Magnetism in ultrathin films

W. Weber

IPCMS Strasbourg

Orbital and Spin moment

1 with

222

)(2

)(2

22

lBlorb

orb

glgm

lm

ql

m

qL

m

q

mrm

qrqFIm

Intuitive : Orbital moment Mysterious : Spin moment

2 with sBsspin gsgm

s : momentumspin Angular

FerromagnetismParamagnetic behavior: usually one has to apply an external magnetic field in order to align the magnetic moments

T

H

Ferromagnetic behavior: magnetization without an external magnetic field at non-zero temperatures possible

H

FerromagnetismHow can we explain magnetic order up to temperatures of 1000 K?

Curie temperature

FerromagnetismEarly explanation (1907): Weiss’ molecular field

A molecular field exists within the ferromagnet which orders the moments against the thermal motion. It is so large that the ferromagnet can be saturated even without an external magnetic field.

Order of magnitude:

mBcB HTk 0K 1000cT A/m 109mH

Ferromagnetism

What is the physical interaction responsible for it?

Dipole-dipole interaction?

rmrmr

mmr

Edip 215213

31

K 1 3

20 a

BStrength Too weak!

Ferromagnetism

Interplay of Pauli principle and Coulomb interaction

Two electrons of opposite spin can share the same orbital and come close

Two electrons of same spin cannot farther apart Lower Coulomb energy

This interaction does not act like a real magnetic field

J positive : parallel orientation (ferromagnetic)J negative : anti-parallel orientation (anti-ferromagnetic)

Exchange interaction in a solid

ji

ji SSJH

The strength of the interaction depends on the orbital overlap between neighbouring atoms decreases exponentially with distance

Indirect exchange coupling in multilayers

FM1

FM2

nonmagnetic metal

Indirect exchange coupling

Unguris et al., Phys.Rev. B 49, 14 (1994)

Indirect exchange coupling in multilayers

Amplitude of the coupling strength decreases with thickness

Parkin et al., Phys.Rev. B 44, 7131 (1991)

Co80Ni20 / Ru / Co80Ni20Co80Ni20 / Ru / Co80Ni20

Indirect exchange couplingRKKY interaction (Ruderman, Kittel,Kasuya, Yosida).

It explains for instance the coupling in rare earth systems

Virtually no overlap between magnetic 4f-orbitals

Indirect exchange through conduction electrons

RKKY interaction

distance

Spin density

RKKY interaction

distance

Spin density

RKKY interaction

distance

Spin density

RKKY interaction

distance

Spin density

RKKY interaction

distance

Spin density

RKKY interaction

RKKY interaction

RKKY interaction

RKKY interaction

)2sin(1

2Rk

RJ F

Giant magnetoresistance

Baibich et al., PRL 61,2472 (1988)

Magnetic

Magnetic

Nonmagnetic

Fe

Cr

Fe

Spinfilter effect

E

EF

)(ED)(ED

Paramagnet

Spinfilter effect

E

EF

)(ED)(ED

Ferromagnet

strong scattering

weak scattering

Giant magnetoresistance

22

RrRRtot

r

r

R

R

Giant magnetoresistance

R R

r r

rrR

RrRtot 2

2

GMR read head

voltage

voltage

voltage

voltage

voltage

voltage

voltage

voltage

Spin-resolved photoemission spectroscopy on MnPc/Co(001):

spin-polarized interface states

Insulating spacer layer : tunneling MR

min

min

NN

NNP

maj

maj

21

21

PP1

P2PTMR

Pi = polarisation

=

DOSDOS

DOS-DOS

Jullière’s model

De Teresa et al., Science 286 (1999)

The polarisation dependson the interface !!LSMO

LSMO

PP1

P2PTMR

Co

Co

STO LSMOCo / / ALO LSMOCo / STO //

Mn(II)-phthalocyanine : Mn-C32H16N8

MnPc

Cu(001)

Co(001)

Advantage:large spin diffusion length expecteddue to weak spin-orbit coupling inlow-Z materials.

Photoemission spectroscopy

Spin detector

nPfNL 1 nPfNR 1

nPfNN

NNA

RL

RL

Au foiln

Spin-resolved spectra

E

EF

)(ED)(ED

Spin-resolved spectra

Spin-resolved spectra

Spin-resolved spectra

Spin-resolved spectra

Interface state

Difference spectra

Difference spectra

Difference spectra

Difference spectra

first layer second layer third layer

contribution of the different Pc layers to the interface states

Polarization of difference spectra

Character of interface states

Determination of the character by exploiting the variation of the cross section with photon energy. By going from 20 to 100 eV the cross sections change by the following factors:

Co 3d: 1.4

Mn 3d: 0.7

C 2p: 1/40

N 2p: 1/20

0,0 0,5 1,0 1,5 2,0

0

100

200

2,6 ML Pc/Co(3 ML) - Co(3 ML)

h=100 eV

Inte

nsity

(ar

b. u

nits

)

Binding energy (eV)

spin up spin down

Character of interface states

EF

Co Interface Pc/Co

EF

C. Barraud et al., Nature Phys. (2010)

EF

Co Interface Pc/Co

EF

C. Barraud et al., Nature Phys. (2010)

EF

Co Interface Pc/Co

EF

Electron spin motion: a new tool to study ferromagnetic films

M

Spin up

0

1

Spin down

1

0

1

0

0

10

1

0

0

1 ii erer

?

x

y

z

P0

M

x

y

z

M

x

y

z

M

x

y

z

M

x

y

z

ε

M

M

Spin up

0

1

Spin down

1

0

1

0

0

10

1

0

0

1 ii erer

rr

rr

2arctan

22

?

x

y

z

ε

M

εx

y

z

M

εx

y

z

M

εx

y

z

M

εx

y

z

M

Experiment

Spin-dependent band gaps and their influence on the

electron-spin motion

Typical electronic band structure

Theory

Experimental results

Joly et al., PRL 96, 137206 (2006)

Spin-dependent band gaps and their influence on the

electron-spin motion

Fabry-Pérot experiments with spin-polarized electrons

Cu (001)

0P

Co

Quantum interference

0P

Cu (001)

Co

Quantum interference

Cu

0P

Cu (001)

Co

Quantum interference

Cu

0P

Cu (001)

Co

Quantum interference

Cu

0P

Cu (001)

Co

Quantum interference

Cu

Experimental results and simulations

Joly et al., PRL 97, 187404 (2006), Joly et al., PRB 76, 104415 (2007)

Joly et al., PRL 97, 187404 (2006), Joly et al., PRB 76, 104415 (2007)

Spin-dependent band gaps and their influence on the

electron-spin motion

Fabry-Pérot experiments with spin-polarized electrons

Morphology-induced oscillations of the electron-

spin precession

Tati Bismaths et al., PRB 77, 220405(R) (2008)

Fe/Ag(001)

A/B without relaxation at the islands edges

A/B with relaxation at the islands edges

coverage

para

met

er

coverage

para

met

er

coverage

para

met

er

coverage

para

met

er

coverage

para

met

er

coverage

para

met

er

coverage

para

met

er

coverage

para

met

er

coverage

para

met

er

coverage

para

met

er

Spin-dependent band gaps and their influence on the

electron-spin motion

Fabry-Pérot experiments with spin-polarized electrons

Morphology-induced oscillations of the electron-

spin precession

Influence of sub-monolayer MgO coverages on the spin-dependent

reflection properties of Fe

T. Berdot et al., PRB 82, 172407 (2010)

d (ML)

H.L. Meyerheim et al., Phys. Rev. B 65, 144433 (2002)

MgO-induced perpendicular relaxation of the Fe surface

MgO-induced normal relaxation of the Fe surface

H.L. Meyerheim et al., Phys. Rev. B 65, 144433 (2002)

MgO-induced normal relaxation of the Fe surface

0,0 0,5 1,0 1,5 2,0 2,5 3,00

5

10

15

20

Rel

axat

ion

(%)

MgO thickness (ML)

H.L. Meyerheim et al., Phys. Rev. B 65, 144433 (2002)

Ab initio calculations based on linear muffin-tin orbital method (LMTO) and the Korringa-Kohn-Rostoker (KKR) method.

Ab initio calculations

- 9 ML Fe

- First interlayer distance is relaxed without actually putting MgO on top of Fe

d=dFe bulk=1,43 Å

d = ?

Fe(001)

0

10

20

30

40

0,0 0,2 0,4 0,6 0,8 1,0-20

-10

0

10

20

30

40

50

60

10

15

20

25

30

35

40

-5

0

5

10

15

20

25

(de

g.)

Theo

Exp

MgO thickness (ML)

(de

g.)

Theo

(d

eg.)

Exp

(d

eg.)

T. Berdot et al., PRB 82, 172407 (2010)

0,0 0,5 1,0 1,5 2,0 2,5 3,00

5

10

15

20

Re

lax

ati

on

(%)

MgO thickness (ML)

Spin-dependent band gaps and their influence on the

electron-spin motion

Fabry-Pérot experiments with spin-polarized electrons

Morphology-induced oscillations of the electron-

spin precession

Influence of sub-monolayer MgO coverages on the spin-dependent

reflection properties of Fe

Influence of lattice relaxation on the spin precession in Fe/Ag(001)

prec

essi

on a

ngle

(de

gree

s)

A. Hallal et al., PRL 107, 087203 (2011)

prec

essi

on a

ngle

(de

gree

s)

A. Hallal et al., PRL 107, 087203 (2011)

prec

essi

on a

ngle

(de

gree

s)

A. Hallal et al., PRL 107, 087203 (2011)

prec

essi

on a

ngle

(de

gree

s)

A. Hallal et al., PRL 107, 087203 (2011)

prec

essi

on a

ngle

(de

gree

s)

A. Hallal et al., PRL 107, 087203 (2011)

prec

essi

on a

ngle

(de

gree

s)

A. Hallal et al., PRL 107, 087203 (2011)

prec

essi

on a

ngle

(de

gree

s)

A. Hallal et al., PRL 107, 087203 (2011)

MgO/Fe(001)

pseudomorphic growth

dislocations

Ramsauer-Townsend effect

Resonance condition weak scattering

on-resonance scattering phase is zero

off-resonance scattering phase is non-zero

Energy

Eex

A. Hallal et al., PRL 107, 087203 (2011)

Spin-dependent band gaps and their influence on the

electron-spin motion

Fabry-Pérot experiments with spin-polarized electrons

Morphology-induced oscillations of the electron-

spin precession

Influence of sub-monolayer MgO coverages on the spin-dependent

reflection properties of Fe

Influence of lattice relaxation on the spin precession in Fe/Ag(001)

Organic molecules on ferromagnetic surfaces

0,0 0,2 0,4 0,6 0,8 1,0

0

5

10

15

20

25

of H2Pc

of C60

(vert. shifted by 2o)

of Pentacontane (vert. shifted by 4o)

of carbon (vert. shifted by 12o)

prec

essi

on o

r ro

tatio

n an

gle

(deg

rees

)

thickness (ML)

Laser

Polarizer

Pockels cell

Deflector

GaAs

Coils

Electron optics

SampleCoils

Electron optics

Retarding field analyser

Spin detector

GaAs : Source of polarized electrons

% 50

NN

NNP