Magnetic Sensitive Force Microscopy€¦ · Magnetic Sensitive Force Microscopy Alexander Schwarz...

Fachbereich Physik

Institut für Angewandte Physik

Zentrum für Mikrostrukturforschung Alexander Schwarz: [email protected]

Magnetic Sensitive Force Microscopy Alexander Schwarz

Institut für Angewandte Physik, Universität Hamburg, Jungiusstr. 11, 20355 Hamburg, Germany

• Magnetism Basics (Part I & II) • atomistic approach (origin of magnetism, magnetic exchange mechanisms) • phenomenological approach (hysteresis, domains, domain walls)

• Magnetic Force Microscopy (MFM; Part I)

• tip preparation and tip properties • separation of forces • examples (thin films, superconductors, …)

• Magnetic Exchange Force Microscopy (MExFM; Part II)

• tip preparation and tip properties • separation of forces • examples (imaging, spectroscopy, switching, dissipation …)

• CO molecule: contrast formation (role of electrostatic forces)

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MFM on Superconductors

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Imaging of Flux Lines with MFM

MFM-tip

1 µm

Abrikosov Flux Line Lattice Bi2Sr2CaCu2O8: λ ≈ 180 nm

λ ξ x

B

nC B

j

nC

MFM

MFM information depth ≈ λ

field cooling: B applied below Tc flux lines (vortices) remain, even if B → 0

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Bi2Sr2CaCu2O8

TC ≈ 85 K λ ≈ 180 nm ξ ≈ 1 nm

c = 3.08 nm

pancake vortex

flux line

VORTEX MATTER

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Straight vs. Curved Flux Lines

5.1 K

1 µm

5.1 K

1 µm

irradiated sample after field cooling ⇓ columnar defects • randomly distributed • strong pinning • Bose Glass

as grown sample after field cooling ⇓ intrinsic point defects • randomly distributed • weak pinning • Bragg Glass

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Flux Line Lattice Melting 5.1 K

1 µm

5.1 K

1 µm

5.1 K

1 µm

5.1 K

1 µm

5.1 K

1 µm

5.1 K

1 µm

5.1 K

1 µm

5.1 K

1 µm

5.1 K

1 µm

5.1 K

1 µm

23.2 K

1 µm

34.5 K

1 µmfield cooling: B = 3.2 mT scan area: 5.5 µm × 5.5 µm

A. Schwarz et al., NJP 12, 033022 (2010).

38.1 K

1 µm

49.7 K

1 µm

54.1 K

1 µm

5.1 K

1 µm

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Thermal Fluctuations and Disorder

1

2

4

5

3

0 50 6040302010T in K

400

360

320

280

240

200

160

FL

R i

n nm

RFL∝√T

E

E

2λ

D

k TB

rr0

∆r∆r thth

rp

E

E

2λ

D

k TB

rr0 rp

∆rth

depinning CuO2- planes

pancake vortex

flux line

Fachbereich Physik



Vortices and Antivortices

dark (antivortex) Mtip ↑↓ flux line

2 µm bright (vortex)

Mtip ↑↑ flux line

2 µm

matching field: number of columnar defect = number of flux lines

field ramp: Mtip ↑↑ B

BSCCO field cooling: Mtip ↑↓ B

BSCCO

A. Schwarz et al., APL 88, 012507 (2006).

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Part II

Magnetic Exchange Force Microscopy

(MExFM)

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Magnetic Exchange

Interaction

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Two Interacting Electrons with Spin

spin states χi χ1+= ↑ χ1-=↓

χ2+=↑ ↑↑ > ↑↓ >

χ2-=↓ ↓↑ > ↓↓ >

2 electron state χ(s,m) s m

0 0 singlett antismmetric

↑↑ > 1 +1 triplett

symmetric 1 0

↓↓ > 1 -1

Coulomb Interaction V(r) + Pauli Principle (Fermi-Dirac & Indistinguishability) ⇒ Alignment of Spins ⇒ Magnetic Order

no spin dependent term!

s = s1 - s2 , …, s1 + s2 = s1 ± s2 = 0,1 and m = -s, +s = -1,0,+1 (∆m = 1)

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Two Interacting Atoms: The H2 Molecule

total wave function = spatial wave function × spin wave function electron = Fermion ⇒ antisymmetric total wave function if spatial wf antisymmetric ⇒ spin wf symmetric if spatial wf symmetric ⇒ spin wf antisymmetric

H = H0 + W ; H0: 2 non-interacting H atoms; W: interaction terms

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Coulomb-, Overlap- and Exchange-Integral

antiparallel spins; s = 0 (singlett) :

parallel spins; s = 1 (triplett) :

ground state energy of one H atom in the 1s state

overlap integral

Coulomb integral

exchange integral

ϕ0 = 1s wave function of the H atom

bonding state

antibonding state

Fachbereich Physik



Connection to Heisenberg Model

antiparallel spins; s = 0 (singlett) :

parallel spins; s = 1 (triplett) :

in general: J ≠ A!

Heisenberg modell :

J = J(r) distance dependent magnetic exchange coupling constant

J > 0 ⇒ ferromagnetic order J < 0 ⇒ antiferromagnetic order

skalar product: no magnetic interaction for perpendicular spins

exchange coupling constant

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Magnetic Coupling in Metals Direct versus Indirect Coupling

f-metals (Gd): no direct exchange, s-f coupling = spin carrying strongly localized f-electrons polarize conduct-tion band electrons (RKKY)

d-metals (Fe, Ni, Co): little direct exchange, mostly s-d coupling = spin carrying localized d-electrons polarize conduction band electrons

≈ half distance to nearest neigbor ≈ half distance to nearest neigbor

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Magnetic Exchange Force Microscopy

(MExFM) suggested 1991, realized 2007 on NiO(001)

U. Kaiser, A. Schwarz, and R. Wiesendanger, Nature 446, 522 (2007).

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Forces in Force Microscopy

Electromagnetic Forces

• electrostatic force • magnetostatic force

• van der Waals force

• chemical force • magnetic exchange force • repulsive forces

z

Fts

MFM (z > 10 nm)

AFM/MExFM

atomic resolution

steps (topography)

-1 nN

-0.3 nm

0 nN

magnitude of forces: magnetic exchange ≈ 0.1 N (d < 0.5 nm) magnetostatic 1 pN (d > 10 nm)

1 nm

10 nm

100 nm

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electron mediated short-range magnetic exchange interaction & chemical interaction

Separation of Short-Ranged Forces

magnetic coating

Heisenberg model for spin-spin interaction:

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Tip Preparation Si-cantilever (f0 ≈ 190 kHz, cz ≈ 40 - 150 N/m; Si surface is oxidized) in-situ coating with magnetic material (Fe, Cr, …) by thermal evaporation antferromagnetic tips: no stray field ⇒ less influence on sample! total coverage (instead of just one side) or bulk tips are Ok, because only

foremost apex atom matters on the fly preparation: intended collisions between tip and surface to create

atomically sharp and magnetically sensitive nanotip trial and error procedure (no real control) with three options

• tip stays as it was: continue preparation • tip becomes worse: continue preparation • tip becomes good: start the real experiment

no magnetic contrast, although tip is magnetic: SNR < 1, spin of foremost tip atom perpendicular to surface spins (Heisenberg model!), fast switching (superparamagnetic) tip

Fachbereich Physik



Z-Height & Dissipation Analysis

Δz < 0 : tip becomes longer (sharper) ΔED < 0: less dissipation due to adhesion hysteresis (more stable) possible transitions : + + + − − + − − wanted transition : − − (sharper and more stable) with magnetic c(2x2) contrast

p(1×1) p(1×1)

p(1×1) c(2×2)

p(1×1) p(1×1)

1. ML (afm) 1. ML (afm) 2. ML (fm) 2. ML (fm)

c(2×2)

Fachbereich Physik



Atomic Contrast on NiO(001)

NiO:

antiferromagnetic bulk insulator due to super-exchange between Ni atoms via O bridges

antiferromagnetic ordered Ni rows on (001) surface

*Ciraci, Baratoff, Batra, PRB 41 2763 (1990) **Teobaldi et al., PRL 106, 216102 (2011)

AFM on NiO(001)

chemical contrast * ⇒ maxima = oxygen

electrostatic contrast ** ⇒ maxima = oxygen

1 nm c(1×1)

Fachbereich Physik



Magnetic Contrast on NiO(001)

NiO:

antiferromagnetic bulk insulator due to super-exchange between Ni atoms via O bridges

antiferromagnetic ordered Ni rows on (001) surface

MExFM on NiO(001)

magnetic contrast on minima = Ni-sites * in **: contrast on maxima!

1 nm c(2×1)

*U. Kaiser et. al., Nature 446, 522 (2007). ** H. Hosoi et al., Nanotech. 15, 506 (2004).

Fachbereich Physik



Raw Data Analysis and Distance Dependence left : chemical contrast only maxima = oxygen (cation) minima = nickel (anion)

4 peaks in Fourier image represent structural surface unit cell

right: recorded closer to surface additional row-wise contrast on nickel atoms

2 additional peaks in Fourier image represent magnetic surface unit cell

H. Hosoi, K. Sueoka, and K. Mukasa in Nanotechnology 15, 506 (2004): modulation on maxima (O-sites!) in unit cell averaged data, but no peaks in Fourier image shown!

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Artefact or Signal? Scan Rotation

additional pair of peaks in FT behaves like signal peaks

→ we can exclude an in phase oscillatory noise source

dissipation

topography

Fachbereich Physik



Magnetic Double Tip: Contrast Transfer

magnetic contrast found on Ni- and O-atoms

Fachbereich Physik



Growth of Fe on W(001)

layer-by-layer growth: ML Fe wetting layer

DL step flow growth

DL island

ML : antiferromagnetic with out-of-plane anisotropy DL : ferromagnetic with in-plane anisotropy A. Kubetzka et al., PRL 94, 087204 (2005) K. v. Bergmann et al., PRB 70, 174455 (2004)

Fachbereich Physik



MExFM on Fe Monolayer on W(001) chemical contrast magnetic contrast

10 p

m

0.25 nm [100]

10 p

m

0.25 nm [100]

Fe/W(001): Fe thin film on high Z substrate ⇓ hybridization and strong spin-orbit coupling

R. Schmidt et al., Nano Lett. 9, 200 (2009)

Fachbereich Physik



Magnetic Exchange Force Spectroscopy

(MExFS) R. Schmidt, C. Lazo, U. Kaiser, A. Schwarz, S. Heinze, and R. Wiesendanger Phys. Rev. Lett. 106, 257202 (2011).

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3D Magnetic Exchange Force Spectroscopy

3D data set: topography + Δf (z) with atomic resolution

x

z

y

c(2×2) magnetic contrast and distance dependence of the tip-surface interaction

∆f is color coded

3D-FFS: ∆f(x,y,z) ⇒ E (x,y,z), F (x,y,z) Hölscher et al., APL 81, 4428 (2002)

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Distance Dependence of the Magnetic Exchange Interaction

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Distance Dependence of the Magnetic Exchange Interaction

magnetic exchange interaction is short-ranged, strongly distance dependent and can be large (about 100 meV)

DFT ⇒ ap-configuration (↑↓) preferred (maxima in topography)

calculated from exp. Δf(z) data

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Spin Dependent Adhesion Hysteresis

E. Y. Vedmedenko, Q. Zhu, U. Kaiser, A. Schwarz, and R. Wiesendanger, Phys. Rev. 85, 174410 (2012).

Fachbereich Physik



Spin-Dependent Dissipation: Spectroscopy

Fachbereich Physik



Magnetization Switching Induced by

Magnetic Exchange Interaction

R. Schmidt, A. Schwarz, and R. Wiesendanger, Phys. Rev. B 86, 174402 (2012).

Fachbereich Physik



Summary and Outlook: MExFM • sensitive to short range magnetic exchange interactions • separation from chemical force

• antiferromagnetic surfaces • non-collinear spin structures (has not been done yet) • field-dependent experiments (has not been done yet)

• spin-dependent dissipation • spin-dependent adhesion hysteresis • spin-excitations (has not been done yet)

• magnetic exchange force spectroscopy (MExFS) • magnetic switching utilizing the magnetic exchange interaction • MExFM on single atoms and molecules (has not been done yet)

Fachbereich Physik



Publications on MExFM Vacuum tunneling of spin-polarized electrons detected by scanning tunnelling microscopy R. Wiesendanger, et al., J. Vac. Sci. Technol. B 9, 519 (1990). first discussion on the feasibility of MExFM

Investigations on the topographical asymmetry of non-contact atomic force microscopy images of NiO(001) surface observed with a ferromagnetic tip. Hosoi, H., Sueoka, K. & Mukasa, K. Nanotechnology 15, 506–509 (2004). first claim of a successful MExFM experiment (see also 1st NCAFM book!), but not generally accepted, because of a dubious data evaluation

Magnetic exchange force microscopy with atomic resolution U. Kaiser, A. Schwarz, and R. Wiesendanger, Nature 446, 522 (2007). first MExFM experiment performed on the afm bulk insulator NiO(001)

Probing the Magnetic Exchange Forces of Iron on the Atomic Scale R. Schmidt, C. Lazo, H. Hölscher, U. H. Pi, V. Caciuc, A. Schwarz, R. Wiesendanger, and S. Heinze, Nano Lett. 9,200 (2009). MExFM experiment on afm Fe monolayer on W(001): much better SNR; itinerant metallic system

Quantitative Measurement of the Magnetic Exchange Interaction across a Vacuum Gap R. Schmidt, C. Lazo, U. Kaiser, A. Schwarz, S. Heinze, and R. Wiesendanger, Phys. Rev. Lett. 106, 257202 (2011). first magnetic exchange force spectroscopy data (MExFS)

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Publications on MExFM Evaluating local properties of magnetic tips utilizing an antiferromagnetic surface U. Kaiser, A. Schwarz, and R. Wiesendanger, Phys. Rev. 78, 104418 (2008) magnetic double tips in MExFM data

Atomic-scale magnetic dissipation from spin-dependent adhesion hysteresis E. Y. Vedmedenko, Q. Zhu, U. Kaiser, A. Schwarz, and R. Wiesendanger, Phys. Rev. 85, 174410 (2012). first data on spin dependent dissipation

Magnetization switching utilizing the magnetic exchange interaction R. Schmidt, A. Schwarz, and R. Wiesendanger, Phys. Rev. 86, 174402 (2012). utilizing magnetic exchange interaction (instead of external magnetic field) for magnetic switching

Spin Resolution on NiO(100) by Force Microscopy utilizing Bulk Ferromagnetic Tips F. Pielmeier and F. J. Giessibl, Phys. Rev. Lett. 110, 266101 (2013). second true MExFM paper on NiO; first MExFM paper not from Hamburg Theory:

Foster & Shluger (NiO, very simple tip): Surf. Sci. 490, 211 (2001). Momida & Oguchi (NiO, one atom Fe tip): Surf. Sci. 590, 42 (2005). Lazo & Heinze (Fe/W; realistic multi-atom tips with relaxation): Phys. Rev B 84, 144428 (2011).

2nd NCAFM Book: chapter on experimental data and a separate chapter on theory

Fachbereich Physik



Carbon Monoxide and Metallic Tips Contrast Formation and Role of

Electrostatic Interactions

Fachbereich Physik



CO on Cu(111), NiO(001) and Mn/W(001)

CO on Cu(111) CO on Mn/W(001) CO on NiO(001) x in nm

closer by 0.2 nm

A. Schwarz et al., Appl. Phys. Lett. 105, 011606 (2014)

10 nm

Co on Mn/W

constant ∆f overview image: CO on Cu(111) imaging with metal coated Si tips: f0 ≈ 190 kHz, cz ≈ 150 N/m, A ≈ 1 nm

Fachbereich Physik



Point Dipole Model for Metallic Tips

• 3 layer pyramidal tip: 5 D

• electrostatic potential can be represented by 3 D point dipole at foremost tip atom

Smoluchowski effect ⇒ tip apex exhibits electric dipole moment with its positive pole pointing towards surface: Teobaldi et al., PRL 106, 216102 (2011).

D. Gao et al., ACS Nano 8, 5339 (2014).

Fachbereich Physik



Electric Dipole Moment of Carbon Monoxide

• gas phase: dative bond overcompensates electronegativity effect

⇒ small permanent dipole (0.12 D)

•CO adsorbs upright via C on top, bridge and hollow sites

⇒ charge redistribution •CO donates electrons from 5σ state into metallic d-state

•metal d-state back donates into 2π* antibonding state

⇒ dipole remains, but can possess different orientation and magnitude

G. Blyholder, J. Phys. Chem. 68, 2772 (1964).

CO on Cu(111): 0.2 D, same orientation B. N. J. Perrsson & M. Persson, Solid State Comm. 36, 175 (1989).

CO on NiO(001): 0.4 D, same orientation D. Gao et al., ACS Nano 8, 5339 (2014).

Fachbereich Physik



Simulation: Constant Height Mode

Vdipole

Vsr-vdW

constant height mode

h = constant r2 = x2 + h2

tan(θ ) = x/h

Fachbereich Physik



Irregular Contrast Patterns

2 nm 2 nm

Cr-tip; CO/Cu(111): closer by 0.2 nm

Cr-tip on CO/NiO(001)

experimental AFM image

vAFM simulation (two point dipole tip)

Fachbereich Physik



Electrostatic Double Tip ⇔ Subatomic Features

2 nm 2 nm

CO/Cu(111) with Cr tip: closer by 0.2 nm

J. Welker & F. Giessibl, Science 336, 444 (2012): CO/Cu(111) with W-tip

electrostatic dipole double tip

subatomic resolution stemming from electronic fine structure of W-tip apex atom, but:

• poking of W tip into Cu substrate ⇒ Cu tip • a single atom tip exhibits a spherical charge density in

the vacuum region • tip induced translation prevent too small tip-sample

separartions ⇒ non-spherical electronic fine structure cannot be easily detected

Fachbereich Physik



MFM: Marcus Liebmann Ung Hwan Pi Uwe Kaiser MExFM: Uwe Kaiser Rene Schmidt Ung Hwan Pi Cesar Lazo (Stefan Heinze, CAU) CO: Josef Grenz Arne Köhler David Gao (Alex Shluger, UCL)

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Magnetic Sensitive Force Microscopy€¦ · Magnetic Sensitive Force Microscopy Alexander Schwarz...

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