer back toRaue et al. [29] who used a 100 kV Mottpolarimeter in which Seff was stated, without furtherdetail, to be 0.16. Kurazawa data show quite aspread in values

Dedkov et al. [190]

35 � 5 2 eV 2y electrons from Cogrown on Cu(001)

P value refers back to Kisker et al. [294] in which aclassical Mott polarimeter operating at 100 kV wasused

Winkelmannet al. [64]

8.2 � 0.5 2 eV 2y electrons from Ni(110)

P value refers back to Hopster et al. [295] in which aclassical Mott polarimeter operating at 100 kV andestimated to be correct to 10 % was used

Okuda et al.[65]


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Typical instrumental asymmetries for retarding-potential Mott polarimeters are around 10 %, thoughvalues much lower than this have been reported. Values quoted for exchange scattering polarimeters aresimilar though with extreme attention to detail values of 0.3 % [64] and even down to 0.03 % [20] havebeen reported. This latter, particularly low value, was reported for the exchange scattering polarimeterdescribed in “Exchange Scattering Polarimetry” which utilized a single detector and for which extra carehad been taken to minimize stray magnetic fields and with component design. In general exchangescattering polarimeters are less sensitive to beam alignment issues than Mott polarimeters as Seff has onlya weak dependence on both the incident angle and spot position at the target [61].

Polarimeter ErrorsTaking Mott scattering as an illustrative example, the absolute error of a measured polarization, DP, isgiven by

DP ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA

S2DS

� 2

þ DAS

2s

(21)

where the former term gives the systematic error and the latter term the statistical error [42]. Leaving asidesystematic errors for the moment, the absolute statistical error is related to the error in the asymmetrymeasurement by

DPstat ¼ 1

SeffDA (22)

Assuming that the effective Sherman function is circa 0.2, then 1S2eff

> 10P2 and [49, p. 243]

DPstat � 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2eff NL þ NRð Þ

q ¼ 1

SeffffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNL þ NRð Þp (23)

The above equation can be reexpressed as

DPstat � 1ffiffiffiffiffiffiffiffiffitI0F

p (24)

where tI0 is the total number of incident electrons and F is the FOM. This emphasizes the fact that onmoving from a spin-integrated intensity measurement involving single-electron counting, where thestatistical uncertainty in the intensity is given by DI0 ¼ 1=

ffiffiffiffiffiffitI0

p, to a polarization measurement of the

same statistical uncertainty requires a factor of 1/Fmore time [20, 42, 45, 49 pp. 242–243]. Following onfrom the above arguments, the relative statistical error of the polarization, dP, is

dP ¼ DPP

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNL þ NR

pNL � NRð Þ (25)

Fletcher et al. [92] considered in some depth the systematic effects associated with classical Mottpolarimeters. They concluded that these effects result in polarization, measurements with an absoluteuncertainty of approximately �5 % and that a similar absolute error was appropriate for retarding Mottpolarimeters. The effects of systematic errors on DP get smaller as the Sherman function increases.


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It was also noted in the above work (with regard to Mott scattering) that many papers had quoted “. . .absolute values of electron polarisation with fractional uncertainties below �1%” and that these smallvalues of uncertainty are applied to relative values of the polarization only. Certainly, on undertaking thisreview, it became clear that papers have appeared – involving a range of polarimeters – with absolutevalues of electron polarization that appear less certain than quoted.

Lancaster et al. [57] stressed the importance of performing regular checks after they observed (andanalyzed) an unexpected, intermittent source of systematic error in their asymmetry measurements with aretarding-potential Mott polarimeter.

Peak FittingAn interesting feature of SRPES data is that they can be used to determine spin splittings that are smallerthan the instrumental resolution. This is a consequence of the extra information determined, i.e., thepolarization of the beam, and is clearly shown for the case of 6 to 22 MLs of Pb on Si(111) where fittingthe polarization data allowed splittings of between 11 and 15 meVat k ~ 0.1 Å�1 to be determined [93].

This effect can be shown clearly with synthesized data. In Fig. 11, a hypothetical polarization curvederived from two spin-resolved peaks shows a marked up-down deflection. Within the constraint that thespin-resolved peaks must sum to the width of the spin-integrated peak, the up-down deflection increasesin magnitude as the spin splitting is increased. On summing the two spin-resolved peaks, as in the inset inFig. 11, to give a spin-integrated peak, no splitting can be seen.

Fig. 11 Summation of two spin-resolved Gaussian peaks (inset red and blue) to give a single spin-integrated peak (inset black)and the polarization for the two peaks where spin splitting is varied in 1 meV steps. The red curve indicates the splitting valuechosen for the two spin-resolved peaks in the inset (Taken from Dil et al. [93]) (Reproduced with permission from PhysicalReview Letters, Copyright 2008 American Physical Society)


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Of importance in SRPES is the allocation of a suitable background as polarization curves areparticularly affected in terms of both shape and amplitude. Photoemission backgrounds are affected bymany factors, for example, sample and photon beam quality, scattered electrons, and unpolarized (bulk)bands [94].

Recently attention has focused on cases for which the polarizations of interest are noncollinear and thepeaks overlapping. This is, for example, the case for Bi/Ag(111). A two-step fitting routine, summarizedbelow, has been developed by Osterwalder and coworkers [94–96] to allow the determination of the spinpolarization vector of each band in complex situations such as this. While the equations below are givenfor quantities which are functions of energy, they could just as well be given as functions of wave vector.

The first step involves fitting the measured spin-integrated intensity data with an appropriate number ofGaussians (or other appropriate functions), Fig. 12a. The result of the fit is then

I tot Eð Þ ¼Xni¼1

aiIi Eð Þ þ B Eð Þ (26)

where aiIi(E) represents the individual peaks and B(E) the background. Next a spin polarization vector is

allocated to each band, viz.,

Pi ¼ Pix,P

iy,P

iz

� �¼ ci cos yi cos’i, cos yi sin’i, sin#ið Þ (27)

where yi and ’i are the two polar angles and ci defines the magnitude and direction of the polarizationvector of band i and takes the value 0 ci 1.

Assuming the background is constant and distributed equally between the different spatial directions,the spin-resolved spectra are then simulated by

I i;", #a ¼ I i Eð Þ 1ð � Pia

�=2 (28)

Fig. 12 Illustration of the process of vectorial spin analysis with artificial data [95] (Reproduced with permission fromPhysical Review B, Copyright 2008 American Physical Society)


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where a = x, y or z. The total spin intensity is then given by an unpolarized background, B, and apolarized part, the latter of which is summed over all the peaks:

I"a ¼B Eð Þ6

þX

aiI i, "a Eð Þ6

(29)

I#a ¼B Eð Þ6

þX

aiI i, #a Eð Þ6

(30)

This is illustrated in Fig. 12b for hypothetical y spin components.The polarization, Fig. 12c, for each component a is then calculated, on a point by point basis, for each

energy using

Pa Eð Þ ¼ I"a Eð Þ � I#a Eð ÞI"a Eð Þ þ I#a Eð Þ (31)

By taking all of the constituent peaks and varying yi, ’i, and ci, a fit to the measured polarization data canbe obtained. A convenient visual representation of the in-plane and out-of-plane components of the spinpolarization vectors of a peak is given in Fig. 12d. Of course the assumption of an unpolarized, constantbackground is not always warranted, but the model described above can be extended, with the adoption offurther fitting parameters, to include a structured, polarized background.

The two-step fitting model has been extensively used by the group of Osterwalder, especially fordetermining the polarization vectors of Rashba systems (see “Non-magnetic Surfaces and Thin Films”)where both in-plane and out-of-plane polarizations are evident depending on the state involved.

Spin-Resolved Electronic Structure Determination

SRPES in a broad sense and from a range of systems has been reviewed on a number of occasions [5–7,11, 15, 94, 97–102]. Here specialist reviews are referred to under the appropriate headings. This sectionaims to provide an introductory overview of a number of topical examples of systems of relevance tospintronics that have been investigated by SRPES.

Nonmagnetic Surfaces and Thin FilmsSpin-resolved and angle-resolved photoemission spectroscopy (SRARPES) has been used to show thatnonmagnetic materials may give rise to large polarizations due to the Rashba-Bychkov (or simplyRashba) effect [103, 104]. Rashba systems have spin structures for which it is impossible to define asingle quantization axis, but, for an ideal Rashba system, the spin is defined tangentially to the Fermisurface (FS) contour; see Fig. 13. That is, the quantization direction is perpendicular to both the surfacenormal and the electron wave vector. However, recent studies have shown that this ideal situation is notthe rule and that competing effects can give rise to spins that are oriented out-of-plane.

The following sections give a brief explanation of the Rashba effect and cover a number of exampleswhere it is of particular importance. More in-depth coverage is provided in reviews by Dil [94],Heinzmann and Dil [11], and particularly Okuda and Kimura [100]. The review by Osterwalder [6]provides a particularly clear explanation of spin-resolved photoemission from the SSs of Au(111).


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The Rashba EffectTime-reversal symmetry, E ",kð Þ ¼ E # , � kð Þ, and space-inversion symmetry, E ", kð Þ ¼ E ", � kð Þ, inthe bulk of crystals result in degenerate spin states E ", kð Þ ¼ E #, kð Þ . However, at surfaces orinterfaces – where inversion symmetry is broken – the spin degeneracy is lifted and the free-electron-like SSs in heavy atom systems, where the SO interaction is significant, are shifted in k-space relative toeach other. This momentum-dependent splitting is known as the Rashba effect and the quantum mechan-ics behind it is well established [103, 104].

The energy splitting of the bands is described by

E� kð Þ ¼ E0 þ ħ2k2

2m � aj j kj j (32)

where a is the Rashba parameter and m* is the electron effective mass. While ideal dispersions and spinorientations for a 2D electron gas in the Rashba model are given in Fig. 13, note that the spin orientationsdepend on the signs of both a and m* [105]. The magnitude of the Rashba splitting is proportional to theelectric field gradient perpendicular to the surface/interface and the splitting disappears for k = 0. Its signis determined by the charge distribution asymmetry close to the atomic nuclei [105]. Although space-inversion symmetry is broken in Rashba systems, time-reversal symmetry still holds and the spin-dependent bands must cross at time-reversal invariant momentum points (e.g., at G and M for a surfacewith a hexagonal lattice).

Shockley Surface States of Au(111) Following early work by Osterwalder and coworkers [106, 107], anumber of groups have measured spin-resolved momentum distribution curves for the Shockley SSs ofAu(111). A recent high-resolution example, obtained using a frequency quadrupled Ti-sapphire oscillator(photon energy 5.99 eV), is given in Fig. 14 [108].

The electronic structure and SRARPES of the SSs of Au(111) have also been investigated byrelativistic first-principles calculations [109] which predicted a tangential polarization and no significantthreefold modulation. The predicted photoemission polarization (�75 %) is however larger than thatrecorded experimentally (�45 %); see below.

Photoemission data taken with linearly polarized radiation at 21.21 eV revealed two energy-split andmomentum-displaced parabolic subbands with m* = 0.25me and a momentum splitting of

Fig. 13 Schematic diagram of the effect of spin-orbit splitting on parabolic energy bands and tangential spin quantization axes


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Fig.1

4Mom

entum

dispersion

mapsalongk x

oftheShockleysurfacestates

ofAu(111).(a)

Spin-integrated,(b)and(c)spin-resolved,

and(d)thespin

polarizatio

n[108

](Reproducedwith

perm

ission

from

Reviewsof

ScientificInstruments,C

opyright

2013

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Publishing

LLC)


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2k0 = 0.026 Å�1 [106, 107]. Irregularities in the FSs observed in spin-integrated measurements wereattributed to nonuniformities in the sample surface. They were not observed in the spin-resolvedmeasurements (see Fig. 15), which revealed two concentric FSs both enclosing the G point and withopposite senses of in-plane polarization tangential to the FS. The spin of the inner surface points in aclockwise direction and that of the outer surface points in an anticlockwise direction. The two spincomponents exhibit a large overlap which results in polarization values that reach a maximum of around

projectionaxis forin-planepolarization

k|| (Å

-1) 00.1

0.2total intensity

spin-up intensity spin-down intensity

in-plane polarization map

inte

nsi

ty

a

b c

d e

inte

nsi

typ

ola

riza

tio

n (

%)

40200−20−40 out-of-plane polarization map

k|| (Å

-1) 00.1

0.2k

|| (Å-1) 0

0.10.2

Fig. 15 Spin-resolved momentum distribution maps for EB = 170 meV using hn = 21.21 eV [106]. (a) Total intensity, (b)in-plane spin polarization – red (blue) indicates an anticlockwise (clockwise) spin orientation relative to the projection axesgiven in (a), (c) out-of-plane spin polarization, (d) spin-up intensity map, and (e) spin-down intensity map. (d) and (e) arederived from (a) and (b) (Reproduced with permission from Physical Review B, Copyright 2004 American Physical Society)


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45 % [107]. The out-of-plane spin polarization, which theoretically is small but non-zero, is zero withinthe polarization error bars of �5 %.

Spin-resolved momentum distribution curves (MDCs) have also been obtained for three vicinalsurfaces of gold: Au(11 12 12), Au(7 8 8), and Au(2 2 3) [110]. In each case, the sub-bands are all100% polarized with spin vectors essentially tangential to the Fermi circles and with the same helicities asAu(111), i.e., they are closely related to those of the flat Au(111) surface. The largest spin splitting isobserved for the highest step density as a result of the high-surface corrugation.

W(110) and W(110) � (1 � 1)H Investigation of W(110)�(1 � 1)H by SRARPES provided the firstexplicit observation that the SSs of a nonmagnetic material may be split and spin-polarized [111]. Thestudy revealed very high in-plane polarization tangential to the Fermi contours and reversal of the spinpolarization for equivalent SSs on opposite sides of the BZ center. A more recent, combined ARPES/SRARPES study on W(110) [112] revealed that the S1 surface state displays almost linear dispersion andhybridization between one spin component and an unpolarized surface resonance. This results in ahybridization gap opening up for one spin component only.

(ffiffiffi3

p � ffiffiffi3

p)�Au/Ge(111)

ffiffiffi3

p � ffiffiffi3

p� �-Au=Ge 111ð Þ is a 2D metallic system whose structure (known as a

conjugated honeycomb chained-trimer) is depicted in the inset of Fig. 18 [113, 114]. The surface Au andGe atoms exhibit significant hybridization, strong SO coupling, and marked potential gradients parallel tothe surface – all of which lead to a complex electronic picture.

Recent combined SRARPES and DFT (density functional theory) studies have revealed that the simpleRashba model is insufficient to describe the electronic structure of the system. Rather the observed spectrawere well-modeled using DFT in which SO coupling was described by a combination of Rashba-andDresselhaus-like terms [115, 116]. The 21-layer DFT model, performed in the local density approxima-tion and including both SO interaction and a self-interaction correction for the Au 5d states, predicts twospin-split surface bands S1A and S1B in the first surface BZ as shown in Fig. 16. In this figure, the smallarrows along the FS indicate the predicted magnitudes and directions of the in-plane spin components,and the green arrows indicate the predicted fully in-plane spin alignments at the corners of the hexagon.Experimental spin polarizations were measured using the COPHEE apparatus (see “Mott Scattering” andFig. 7) at the Swiss Light Source and processed using the two-step fitting routine described in“Peak Fitting.” In order to examine the intricacies of the spin structure a set of 7 FS cuts were taken asshown top-left in Fig. 17. The out-of-plane spin polarisations, Pz, as a function of kk along scan positions1, 4, and 7 are also given in Fig. 17. Clearly scan position 1 shows no out-of-plane polarisation and the Pz

values for cuts 4 and 7 change sign consistent with the presence of a spin-split SS.Deduced theoretically and confirmed by SRARPES in 3D, the key findings about the spin-resolved

electronic structure of this system are that:

1. The hexagonal FS is spin-split due to SO coupling with a splitting that varies with position alongthe FS.

2. The in-plane spin vectors have helical character but move radially close to the hexagon corners.3. At the hexagon corners, the spin is fully aligned in-plane and perpendicular to the momentum vector

(i.e., Rashba-type behavior is dominant in the G� K � G azimuth).4. Away from the corners, the spin vector turns out of plane by up to 75� and has a sign that alternates on

going progressively along each of the six FS sections.5. The out-of-plane spins on either side of G are antisymmetric with respect to each other (i.e., reflecting

the fact that time-reversal symmetry has not been broken).


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These observations are summarized in the 3D plot of the spin along the FS shown in Fig. 18. Suchdetailed analysis of the FS is important as conducting spin-split states are needed to achieve control in, forexample, spin-dependent transport applications.

Rashba Splitting in Other Materials Some other systems for which the Rashba splitting has beendetermined by SRARPES include the surface alloy Bi/Cu(111) [105], Bi/Cu(111) [117], Bi and Pb on Ag

Fig. 16 Fermi surface in the first surface Brillouin zone offfiffiffi3

p � ffiffiffi3

p� �-Au/Ge(111) as predicted using density functional

theory [115]. The two spin-split surface states are labeled S1A (blue) and S1B (red). Small arrows along the Fermi surfaceindicate the magnitude and direction of the in-plane spin component. The green arrows indicate fully in-plane alignment(Reproduced with permission from Physical Review Letters, Copyright 2012 American Physical Society)

Fig. 17 Out-of-plane spin polarization, Pz, as a function ofkk along scan positions 1, 4, and 7 of the Fermi surface in the secondsurface Brillouin zone of

ffiffiffi3

p � ffiffiffi3

p� �-Au/Ge(111) [115] (Reproduced with permission from Physical Review Letters,

Copyright 2012 American Physical Society)


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(111) [95, 96], Bi/Si(111) [118], Sb/Ag(111) [119], quantum well states in Pb films on Si(111) [93], Tl onSi(111)-(1 � 1) [120], Pb on Si(557) [121], Pb/Ge(111) [122], and the one-dimensional system Au-Si(557) [123].

Space limitations do not allow a detailed description here of all of the systems and of the manyinteresting effects that have been observed, but the interested reader should consult the various specialistreviews for additional information [11, 94, 100].

Topological InsulatorsTopological insulators (TIs) are materials with bulk insulating characteristics but conducting states at thesurface. They have been the subject of both in-depth and general reviews [124–126]. Since the first spin-resolved experimental results in 2008, the electronic structures of these materials have attracted sustainedexperimental attention. For detailed overviews of SRARPES results, see Okuda and Kimura [100], Sugaand Sekiyama [7], and Heinzmann and Dil [11].

Topological surface states (TSS) are composed of upper and lower Dirac cones (UDC and LDC,respectively) that meet at the Dirac point (Fig. 19). They exhibit spin-momentum locking – i.e., they areprotected by time-reversal symmetry – resulting in a helical spin texture that makes the materialspotentially attractive for technological applications in spintronics and quantum computing. TIs arequite robust to nonmagnetic disorder and can be tuned by adjusting the surface carrier density, i.e., byadsorption of alkali atoms or NO2 or by photon doping [127].

Though TIs have an energy gap between their bulk-occupied and bulk-unoccupied states, their surfacesare characterized by an odd number of spin-polarized gapless surface states that enclose time-invariantmomentum points [128]. This is shown schematically in Fig. 20 which depicts in (a) the bulk BZ and(111) SBZ of, for example, Bi1�xSbx, and in (b) FS pockets (heavy black lines), some of which enclosetime-reversal invariant momentum points (filled red circles). States that form FS pockets that do notenclose time-invariant momentum points are not relevant to the topology. The surface bands must alsoexhibit partner-switching dispersion (Fig. 20c) between a pair of time-reversal invariant momentumpoints.

In general, topologically ordered phases of matter can be characterized by the Z2 topological quantumnumbers, n0 and nm [129, 130]. Of these, n0 determines whether or not (1 or 0, respectively) the surfaceelectrons support a nontrivial Berry’s phase. If they do, the chirality of the surface spins at the mirror plane(i.e., ky = 0) of the bulk electronic states is then classified by nm which takes a positive value for right-

Fig. 18 (a) 3D plot of the spin vector along the Fermi surface of (√3 � √3)Au/Ge(111) and (b) model of the (√3 � √3)Au/Ge(111) surface showing the unit cell (in red) and the high symmetry directions [115] (Reproduced with permission from PhysicalReview Letters, Copyright 2012 American Physical Society)


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handed rotation of spins and a negative value for left-handed rotation of spins. This combined requirementto gain insight into both the detailed dispersion behavior and the spin texture of the SSs means that thesematerials are generally studied by both high-resolution ARPES and SRARPES.

Bi2Se3, Mn-doped Bi2Se3 and BiTl(S1�dSed)2 While the detailed electronic properties of TIs arematerial specific, Bi2Se3 may be considered as a model system as its surface state is a single Dirac coneand it has a sizeable bulk bandgap (of ~0.3 eV). As a consequence, it has been studied extensively bothfrom theoretical [e.g., 131–134] and experimental spin-polarized photoemission viewpoints [135–139].

As would be expected, the more complex and time-consuming SARPES studies have generally beenpreceded by high-resolution ARPES studies. ARPES data for Bi2Se3 taken over a range of photon

Fig. 19 Representation of the topological surface state in momentum space. The arrows indicate the predicted spincharacteristics [124] (Reproduced with permission from Reviews of Modern Physics, Copyright 2010 American PhysicalSociety)

Fig. 20 Schematic of (a) the bulk Brillouin zone and (111) surface Brillouin zone of, for example, Bi1�xSbx; (b) Fermi surfacepockets (heavy black lines), some of which enclose time-invariant momentum points (filled red circles); and (c) partner-switching band structure topology of the spin-resolved surface states (red and blue lines) [128] (Reproduced with permissionfrom Science, Copyright 2009 AAAS)


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energies, Figs. 21 and 22, show clearly features consistent with the surface state (SS), the bulk valenceband (BVB), and the bulk conduction band (BCB). They also reveal the anticipated linear dispersion ofthe SSs in kx and ky and its nondispersion in kz. As anticipated, confirmation of the spin-momentumlocking of the Dirac cone required SRARPES studies. Synchrotron radiation-based, high-resolutionSRARPES [136] on Bi2Se3 revealed (Fig. 23b) that emission from the TSS gives rise to a large(maximum around +80 %), k-dependent, in-plane Py value consistent with the predicted left-handedspin texture. A small but nonzero value for the out-of-plane Pz value for the TSS was also observed. Ofparticular interest is that the topological effects observed in the SRPES of Bi2Se3 persist at roomtemperature [136, 138]. Unexpectedly, emission from the BVB exhibits a k-independent value for Py

of ~ +25 % at 36 eV photon energy – a finding that was interpreted as arising from the influence of spinmatrix element effects and which points to a nonequivalence of the spin polarization of the quasiparticleswithin the Bi2Se3 and that of the free photoelectrons [136].

Ultrathin films of Bi2Se3 have also been investigated by ARPES and SARPES [135, 139, 140]. ThreeQL films of Bi2Se3 were shown to exhibit a bandgap due to interaction of the top and bottom surfaces of a

Fig. 21 Angle-resolved photoemission data for Bi2Se3 performed at various photon energies [137] (Reproduced withpermission from Physical Review Letters, Copyright 2011 American Physical Society)

Fig. 22 (a) The Fermi surface intensity map as function of kx and kymeasured at 50 en photon energy. The red-dashed circle isa guide to the shape of the FS. (b) The FS intensity map as function of kx and kz measured at photon energies between 30 and100 en in 5 en steps. The red-dashed line corresponds to a photon energy of 50 eV [137] (Reproduced with permission fromPhysical Review Letters, Copyright 2011 American Physical Society)


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film on the order of 90 Å thick [140]. Strong suppression of the spin polarization was observed in thevicinity of the gap, indicating an interplay between quantum tunneling and spin texture modification.Eight QL films grown by Hirahara et al. [135] showed no evidence for a gap, but they exhibited a Diraccone hexagonal in cross section at the EF (indicating the presence of hexagonal warping effects in thesolid) with helical spin structure and low spin polarization values at around 10 %. Unexpectedly, metalliccharacter was found in both the surface and the bulk states at EF.

ARPES and SRARPES of Mn- and Zn-doped Bi2Se3 films have enabled exploration of magneticallyinduced spin reorientation [140]. Direct comparison was made between the surface of Zn-doped Bi2Se3,which is nonmagnetic, and the surface of Mn-doped Bi2Se3 which exhibits out-of-plane ferromagneticorder at low temperature. Some of the experimental results for two films of Mn(2.5 %)-Bi2Se3 arepresented in Fig. 24. In contrast to undoped Bi2Se3, Mn-doped Bi2Se3 exhibits a magnetic gap andsignificant out-of-plane polarizations close to the bottom of the surface conduction band that do notchange sign on going from�kk toþkk and which gradually decrease to zero on going to larger k‖ values.

Fig. 23 (a) Spin-integrated energy distribution curves of Bi2Se3 as a function of momentum. Blue (spin up) and red (spindown) arrows indicate the predicted y-polarization. (b) Spin-resolved EDCs corresponding to the red trace in (a). The spinquantization axes are along the out-of-plane z direction (upper trace) and along the in-plane y direction (lower trace),respectively. (c) Corresponding Py curves. The solid gray circles indicate the polarization after subtraction of a constantbackground indicated by the dashed black line. The vertical green line indicates the EDC location. [136] (Reproduced withpermission from Physical Review B, Copyright 2011 American Physical Society)


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The out-of-plane polarizations of the upper and lower Dirac bands have opposite signs – an example oftime-reversal symmetry breaking at the surface.

This systematic study has thus shown directly that magnetically induced spin reorientation (resulting ina so-called “hedgehog-like” spin texture) and a Dirac-metal to gapped-insulator transition have occurredon the surface of Mn-doped Bi2Se3. In contrast to this, Zn-doped Bi2Se3 retains a helical spin textureprotected by time-reversal symmetry as is found for undoped Bi2Se3 [140].

BiTl(S1�dSed)2 has proved a particularly fruitful system to investigate as its topological properties canbe compositionally tuned [141, 142]. Indeed, Xu and coworkers have visualized, by a combination ofARPES and SARPES, both the transition from a band insulator (LHS; Fig. 25) to a TI (RHS; Fig. 25) andthe 3D spin texture of BiTl(S0Se1)2. While the out-of-plane spin polarization for BiTl(S0Se1)2 showedonly very weak structure, the measured in-plane polarization was sizeable and clearly indicated thechange in chirality from left-handed to right-handed on moving from above to below the Dirac node.Above the Dirac, node a quasiparticle moving in the +k (+x) direction is locked to a +y spin polarization.Below the node, a +k quasiparticle is locked to –y spin polarization. The fitted in-plane vector componentsof the polarization at six points in k-space were mapped onto the high-resolution FSs measured usingARPES. Though not tangential to the Fermi contour (as expected for an ideal Dirac cone), the spins werefound to be approximately perpendicular to a line between the momentum point and the G point.

Bi2Te3, Bi2Te2Se, and Bi2Se2Te Bi2Te3 and the ternary chalcogenides Bi2Te2Se and Bi2Se2Te have allbeen shown by ARPES and SRARPES to be TIs [127, 143–146]. Bi2Te3 only exhibits a single-polarized

Fig. 24 ARPES and SRARPES measurements on two thin films of Mn-doped Bi2Se3. Film 1; (a) spin-integrated momentumdistribution map, (b) spin-integrated MDCs, (c) SR-MDCs, and (d) out-of-plane spin polarization. Film 2; (e) spin-integratedmomentum distribution map, (f) spin-integrated momentum distribution curves, and (g) out-of-plane spin polarization [140](Reproduced with permission from Nature Physics, Copyright 2012 MacMillan Publishers Ltd.)


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Dirac cone at the surface (in common with the ternary chalcogenides) and a single polarized band crossingat EF [143]. The FS of Bi2Te3 is strikingly warped into a concave-edged hexagon (or more poeticallysnowflake shaped), with in-plane spin components locked into a left-handed vortex and out-of-plane spinpolarization components that oscillate between zero (at the hexagon corners) and 30 % (at the midpointsbetween corners), Fig. 26 [127].

Bi2Te2Se and Bi2Se2Te both exhibit Dirac cones within bulk bandgaps with helical spin textures[146]. The magnitudes of the spin polarization in Bi2Te2Se, determined at y = +4.2� and �4.2�, werefound to be significantly different at �67 � 3 % and +87 � 9 %, respectively. This was tentativelyassigned to matrix element effects but was not discussed in detail.

Bi1�xSbx Building on their earlier spin-integrated photoemission work [147], the first experimentalobservation of the chiral properties of a TI by SRARPES was undertaken by the group of Hasan whoinvestigated Bi0.91Sb0.09 and Sb – two members of the materials series Bi1�xSbx [128]. This work wasexpanded upon in subsequent publications both by the same group and others [148–151].

Combined ARPES and SRARPES results on Bi0.91Sb0.09 (Fig. 27) revealed that the time-reversal-invariant momentum points (GandM) are enclosed by spin-polarized FSs only once, atG, and that the spinvector displays a left-handed rotation (i.e., nm = �1). This is illustrated in Fig. 27a–d which showsschematically in (a) that the FS that enclosesG in (b) and is responsible for Fermi crossing 1 in (c) is spin

0.0

0.0

0.6

θ=2π (TQN v0=0) θ=π (TQN v0=1)

0.4

0.2

0.0

−0.2

Spin-orbit insulator

Fermi gas

−0.1 0 0.1 −0.1 0 0.1

BiTI(S1–δSeδ)2

−0.1 0 0.1 −0.1 0 0.1 −0.1 0

1/2 Dirac gas

0.1 −0.1 0 0.1

Topological insulator

k y (

A−1

)

kx (A−1)

EB

(eV

)E

B (

eV)

δ

a

b

c

d

Fig. 25 (a) High-resolution ARPES dispersion maps for a range of d values in BiTl(S1�dSed)2 showing the topological phasetransition. (b) and (c) the native Fermi surfaces and energy distribution curves, respectively, for the different chemicalcompositions of BiTl(S1�dSed)2. (d) Images of the 3D band topology of the ground state over a range of energies (verticalaxis), spin (yellow and green arrows; yellow above the Dirac node, green below the Dirac node), and momentum (horizontalaxes). Each arrow represents the net polarization on a k-space point of the corresponding Fermi surface [141] (Reproducedwith permission from Science, Copyright 2011 AAAS)


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down (relative to the sample in-plane y-axis), that the teardrop feature responsible for crossings 2 and 3 in(c) is both spin up and not at a time-reversal invariant momentum point, and finally, that the time-reversalinvariant momentum point at M is enclosed (with an undetermined spin) an even number of times.

Results for Sb [148] showed that it also has a single surface FS that encloses G once and that the spinvector displays a clockwise rotation (i.e., nm = �1). Though a small out-of-plane spin component wasobserved, the in-plane spin was by far the major component.

Investigations on Other Topological Insulators SRARPES results have also been reported for Sb2Te3[152], GeBi2Te4 [153], GeBi4Te7 [154], Bi0.3Pb0.35Sb0.35 [151] and PbBi4Te7 [155].

Magnetic SystemsSRPES has been a pivotal complement to theoretical studies for understanding the detailed electronicstructure of transition metal and rare-earth magnets and their alloys and compounds – a fact that has beenrecognized in the reviews that have already covered many aspects of this topic; see, for example, [5, 7, 97,101, 102 and references therein, 156–159].

After the foundations were laid for a clear appreciation of the surface magnetism of bulk ferromagnets,the focus of studies moved to thin films, and SRPES, in its various guises, has been and continues to bekey in the exploration of a plethora of interesting phenomena that occur as parameters such as filmthickness, temperature, composition, etc. are varied. In their recent overview, Johnson and G€untherodt[101] presented, inter alia, spin-resolved electronic structure effects that vary with film thickness[focusing particularly on silver films on Fe(001) and copper films on Cu(001)]. This work is suggestedas the first port-of-call for those readers who particularly want more information on this interesting area ofmagnetism.

This section aims to highlight, with just a few examples, some current developments involvingferromagnetic films that have general relevance to spintronics.

Fig. 26 (a) ARPESmeasurement of the 3D surface Dirac cone of Bi2Te3 with arrows indicating the in-plane component of thespin (Reproduced from arXiv:1101.3985) [127]


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Surface and Bulk Electronic StructureDetails of the spin-resolved electronic structures of the ferromagnetic 3d transition metals Fe, Co, and Nihave been explored from both experimental and theoretical viewpoints many times over the last 30 years[5, 97, 101, 102, 157–161]. These are systems that reflect a fascinating interplay between exchange andSO effects together with significant correlation and whose electronic structures are a key factor deter-mining device performance and yet even now questions remain.

A recent comparison of SRARPES results on this series of metals with fully relativistic, one-stepphotoemission calculations based on DFT-LDA, but including approaches to account for local many-body effects (via dynamical mean-field theory or the three-body scattering approximation) showed thatcorrelation effects are important for all three elements. The comparison also highlighted that withincreasing Z, nonlocal correlation effects get weaker while local effects get stronger [162–164].

With some exceptions, experimental binding energy positions (including the polarized 6 eV satellite inNi) were quite well reproduced computationally; see Fig. 28. However, scattering rates and therefore peakwidths for all three were consistently underestimated. Overall, it was noted that further consideration ofnonlocal interactions and spin-flip exchange scattering would be required to improve further the fit toexperimental peak widths and dispersions. The authors identified a number of approaches to achieve thisand anticipated a better agreement between experiment and theory and a more complete description of theelectronic structure of Fe, Co, and Ni in the near future [164].

Focusing on Fe, some of the SRARPES data used in the comparison discussed above, which wasobtained on 20 ML bcc Fe(110) films (remanently magnetized in the film plane alongGNdirection) at theBESSY II synchrotron source, is shown in Fig. 29 [162]. The experimental spectra show very clearlymomentum-dependent spin character at EF. Close to G (see spectrum labeled 0.21), the electrons with

Fig. 27 (a) Schematic of the surface Fermi surfaces of Bi1�xSbx. (b) and (c) high-resolution ARPES and (d) momentumdistribution curves measured at EB = �25 meV for Bi0.91Sb0.09 [128] (Reproduced with permission from Science, Copyright2009 AAAS)


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smallest binding energy have minority spin character, while on progressing towards N (increasing x),majority spin character gradually dominates.

The assignment of the SRPES data is complicated both by the presence of correlation effects andmultiple contributions to the majority spin peaks; however, see Fig. 29. Close to the G point, a strong

minority spin peak is assigned to aS#1, 3 surface resonance. On probing along GN the intensity of this peak

falls, which is consistent with the prediction that the S#3 component crosses the Fermi level before

N leaving only the S#1 component to contribute to the intensity. The majority spin picture is less clear as

S"1, 3 SSs, S

"1, 3 bulk-like states and S"

1, 4 bulk-like states all contribute. At 2.2 eV binding energy, broad

nondispersing majority spin peaks are assigned toS"1, 3 SSs. At smaller BE, peaks at 0.7 eVare assigned to

theS"1, 4 bulk-like states. To larger (smaller) binding energy of theS"

1, 4, peak maximum are peaks assignedtoS"

1, 3 bulk-like (S"1, 3 SSs), respectively. AtG andN the experimental mass enhancements,m*/m0, are 1.7

and 1.1, respectively.

Fig. 28 Comparison of spectral functions for bcc Fe(110), hcp Co(0001), and fcc Ni(111) (upper panels majority spin states,lower panelsminority spin states) and experimental peak positions from SRARPES measurements using p-polarized light (reddiamonds) and s-polarized light (yellow circles) [164] (Reproduced with permission from Physical Review B, Copyright 2012American Physical Society)


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In addition to the above identification of SSs in the Fe(110) surface, the surface electronic structure ofFe(100) films has been the focus of a number of photoemission studies over the years [e.g., 165–167]. Arecent reexamination of 30 Å- thick epitaxial Fe(100) grown on tungsten using SRARPES at 100 K andcomplemented with high-quality DFT slab calculations has been reported [168]. The study establishedtheoretically the presence of a minority spin state with dxz+yz character alongGX, which crosses EF close tothe G point and which disappears near G and near X. A set of spin-integrated ARPES data was recordedwith a range of photon energies and emission angles designed to probe theGΗ direction of the bulk BZ. Anondispersing SS peak was identified close to EF. Spin analysis of selected spectra then revealed that thepeaks close to the EF, especially for 67 eV, 12�, and 72 eV, 20�, had minority spin character. As predictedthe SS peak is absent at 67 eV, 16� which is close to the X point [168].

Temperature Dependence and the Persistence of Short-Range Order Above TC

Themagnetic order and electronic structure of bulk and thin-film transition metals and alloys are very wellstudied and reviewed [5, 97, 101, 102 and references therein, 156–159]. However, they still serve toinspire.

As is well known, on warming ferromagnetic systems, long-range magnetic order is lost at TC and amajor preoccupation in the 1980s and 1990s was the mechanism for this transition; i.e., is there a gradual

Fig. 29 Momentum distribution curves for bcc Fe(110) taken with p-polarized light, (~) majority spin, (▼) minority spin[164] (Reproduced with permission from Physical Review Letters, Copyright 2009 American Physical Society)


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reduction in exchange splitting and associated atomic moments (as predicted by the Stoner model) or doatomic moments persist in a mode that is either totally disordered (as per the disordered local momentmodel [169–172]) or with short-range order [173]. In the event, for Ni simple interpretation of therecorded spectra is precluded by the fact that the observed behavior depends upon the part of the BZprobed [174].

Although for Ni the picture is complex, a clearer situation exists for Fe with theory and temperature-dependent spin-resolved studies, leading to the conclusion that short-range order of ~5 Å persists aboveTC. Recently Donath and coworkers have shown very clearly, using SR-2PPE and image potential statesas a sensor, that at TC long range, magnetic order breaks down but local magnetic order persists [175].

The SR-2PPE process for a ferromagnetic metal is shown schematically in Fig. 30. It involved in thiscase separate experiments with s- and p-polarized 4.68 eV pump pulses, ħoa, followed by 1.56 eV probepulses, ħob. The pump pulses excite electrons into intermediate, exchange split, image potential states (E"and E#) whose population is spin dependent due to matrix element effects. The probe pulses then causeejection of the electrons, allowing their spin- and time-dependent energy (via the measured kineticenergy) and population (via the measured intensity) to be established.

The SR-2PPE spectra for 7 ML Fe on Cu(001) [175] obtained by this process are shown in Fig. 31. Onthe LHS of Fig. 31, the spin-resolved spectra (red and green triangles) exhibit a spin splitting,DΕ"#, whichindicates the presence of long-range ferromagnetic order. On summing the spin-resolved data, spin-integrated spectra (blue circles) are obtained, RHS of Fig. 31, which exhibit a small energy shift, DΕps,with respect to each other. The energy shift indicates that the initial states are spin dependent and that theimage states are exchange split. This only occurs if there remains short-range magnetic order over thelateral extension of the image potential states, i.e., circa 50 Å.

Fig. 30 The SR-2PPE process for a ferromagnetic metal [175] (Reproduced with permission from Physical Review Letters,Copyright 2010 American Physical Society)


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On raising the sample temperature from 252 to 335 K, the spin-resolved spectra clearly show an abruptloss of spin splitting and polarization at TC (Figs. 32 and 33). However, no such abrupt change is shown inthe p-s splitting which shows instead a monotonic decrease. This can be explained in terms of the collapseof long-range order at TC but the persistence of short-range magnetic order, i.e., the alignment of magneticmoments within, but not between, microdomains, up to 1.2 TC. Random microdomain orientation, i.e.,zero global magnetization, results in the lack of a well-defined magnetic quantization axis and zero spinsplitting. However, the microdomain moments result in an energy splitting regardless of their orientation.

Of particular note is that the integrated linewidth and p-s energy shift are not affected at the magneticphase change and that the linewidth decreases rather than increases with temperature. The latter wasattributed to progressively reduced exchange splitting above TC [175].

Spin Axis ReorientationThe details of the long-range magnetic order of thin films are governed by the interplay between theexchange interaction (a short-range interaction between nearest neighbors), the dipolar interaction(a long-range but relatively weak interaction), and the magnetocrystalline anisotropy (an on-site interac-tion with the crystalline lattice) which gives rise to a rich variety of behavior that is sensitive totemperature, film thickness, composition, etc. Easy magnetization directions can be in-plane or out-of-plane and reorientations are common. Accessible overviews of theoretical and experimental (though notSRPES) work in thin-film magnetism include those written by De’Bell et al. [176], Vaz et al. [177], andMiao et al. [178].

Fig. 31 The SR-2PPE spectra for 7 ML Fe on Cu(001) obtained with (a) p-polarized and (b) s-polarized pump beams [175](Reproduced with permission from Physical Review Letters, Copyright 2010 American Physical Society)


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For thin Fe films, out-of-plane magnetizations tend to occur for very thin films (a fewMLs) at moderatetemperatures (i.e., 350 K), the easy axis changing to in-plane as the thickness grows. However, thisbehavior is very material dependent, for example, in the low thickness regime, Ni on Cu(001) exhibits theopposite behavior [179]. Out-of-plane to in-plane magnetization reorientations generally occur at smallcritical thicknesses. For Fe/Cu(100), and Fe/Ag(100) the critical thickness is around 5 ML due to the factthat the shape and the surface anisotropies are comparable in magnitude [180, 181].

Thicker (between 40 and 43 ML) Fe(110) films grown on W(110) have been shown by SRPES toundergo a sharp in-plane spin reorientation from the [110] to the [001] direction. In this case, the surfaceanisotropy which favors the in-plane [110] direction initially dominates the bulk anisotropy which favoursthe [001] direction. With increasing film thickness the bulk anisotropy eventually dominates[182]. Adsorption of Ag or Au reduces the critical thickness at which the transition occurs while oxygenadsorption has the opposite effect. The data pointed to the coexistence of both [110] and [001] domainsrather than rotation of a single domain [182]. Further work [183] has shown that the easy magnetizationdirection in a 70 ML-thick Fe film undergoes an in-plane reorientation back to the [110] direction if thetemperature is raised to around 700 K. The spin reorientation phase diagram is given in Fig. 34.

Fig. 32 Temperature dependence of the SR-2PPE spectra of the n = 1 image potential state for 7 ML Fe on Cu(001) usingp-polarized pump pulses with a photon energy of 4.43 eV [175] (Reproduced with permission from Physical Review Letters,Copyright 2010 American Physical Society)


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Half-MetalsThough first proposed some thirty years ago [184], half-metals have received considerable attention inrecent years as they offer the promise of very high spin polarization at EF – a goal difficult to realize butpotentially of considerable importance. Idealized half-metals have an electronic structure consistent witha metallic conductor in one spin channel and a semiconducting or insulating gap in the other spin channel[185]. (Half-metals should not be confused with semimetals which have small but equal numbers ofelectrons and holes due to a small overlap between the valence and conduction bands.) Schematicrepresentations of possible DOS of half-metals depicting (a) only majority spin or (b) only minorityspin electrons at EF are shown in Fig. 35.

A broad classification scheme and overview is presented in the review by Coey and Venkatesan[186]. The area has been reviewed a number of times [187, 188]; however, it is fraught with controversypartly because photoemission is very surface sensitive and surface electronic structure and magnetism arefrequently different to those of the bulk. Difficulties with reliable sample preparation and different degreesof sampling of the BZ have also contributed to divergent results. Extra care is in addition required because

Fig. 33 (a) Temperature dependence of the spin polarization, spin splitting, and p-s splitting of the n = 1 image potential stateof Fe on Cu(001) (7 ML). (b) Temperature dependence of the spin-resolved and spin-integrated peak widths [175](Reproduced with permission from Physical Review Letters, Copyright 2010 American Physical Society)


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the definition of spin polarization used in photoemission is different from that of transport measurements(which is weighted by corrections for the Fermi velocity and spin relaxation) [188, 189].

Half-metallic behavior has been proposed for a range of oxides such as CrO2, Fe3O4, and variousmanganites, various sulfides, and many Heusler alloys. Some illustrative cases are presented in thefollowing sub-sections.

CrO2 Chromium dioxide is a ferromagnet (TC = 393 K) with metallike electronic characteristics. Itcrystallizes in a tetragonal rutile-like structure and has a magnetic saturation moment of circa 2mB per Cr

4+

center. Theoretical work on CrO2, backed by SRPES data [190, 191] and a range of other spectroscopicresults [e.g., 192], support half-metallicity.

Fig. 34 Spin reorientation transition phase diagram for Fe(110) films (Reproduced courtesy of E. Vescovo)

4s

Δ↓ΔsfEF

3d

2p

↑

↑

a

Δ↑

Δsf EF

3d

2p

4s

↑

↑

b

Fig. 35 Simplified representations of the densities of states for half-metals with (a) only majority spin electrons at EF and (b)only minority spin electrons at EF [185] (Reproduced with permission from Journal of Physics D: Applied Physics, Copyright2004 IOP Publishing)


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High-quality, epitaxial thin films of CrO2(100) grown on TiO2 have been shown (see Fig. 36) to have aroom-temperature polarization of up to +90 % (�10 %) at EF. The majority spin channel shows a metallicFermi cutoff, while the minority spin channel exhibits a loss of spectral weight near EF consistent with thepresence of a gap. The Cr d-band was reported to be at 2.3 eV below EF [190, 191]. The measurementswere clearly angle resolved though the precise details of the angular acceptance were not included. EarlySRPES work (by the same group) which found a high polarization at 2 eV binding energy but extremelylow intensity and no evidence of a metallic cutoff at EF [193] have since been attributed to difficulties withsurface preparation [191].

The polarization is very sensitive to sputtering, reflecting the balance between initial removal of surfacecontamination and eventual generation of surface disorder. 500 eV argon ion sputter cycles of the “as-prepared” surface for up to 210 s resulted in an increase in P from +80 % to +90 %, but further sputtering(up to 750 s) resulted in a dramatic reduction of P to lower than 10 %. However, the polarization could belargely recovered (i.e., up to +85 %) by lengthy annealing [191]. Strong correlation effects are importantin this material.

Fe3O4 Fe3O4 crystallizes with an inverse spinel structure with the Fe ions in either tetrahedrallycoordinated (A) or octahedrally coordinated (B) sites. Though the moments within each iron sublatticeare ferromagnetically aligned, the coupling between the two sets of moments is antiferromagnetic, leadingto a bulk ferrimagnet with a magnetic moment of 4.1 mB per formula unit. From the earliest SRPES workon Fe3O4 [10], it has been known that photoelectrons emitted from states close to Ef are stronglynegatively polarized. However, the interpretation of SRPES results for Fe3O4 has been the subject of

100

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Fig. 36 Spin-resolved photoemission spectra (obtained with He I radiation, left-hand side) and spin polarization (right handside) versus binding energy of epitaxial CrO2(100) after sputtering at 500 eV (a) and then annealing (b). Total photoemissionintensity (solid circles), spin up (upward pointing triangles), and spin down (downward pointing triangles) [190] (Reproducedwith permission from Applied Physics Letters, Copyright 2002 AIP Publishing LLC)


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heated debate, much of which has revolved around the implications of spin polarizations of less than�100 % at zero binding energy and the appropriateness of various theoretical models to this stronglycorrelated system. Over recent years, the focus has largely been on epitaxial thin films studied either bySRPES (i.e., angle integrated) or SRARPES. For example, thin films of Fe3O4 with (111), (110), and(100) surface orientations have been studied extensively by the groups of G€untherodt [194–198], Chen[199], Vescovo [200], Hricovini [201], and Tobin [202, 203]. A summary of the findings is presented inTable 2.

It is important to emphasize that the conclusion of half-metallicity, or not as the case may be, is notderived from the polarization value alone and other features such as the emergence of a bandgap in theminority spin channel must also be present in the spectra. The range of polarization values listed in Table 2is particularly striking and may result from differences in the material itself (e.g., as a result of differentpreparation techniques, different levels of contamination, differences in surface morphology and surfacehomogeneity, etc.) or from variations in experimental parameters (e.g., photon energy, takeoff angle,analyzer angular acceptance, etc.). As photoemission using UV to soft X-ray photons is very surfacesensitive, it may also be an effect of reduced surface magnetization compared with the bulk. Alternatively,it may be due to processes such as initial-state broadening, inherent in the photoemission process itself.

The most recent report by Hricovini and coworkers [201] combined theory and both spin-integratedand spin-resolved ARPES measured using laser photons of 6.20 and 4.65 eV; see Fig. 37. It concluded,from the combination of (a) the Fe t2g band dispersion close to EF, (b) the presence of a FS, (c) the largespin polarization value (�72 %), and (d) the good agreement between the experimental data and bandstructure calculations, that Fe3O4 is a half-metal. Polaron and initial-state lifetime broadening in thephotoemission process were concluded to be responsible for polarization values of less than 100 % for thestates close to the Fermi level. The authors go further and state that for spin-polarized photoemission“. . .due to intrinsic phenomena, such as the initial lifetime, it is impossible to measure 100 % polarisedelectrons in a half-metal”.

Lanthanum StrontiumManganite La0.7Sr0.3MnO3 exhibits the hallmarks of a half-metallic ferromag-net. Angle-integrated SRPES [204, 205] (see Fig. 38), measured at 40 K (well below TC) revealed that themajority spin channel had a metallic cutoff at EF, while the minority spin channel decayed to zero close toEF consistent with an insulating gap. The polarization at EF was (100 � 5)%.

The difference spectrum shown in the lower half of Fig. 38 is a measure of the Mn 3d state spectrum asthe O 2p states are fully occupied for both spin states. The two peaks at 1.2 and 2.2 eV binding energieshave been interpreted as being due to electron removal from the eg and the t2g levels, respectively. Recentwork on La0.67Sr0.33MnO3 has revealed a very rich but complicated photoemission picture that never-the-less supports its half-metallic status [206].

Table 2 Summary of SRPES results on thin-film Fe3O4

Film orientation Polarization (%) at, or close to, zero BE Conclusions Reference

(100) �55.5 Not half-metallic Huang et al. [199]

(100) ~ �50 Not half-metallic Vescovo et al. [200]

(001) �30 to �40 Half-metallic Morton et al. [202]

(100) �55 Not half-metallic Fonin et al. [196, 197]

(001) �72 Half-metallic Wang et al. [201]

(001) �20 (at RT) to �40 (at 127 K) Not half-metallic Tobin et al. [203]

(111) �80 Half-metallic Dedkov et al. [194]

(110) �60 Half-metallic Fonin et al. [195]


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Heusler Alloys and Other Materials With high Curie temperatures and the potential to “tailor” theirelectronic structures by compositional variation, Heusler alloys have been the subject of many spin-polarized photoemission studies, for example

Co2FeSi [207–209]

Co2Cr0.6Fe0.4Al [210, 211]

Co2MnGa [212]

Co2MnSi [213]

NiMnSb [214–217]

Co2MnaSi (a = 0.69 and 1.19) [218]

However, none to date has revealed a polarization value at EF of anything close to 100 %. Indeed, thepolarizations exhibited are mostly moderate to small though NiMnSb has a polarisation of 50 % at 10 Kthat reduces to 40 % at room temperature [214]. The low surface polarizations may be due to composi-tional or magnetic disorder in the surface layers or to modification of the surface electronic structure.Certainly, Aeschlimann and coworkers have shown that the detailed surface preparation can have a hugeimpact on the reproducibility and magnitude of the measured polarization [210, 211]. Dowben andSkomski have presented arguments for coupling of optical phonon modes with magnons which reducesthe magnetization even at low temperature [219].

Fig. 37 (a) Upper panel: Spin polarization values for thin-film Fe3O4 using 4.6 eV photons (red circles) or 6.20 eV photons(green circles). (a) Lower panel: Blue line, spin polarization at X extracted from (b), red and green lines, spin polarizationsimulations for photoemission using 4.6 and 6.20 eV photons. (b) Simulation of the spin polarization in theGX plane for 12 eVphoton energy [213] (Reproduced with permission from Physical Review B, Copyright 2013 American Physical Society)


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Ferromagnet/Adsorbate InterfacesInduced ferromagnetism in thin metal films deposited on ferromagnetic substrates was a particular interestof the 1990s and has been observed in a number of systems, for example, Ru and Rh on Co(0001) [220],Pt/Co(0001) [221, 222], Pd(111) on Fe(110) and on Co(0001) [221, 223], and Ag/Fe(001) [224]. Ifpresent, it manifests itself as a reproducible polarization from which a small magnetic moment and anexchange splitting may be inferred. In general the spin polarization is observed in the first few MLs andthen decreases rapidly.

Adsorbates can cause a range of effects on substrate magnetic order, and measuring the spin characterof adsorbate photoemission peaks can provide direct evidence for the presence, or otherwise, of exchangesplitting and for the nature of any magnetic coupling. It has proved invaluable for unraveling theassignment of overlapping spectral features observed in spin-integrated photoemission spectra. Earlyspin-resolved reports of exchange splitting in adatom photoemission bands include results on, forexample, c(2 � 2)O/Fe(100) [225], p(1 � 1)O/Fe(001) and c(2 � 2)S/Fe(001) [226, 227], p(1 � 1)O/Fe/W(100) [228], O/Fe(110) [225, 229, 230], and O/Co(0001) [231]. Exchange splittings were generallyless than 1 eV (smaller for sulfur than oxygen) and the coupling ferromagnetic in character. Antiferro-magnetic coupling has been reported for graphene on Ni(111) [232]. Examples of early molecularadsorption studies reporting the absence of adsorbate exchange splitting include [233, 234].

A range of overlayer/Fe systems of particular interest in the field of spintronics has been the subject ofspin-resolved studies, for example, MgO/Fe(001) [168, 235], MgO/Fe/GaAs [236], and a-Al2O3/Fe(110)[237]. The ferromagnet-oxide interface has been discussed further by Johnson and G€untherodt [101].

Recently attention has focused on induced moments in large molecule adsorption.

Fig. 38 Spin-resolved photoemission and spin difference data for La0.7Sr0.3MnO3 measured at 40 K, adapted from [204, 205](Reproduced with permission from Physical Review Letters, Copyright 1998 American Physical Society)


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Organic Semiconductor/Ferromagnet Interfaces Organic semiconductors (though very often metallo-organic or organometallic semiconductors) and their interaction with ferromagnetic electrodes havebecome a particularly active area of research as the resultant materials have potential for spintronicsdevices due the long spin relaxation times they exhibit, their flexibility, and the possibility of chemicaltailoring.

FM/OSC interfaces, known as spinterfaces, are characterized by the presence of spin-polarized hybridinterface states (HISs) that act as spin traps and therefore have a major influence on spin-dependenttransport properties, i.e., the tunnel current may well no longer reflect the polarization of the DOS at EF.For an overview of spin injection and transport in organic semiconductor (OSC) materials, see Dediuet al. [238]. In addition to single-photon SRPES, SR-2PPE has proved to be a very useful technique fortheir study.

A schematic of a mechanism proposed recently for interaction between ferromagnetic metalsand molecular species [239, 240] is shown in Fig. 39. In this, adsorbate molecular orbitals of theappropriate symmetry interact with the exchange split metal d-states resulting in spin-dependentbroadening of the molecular orbitals and the possibility of spin-dependent energy shifts. Since theabove mechanism was proposed, a second mechanism, which operates when only one spin channel ispresent at EF and which can act in conjunction with the above mechanism, has been described [241];see “Ferromagnet/Metal Phthalocyanines.”

A range of FM-metal/molecular-semiconductor interfaces have been studied, for example, Co/CuPc[242], Fe(110)/CuPc [243], Co/Al(OP)3 [244], and Co/Alq3 [245]. In these, MPc represents metal-phthalocyanine; Al(OP)3 and Alq3 are tris-(9-oxidophenalenone)aluminum and tris-(8-hydroxyqui-nolinato)aluminum, respectively; and the molecular structures are represented in Fig. 40. As is evident,the adsorbates have extensive delocalized p-systems. Not surprisingly, the differences in their molecularelectronic structures and the details of their interactions with surfaces lead to spinterfaces that havedifferent characters. In particular, the interplay of spin filtering mechanisms at spinterfaces is governed bythe character of the HIS and its energy with respect to EF. Some key illustrative examples are presentedbelow.

Co/Al(OP)3 Tetragonally distorted fcc-Co films exhibiting in-plane magnetic uniaxial anisotropy alongthe Cu(110) direction were grown in the study of Al(OP)3 on Co by M€uller et al. [244]. Al(OP)3 film

Fig. 39 Schematic of the interaction of the HOMO of an organic molecule and magnetic metal (a) at a large separation, (b) and(c) the molecule in contact with the metal but with different orientations relative to the surface atoms [239] (Reproduced withpermission from Nature Physics, Copyright 2010 MacMillan Publishers Ltd.)


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thicknesses between 0.5 and 5 nm were reported and three coverage regimes considered. The first regimewas characterized by a sub-ML coverage of the molecular semiconductor; the second by a complete ML,i.e., the spinterface; and the third by one or more further layers of adsorbate.

The SRPES of Co/[0–5 nm]Al(OP)3 is given in Fig. 41. Film thicknesses up to 1 nm fit into regime1: the photoemission spectra reflect both the substrate and the adsorbate, but the adsorbate peaks arebroadened and shifted relative to those of the free molecules. The 1.5 nm layer represents regime 2: acomplete ML and the photoemission spectrum is characteristic of the spinterface. The 2 to 5 nm films fitinto regime 3: the photoemission spectra reflect that of the surface molecular layer with additionalcontributions from underlying molecules. Interestingly, the peak corresponding to the HOMO (markedwith a circle) shifts approximately linearly to lower energy as the film thickness increases; see insetFig. 41. DFT calculations were performed on Al(OP)3 using the hybrid exchange correlation functionalB3LYP and 6-31G* basis sets. Ionization energies were calculated using the DSCF method, and a directcomparison was made between the theoretical results and the adsorbate system. Moderate agreement butwith some unexplained discrepancies was found between the two.

Photoemission from two hybrid interface states was described at positions between the HOMO ofmolecular Al(OP)3 and the valence band of the Co substrate; see Fig. 42a. The polarization of the HISsrelative to Co is shown in Fig. 42b. The spinterface (dark blue line) is characterized by HIS1 at �0.9 eVthat exhibits a polarization 8 % higher than that of Co and by HIS2 at�1.6 eV that exhibits a polarization4 % lower than that of Co [244]. These results indicate that HIS1 has a polarization parallel to that of Coand HIS2 is either unpolarized or has a polarization antiparallel to that of Co.

Co/Alq3 Co electrodes covered with discrete MLs of tris(8-hydroxyquinolinato) aluminum (Fig. 40b)have been the focus of a body of work clarifying the character and fs spin dynamics of hybrid interfacestates [245]. A transient spin population in the unoccupied HIS of Co/Alq3 was generated by excitation ofCo electrons (using 3.25 eV photons) and its decay followed by SR-2PPE. From the spin-dependentpopulation decays, the lifetimes of the minority spin electrons at E* � EF = 1.5 eV were found to be

Fig. 40 The structures of (a) Cu-phthalocyanine, (b) Alq3 [245] (Reproduced with permission from Chemical Communica-tions, Copyright 2002 The Royal Society of Chemistry), and (c) Al(OP)3 (hydrogen and solvent molecules omitted for clarity)[244] (Reproduced with permission from New Journal of Physics, Copyright 2013 IOP Publishing)


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800 fs – almost twice as large as the majority spin lifetime of 450 fs; see Fig. 43. These lifetimes are bothmuch longer than those observed for Co without adsorbate, and they also have the opposite sense, i.e., forCo alone, the majority spin lifetime is greater, by a factor of up to 2, than the minority spin lifetime [24,25]. The lifetimes are also longer than those typically found for these types of interface state [246]. Thelifetime in bulk Alq3 is much longer – in the ns to ms range [247]. At energies above and below that of theunoccupied HIS, the difference in spin lifetimes disappears.

The depopulation of the HIS occurs by inelastic electron scattering mediated by the Co d-bands, and itgives information about the degree of hybridization between the Alq3 MOs and the cobalt bands. The HISacts as an interfacial spin trap, and this is the origin of the spin filtering at the Co/Alq3 spinterface. Indeed,it was proposed [245] that in general systems with significant metal/organometallic hybridization will actas spin filters because of this effect. The manipulation of spin-dependent injection barriers by chemicallyengineering spinterfaces with transport levels closer to EF than that found for the Co/Alq3 interface isclearly a strong possibility.

Ferromagnet/Metal-Phthalocyanines A particularly interesting set of results for fcc-Co(001)/MnPc,which supports a large positive, room temperature, polarization of 80 � 10% at EF, has been published bya major consortium led by researchers from the University of Strasbourg [241]. Using primarily acombination of SRPES and inverse photoemission (Fig. 44) together with extensive use of densityfunctional theory, they established that the interface states between the cobalt surface and the manganesephthalocyanine molecules were strongly spin-polarized by mechanisms that were different for each spinchannel.

They proposed that the mechanism for the minority channel was the well-established scheme depictedin Fig. 39. That is, when well separated from each other, the cobalt has bulk states and theMn-phthalocyanine molecules have MOs with the correct symmetry, orientation, and energy to allow

Fig. 41 Center panel: SRPES of Co/[0–5 nm] Al(OP)3. Right panel: 0–5 eV binding energy region magnified. Left panel:low-energy cutoff region magnified. Inset: Plots of the shift in the work function (black) and of the HOMO (red dashed) versusAl(OP)3 coverage. Thick blue line (1.5 nm) represents a single ML [244] (Reproduced with permission from New Journal ofPhysics, Copyright 2013 IOP Publishing)


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Fig. 42 (a) Near threshold photoemission spectra of Co/[0.5–5 nm] Al(OP)3 showing (with short vertical bars) the energeticpositions of the two hybrid interface states, HIS1 and HIS2. (b) The relative spin polarization of Co/[0.5–5 nm] Al(OP)3 andthe multi-peak fit for Co/[1.5 nm] Al(OP)3 as an illustrative example. Spinterface polarization, dark blue line (1.5 nm) [244](Reproduced with permission from New Journal of Physics, Copyright 2013 IOP Publishing)

800

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Fig. 43 Spin-dependent lifetimes of the unoccupied HIS of Co/Alq3 extracted from SR-2PPE measurements [245](Reproduced with permission from Nature Physics, Copyright 2010 MacMillan Publishers Ltd.)


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strong mixing.When together, they form broadenedminority spin interface states, so-called band-inducedspinterface states (BISS), that display a flat, continuous, energy profile across EF. A novel mechanism forthe majority spin channel was proposed by the authors. This involves majority spin surface states of Coclose to, but not at, EF that interact with the same spin MOs of MnPc that are initially rather distant inenergy from EF. The Co SSs act to pin the resultant surface-induced spintronic states (SISS) so close to EF

that they intersect it.The result of these two processes is a spinterface in which there is very strong hybridization between the

carbon and nitrogen atoms of the phthalocyanine molecules and the Co surface atoms. In contrast to thepolarization at EF of Co itself which, as a strong ferromagnet, is dominated by minority spins [70], themajority spins of the spinterface now dominate. The manganese center was found to play only a minorrole in the electronic structure of the spinterface.

The authors further considered the observed resilience of the spinterface against thermal disorder.A major contributor to this is undoubtedly the high TC of Co, but rather complex, direct exchangecoupling, which results in moments on the C and N atoms, was also predicted to play a significant role.X-ray magnetic circular dichroism (XMCD) evidence for moments on the N p states was presented.

In the light of their results, the group proposed that particularly robust spinterfaces form when thedominant hybridization mechanism between states of the ferromagnetic metal and the OSC involves justone spin channel at, or very close to, EF. The broader implications of this work as a general route towardshigh-quality spintronics materials were also considered [241].

Other FM/metal-phthalocyanines that have been studied include Co/CuPc, Fe/CuPc, and Co/MPc.

Co/CuPc By using SR-2PPE, the Co/CuPc interface has been shown to exhibit a spin injection efficiencyof 85–90 % for room temperature injection from Co to the unoccupied MOs of CuPc [242]. In addition,the spin diffusion length in CuPc was shown to be dominated by quasi-elastic spin-flip processes withenergy loss 200 meV. The impact of alkali-metal doping on Co/CuPc has also been investigated[248]. While the alkali atoms influence the energy level alignment of the interface allowing an

Fig. 44 Direct and inverse photoemission of phthalocyanine on Co(001) (2.6 MLMnPc for spin-resolved photoemission and2 MLMnPc for inverse photoemission) following subtraction of sub-surface contributions to the spin-resolved photoemissionintensity [241] (Reproduced with permission)


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improvement in the spin injection efficiency, they also increase the spin-flip probability for those electronscrossing the interface.

Fe/CuPc A combination of UV SRPES, spin-resolved scanning tunneling spectroscopy (SR-STS), andDFT calculations has revealed two characteristic regions in the electronic structure of the Fe(110)/CuPcinterface [243]. The first region, away from EF, encompasses spin-polarized HISs that act up to roomtemperature and which modify the energy dependence of the Fe substrate polarization. The second region,close to EF, is clear of interface states, and the interface merely acts as a featureless scattering barrier withan energy-independent spin-flip probability, i.e., spin transport close to EF retains the energy dependenceof the underlying ferromagnetic Fe substrate [243]. This paper also explores the complementarity of theinformation resulting from SR-STS with that from SRPES.

Co/MPc Rather than changing the substrate, SRPES (using He I and He II radiation) results have shownthat it is possible to tailor the electronic structure at FM/MPc spinterfaces by changing the central metalatom [249]. This is clearly of interest from an applications point of view.

Other systems studied by SRPES and for which strong hybridization between molecular orbitals andthe spin-split bands of a ferromagnet have been proposed include Ni(111)/graphene [232], Co/FeOEP, andc(2 � 2)O/Co/FeOEP [250].

Spin-Resolved ImagingWhen considering spin-resolved imaging, the first thing that generally comes to mind is the well-established technique known as SEMPA (scanning electron microscopy with polarisation analysis)[251–253]. This technique extends the capabilities of standard electron microscopy, and though it canprovide very detailed images, it does not give the detailed electronic structure information that comes withphotoemission.

In pioneering work at the BESSY synchrotron, a spin-resolving photoemission electron microscope(SRPEEM) was developed to image materials either via core-level photoemission or via secondaryelectron emission [254, 255]. Determination of all three components of the spin polarization, potentialspatial resolution of around 20 nm, and the added benefit of chemical sensitivity (when using core-levelphotoemission) are strong selling points of this apparatus. However, the quality of the spin-resolvedimages obtained meant that this approach was not competitive with images recorded using XMCD, forexample.

Recently a much improved SRPEEM utilizing the multichannel spin polarimetry principles detailed in“Spin-Polarised Low-Energy Electron Diffraction (SPLEED) Polarimetry” has started to operate at Halle[75, 256]. This instrument combines a PEEM column with an aberration-corrected electron energyanalyzer followed by a W(100) imaging spin filter. Spatial information is encoded in the angle ofincidence, and this is conserved upon specular reflection at the tungsten. By measuring the contrast andthe absolute intensity of the spin filter images at two scattering energies, the sign and magnitude of thespin polarization are obtained for every point [256].

As an illustrative example of the power of this instrument, 2PPE (using 3.1 eV photons from aTi:Sapphire laser with a 20 fs pulse length and an 80 MHz repetition rate) was used to generate 0.8 eVbinding energy photoelectrons from 8 to 12 ML cobalt films grown on Cu(100); see Fig. 45. The imageshave a spatial resolution of 300 nm and require a total acquisition time for the two scattering energies ofonly around 10 min.

Though the magnetic domains are visible in Fig. 45a, b the spin information (shown by the blue- tored-colored scale of Fig. 45c) is necessary to establish the orientation of the magnetization. In Fig. 45c theaverage spin polarization is +0.40 �0.05 (red) and �0.40 �0.05 (blue). Fig. 45c also reveals that the


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defects labeled A and C have positive spin polarization but that labeled B is a small domain with anegative spin polarization of�0.15�0.05, a value that could be the result of either defects or a rotation ofthe direction of magnetization.

Figure 45d shows the polarization along the arrow in Fig. 45c revealing a sharp transition from positiveto negative, and Fig. 45e shows a spin image for a 12 ML cobalt film. In this case, 0.3 eV binding energy

Fig. 45 (a) Spin-filtered PEEM images of an 8 ML Co film measured at a scattering energy of (a) 26.5 eVand (b) 30.5 eV. (c)Calculated spin polarizations from images (a) and (b). (d) Spin polarization along the line indicated in (c); the red solid line is afit assuming Gaussian broadening. (e) Spin-resolved PEEM image of a 12 ML Co film. (f) Spin polarization along the line in(e); the horizontal dashed lines indicate P ¼ �0:4 [256] (Reproduced with permission from Ultramicroscopy, Copyright 2013Elsevier B.V.)


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electrons were imaged, and once again the average spin polarization is +0.40 �0.05 (red) and �0.40�0.05 (blue). This is anticipated as the 2PPE involves resonant transitions to unoccupied Co states andunpolarized electrons from the Cu substrate are insignificant.

It is clear that the spin filter imaging reported above has considerable potential for time-resolvedimaging.

DynamicsMagnetodynamics is a very active and important field (from both pure and applied viewpoints) to whichthe results of many spectroscopic techniques have contributed and about which much has been written[101, 257–263].

Dynamical processes have long been studied by time-resolved photoemission. However, time- andspin-resolved studies are far fewer in number – unsurprisingly given the extra experimental demandsimposed. This section aims to provide a flavor of recent contributions made by SRPES techniques toultrafast magnetodynamics in the itinerant ferromagnets Fe and Co.

Early spin-resolved studies focused on transitions taking place on ns to ps timescales [264–267]. Morerecently experiments have established that upon laser excitation, itinerant ferromagnets lose their long-range magnetic order within a few hundred fs [268–271]. Very recently, for example, the ultrafast surfacedemagnetization of an 8 ML Fe(110) film was explored in a near IR (1.5 eV)/X-ray (182 eV) pump-probeexperiment using a Ti-sapphire laser synchronized to the FLASH FEL at DESY [12]. By probing the spinpolarization of the cascade electrons, the total magnetization of the sample was shown very directly to bequenched within a 1/e decay time of 100 fs.

While the fact of ultrafast demagnetization is now well established, the specific microscopic mecha-nisms that underlie reductions in magnetization operating in particular cases have been hotly debated.

The lifetime of hot electrons (i.e., those electrons that are excited to energies just above EF) is controlledby the availability of decay channels which includes interaction with other electrons, holes, phonons,impurities, etc. In addition to transfer of energy between the spin, orbital, and charge degrees of freedom,angular momentum must also be taken into account as both energy and angular momentum are conservedquantities even on fs timescales [261].

The band structure has a particularly important role for inelastic events, and for ferromagnets where thebands are spin-split, lifetimes are expected to be spin dependent. To first order, the lifetime of an excitedelectron depends upon the phase space available for its decay. However, this simple picture breaks down ifhigher-order effects come into play.

Spin-flip of a hot electron is associated with a change in angular momentum, and while this could inprinciple be achieved directly by SO coupling, in the first row transition metals, this effect is too weak.The main mechanisms by which an excited electron in a ferromagnet may flip its spin are:

1. Stoner excitations – electron-hole pair excitation also known as exchange spin-flip scattering[272]. (That is, the hot electron transfers energy (via the Coulomb interaction) to an electron ofopposite spin within the material which is then excited to above EF.)

2. Electron spin-wave scattering (magnon excitation) – a collective electron process.3. Elliott-Yafet scattering [273, 274] – from phonons or impurities.4. Superdiffusive spin transport into the bulk [275].

Overall, the excited electron ends up with lower energy and the opposite spin; see schematic in Fig. 46in which the vertical arrows depict exchange spin-flip scattering and the wavy line represents collectiveelectron spin-wave scattering [276]. Multiple interactions of this type are further discussed in the reviewby Zhukov and Chulkov [263].


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In addition to spin, the dynamics of photoexcited electrons in metals depends on a range of factors suchas excitation energy, band structure, screening, morphology, etc. [277]. Though dynamical informationhas long been extracted from static photoemission peak widths [278], a more direct method involves theirmeasurement in the time domain using SR-2PPE. This technique [26, 277, 279–281] has been particularlyrewarding for revealing fs dynamics in among others Ni [271, 282], Co [270, 283], and Fe [276]. TheTi-sapphire laser is undoubtedly (though not exclusively) the workhorse photon source for theseexperiments.

The first SR-2PPE experiments [24, 25, 28, 277] on Fe, Co, and Ni showed an excited-state lifetimeordering of tCo > tNi > tFe and that the lifetimes are both energy and spin dependent. At excited-stateenergies greater than 1.0 eV lifetimes of under 10 fs were reported, and a sharp increase on approaching EF

was observed. The majority spin lifetimes for all three elements were consistently longer than the minorityspin-lifetimes and the spin lifetime, ratios t"=t# were between 1 and 2, i.e., much smaller than earlytheoretical predictions. It was also clear that the ratio t"=t# decreased towards lower energies. Qualita-tively the lifetime ratio for Co and its low-energy behavior was rationalized, without the need to invokeany spin flipping, in terms of the excess of unfilled minority spin states compared with unfilled majorityspin states [24].

More recent SR-2PPE experiments on the ultrafast magnetization dynamics of cobalt over the timerange 0–1,000 fs [270] revealed a complex temporal evolution of the normalized polarization of electronsat 0.4 eVabove EF. In particular, two maxima were observed at 30 and 120 fs and two minima at 75 and350 fs. This was rationalized in terms of an initial dominance of spin-dependent lifetime effects notinvolving spin flipping (causing the local maximum at around 30 fs) followed by the dominance ofmagnon scattering at around 120 fs. The broad minimum around 350 fs was shown to occur on the sametimescale as the overall magnetization was changing and, given its dependence on the pump fluence, wasattributed to Elliott-Yafet-type spin-flip scattering.

The magnetodynamics in Co were further studied by Donath and coworkers [283, 284] who extendedAeschlimann’s SR-2PPE measurements to lower energies and, consistent with the decreasing spinlifetime ratio previously found, observed hardly any spin-difference in the lifetimes; see Fig. 47. Incontrast to the conclusions of Cinchetti et al. [270] above, this was attributed to the dominance of spin-flip

Fig. 46 Schematic view of exchange spin-flip processes [276]. The vertical arrows depict exchange spin-flip scattering andthe wavy line represents collective electron spin-wave scattering (Reproduced with permission from Physical Review Letters,Copyright 2010 American Physical Society)


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exchange scattering intrinsic to the Co in combination with secondary electron excitation. Spin waves[285] were proposed to contribute to the excited-state decay. Theoretical models in support of theexperimental observations continue to be refined [286] and the area is still very active.

The relaxation processes in Fe have been found to be very spin and energy dependent over the fullenergy range [25, 276], and by probing the spin-dependent decay of image potential states (by SR-2PPE)coupled with extensive modeling, considerable insight has been gained into the relaxation processes[276]. Sub-20 fs lifetimes were recorded as shown in Fig. 48. The decay rate G ¼ 1=t for the minorityspin first image-potential state was found to be twice that of its exchange split majority spin counterpart, afinding that cannot be rationalized just in terms of inter- and intra-band scattering which would tend tofavor very similar rates. Rather, it was established with the aid of ab initio and many-body theorycalculations that magnon emission makes a particularly large contribution to the decay of minority spinelectrons. The energetics of the scattering in this case eliminated single-electron spin reversal (Stonerexcitation) and favored collective electron excitation (spin waves) of acoustic or optical magnons(depending upon the momentum of the primary electron). It was also highlighted [276] that as theefficiency of magnon generation is material dependent, this is a possible route to spin-selectivetuning – important as hot electrons play an important role in the transport of spin-dependent currents.

Overall, the picture that has emerged for the itinerant ferromagnets Fe and Co is one of demagnetizationover a period of a few hundred fs, the microscopic mechanisms of which have been, and still are, thesubject of debate. Various theoretical models have been proposed and developed over the last few yearsand the topic is still one of lively discussion.

Fig. 47 Spin-dependent lifetimes for Co determined by SR-2PPE: green solid triangles, red open triangles, and blue solidcircles (Goris et al. [283]); black solid triangles, black open triangles, and black solid squares (Aeschlimann et al. [24]). The fitis from Zarate et al. [292] (Reproduced with permission from Physical Review Letters, Copyright 2011 American PhysicalSociety)


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SR-2PPE with variable time delay between the two pulses has been used with a PEEM [287] to enablemagnetic sensitivity with nm spatial and fs temporal resolution. This unique combination proved apowerful but demanding technique for microscopic understanding of the electron and spin dynamicsinvolved in the demagnetization of nanoscale magnetic bits [254, 288, 289]. The group also explored thedynamics of the transient demagnetization of a 10 nm Co film in an experiment utilizing pulses of 3.1 eVand with a lateral resolution of around 20 nm. Both the photoelectron yield and the spin polarization werefound to be strongly dependent on the population of the intermediate states above EF, which weremanipulated with the pump pulse intensity (an effect resembling optical bleaching [290]). By using lowpump powers the intrinsic timescale for demagnetization of the Co film was shown to be 130 fs.

In contrast to the area of magneto-dynamics, which has built on a long history of SRPES work uponferromagnets, the spin dynamics of non-magnetic materials in particular TIs is just at its outset [108].

Fig. 48 (a) Contour plots (white maximum) of the spin-dependent (green majority spin, red minority spin) dispersion of thefirst two image potential states of Fe as a function of parallel momentum. (b) Time- and spin-resolved 2PPE data for the n = 1image potential state at the kk values indicated in (a) [276] (Reproduced with permission from Physical Review Letters,Copyright 2010 American Physical Society)


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Outlook

The popularity of SRPES as an electronic structure probe has surged in recent years, driven in no smallpart by its power to reveal details of the electronic structure of non-magnetic materials such as TIs.

Advances in light source technology have led to a burgeoning of studies with laser groups andsynchrotron groups pursuing parallel but equally fruitful lines of investigation. Until recently, advancesin polarimeter technology had not kept pace, but the development (at Halle and Mainz in Germany [76,256]) of systems that allow multichannel spin detection promises to revolutionize time- and spin-dependent domain imaging and bandmapping [291]. In addition, the further development of multichannelspin detection is potentially a key step towards single-shot experiments using ultrabright, short-wavelength, fs sources such as free-electron lasers.

On the route to such challenging developments is the more modest goal of being able to performSRARPES measurements with energy- and angular- resolutions similar to those routinely achieved forspin-integrated measurements as this would undoubtedly lead to improved understanding of spin-dependent coupling of charge carriers with phonons, magnons etcetera.

Acknowledgments

It is with great pleasure that I acknowledge the assistance provided by Tim Gay, Moritz Hoesch, VladimirPetrov, Hugo Dil, Karol Hricovini, Jean-Michel Mariot, Peter Weightman, Paul Durham, and YvesAcremann, all of whom read the manuscript and provided many helpful suggestions. My thanks alsogo to Sihui Wang, Yonghao Gao, and Xiao Collins for their help with the manuscript. In addition I amindebted to Prof Wendy Flavell for many fruitful discussions, to members of the vacuum group and myfamily for their patient support in the light of numerous delays, and to The University of Manchester, theCockcroft Institute, and STFC for their continued support.

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Further ReadingBennemann KH (2004) Ultrafast dynamics in solids. J Phys Condens Matter 16:R995Dediu VA, Hueso LE, Bergenti I, Taliani C (2009) Spin routes in organic semiconductors. Nat Mat 8:707;

corrigendum Dediu VA, Hueso LE, Bergenti I, Taliani C (2009) Nat Mat 8:850Dil JH (2009) Spin and angle resolved photoemission on non-magnetic low-dimensional systems. J Phys

Condens Matter 21:403001Johnson PD (1997) Spin-polarized photoemission. Rep Prog Phys 60:1217Johnson PD, G€untherodt G (2007) Spin polarized photoelectron spectroscopy as a probe of magnetic

systems. In: Kronm€uller H, Parkin S (eds) The handbook of magnetism and advanced materials, vol 3.Wiley, Hoboken, p 1635.

Kessler J (1985) Polarised electrons, 2nd edn. Springer, BerlinOkuda T, Kimura A (2013) Spin- and angle-resolved photoemission of strongly spin-orbit coupled

systems. J Phys Soc Jpn 82:021002Osterwalder J (2006) Spin-polarized photoemission. Lect Notes Phys 697:95


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