Lecture 2: Magnetic Anisotropy...

1K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005

1. Magnetic anisotropy energy = f(T)2. Anisotropic magnetic moment ≠ f(T)

Lecture 2: Magnetic Anisotropy Energy (MAE)

≈ 1µeV/atom is very small compared to≈ 10 eV/atom total energy but all important

Characteristic energies of metallic ferromagnets

binding energy 1 - 10 eV/atom

exchange energy 10 - 103 meV/atom

cubic MAE (Ni) 0.2 µeV/atom

uniaxial MAE (Co) 70 µeV/atom

T=300 K

B (G)

100

100 20000

500

300

300

M (G

)

[111]

[100]

Ni[100]

[111]

0.1 G∆µL ~~


There are only 2 origins for MAE: 1) dipol-dipol interaction ∼ (µ1• r)(µ2• r) and2) spin-orbit coupling ? L S (intrinsic K or ∆Eband)

Structural changes by ≈ 0.05 Å increase MAE

by 2-3 orders of magnitude (~0.2→100µeV/atom)

O. Hjortstam, K. B. et al. PRB 55, 15026 (’97)

R. Wu et al. JMMM 170, 103 (’97)


tetragonal [e.g. Ni, Co, Fe (001) / Cu (001) ]:

hexagonal [e.g. Ni (111), Gd (0001) / W (110) ]:

Ehex = k2 sin2θ + 1/2k2 cos2ϕ sin2θ + k4 sin4θ + k6⊥ sin6θ + k6 cos6ϕ sin6θ + ...

K = k2Y20 + k4mY4

m+ ... Legendre polyn. (B. Coqblin)

each Ki has a „volume“ and „surface“ contribution

Ki = Kiv + 2Ki

s/d

Free energy density of MAE, K

(intrinsic, after substraction of 2πM2)

Etetr = - K2 αz2 - 1/2 K4⊥ αz

4 -1/2 K4 (αx4 + αy

4) + ... (B.Heinrich et al.)

= - K2 cos2θ - 1/2 K4⊥ cos4θ -1/2 K4 1/4 (3+cos4ϕ) sin4θ + ... (Bab et al.)

= (K2 + K4⊥) sin2θ - 1/2 ( K4⊥ + 3/4 K4) sin4θ -1/8 K4 cos4ϕ sin4θ + ...

= K2’ sin2θ + K4⊥sin4θ + K4cos4ϕ sin4θ + ... (traditional)


TC

from B. COQBLINp .

c

PR , 1092 (63)132

33° 60°c

Gdc AXIS

cM

MM

Spin reorientation in bulk Gd

Gd ist not isotropic, it has K2, K4, K6 ≠ 0

Note also finite MAE above TC


Spin reorientation in bulk Ni und Co

T/T~0.8C~

Nifcc

At the extremal value of K2a reorientation and secondmaximum in χ appears

LB III, 19a, p.45

SRT for hcp Cosinθ = (K2/2K4)1/2


Ferromagnetic resonance on Fen/Vm(001) superlattices

Fe

MgO[110] MgO

a =3.05 (+0.8%)⊥ Å

a =2.83 (-1.3%)⊥ Å

[100]Fe/V

0 50 100 150 200-2.5

-2.0

-1.5

-1.0

-0.5

0.0MAE=E[001]-E [110]

b)

MA

E(µ

eV/a

tom

)

T (K)

-2

-1

0

1

2

3

4

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4a)

← K2← K

4⊥

K 4II→

K4

II (µeV/atom

)

K2,K

4⊥(µ

eV/a

tom

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2T/TC

Fe V2 5

510 520 530 700 720 740-1

0

1

2

FeV

x5

prop. µL

prop. µS

Photon Energy (eV)

g<2 g>2

µS µL µS µL

L3 L2

XM

CD

Inte

gral

(ar

b. u

nits

)

XMCD

A.N. Anisimov et al.J. Phys. C 9, 10581 (1997)and PRL 82, 2390 (1999)and Europhys. Lett. 49, 658 (2000)

µµ

L/

S

Fe40 Fenm Fe 4 /V4 Fe2/V54 /V2

bulk Fe

0

0.06

0.12/FMR: (Fe+V)

XMCD: (Fe)µ µL / S

XMCD(V)µ µL / S

µSµL

2.09

2.264

g

2.09

2.268

g⊥

0.045

0.133

µ /µL S µ (µ )L B µ (µ )S B

bcc Fe-bulk

bcc (001) Fe /V superlattice2 5

0.10

0.215

2.13

1.62

-1.4

-2.0

MAEµeV/atom

FMR


For thin films the Curie temperature can be manipulated

P. Poulopoulos and K. B.J. Phys.: Condens. Matter 11, 9495 (1999)

t=T/TC(d)

vacuum

substrate

KS2

KS1

KVε2= -3.2%

ε1= +2.5%

(apNi bulk=2.49Å)

(apCu bulk=2.55Å)


tetragonal [e.g. Ni, Co, Fe (001) / Cu (001) ]:

hexagonal [e.g. Ni (111), Gd (0001) / W (110) ]:

Ehex = k2 sin2θ + 1/2k2 cos2ϕ sin2θ + k4 sin4θ + k6⊥ sin6θ + k6 cos6ϕ sin6θ + ...

K = k2Y20 + k4mY4

m+ ... Legendre polyn. (B. Coqblin)

each Ki has a „volume“ and „surface“ contribution

Ki = Kiv + 2Ki

s/d

Free energy density of MAE, K

(intrinsic, after substraction of 2πM2)

Etetr = - K2 αz2 - 1/2 K4⊥ αz

4 -1/2 K4 (αx4 + αy

4) + ... (B.Heinrich et al.)

= - K2 cos2θ - 1/2 K4⊥ cos4θ -1/2 K4 1/4 (3+cos4ϕ) sin4θ + ... (Bab et al.)

= (K2 + K4⊥) sin2θ - 1/2 ( K4⊥ + 3/4 K4) sin4θ -1/8 K4 cos4ϕ sin4θ + ...

= K2’ sin2θ + K4⊥sin4θ + K4cos4ϕ sin4θ + ... (traditional)


O. Hjortstam, K. B. et al. PRB 55, 15026 (’97)

2b ab initio calculations

anisotropic µL ↔ MAE

ξLSMAE ∝ ∆µL4µB


The surface and interface MAE are certainlylarge (L. Néel, 1954) but count only for onelayer each. The inner part (volume) of a nano-structure will overcome this, because theycount for n-2 layers.

C. Uiberacker et al.,PRL 82, 1289 (1999)

SP-KKR calculation for rigit fcc and relaxed fct structures

R. Hammerling et al.,PRB 68, 092406 (2003)

layer resolved ∆Eb=ΣKi at T=0


(a)

(b)

(c)

(a)

(b)

(c)

0 1

-2

2

[110]

[001]

[100] ||

⊥

K 4 ||

/2 π M 2

K 2 /2 π M 2

1

-1

1 [001]

Ni(111)/rough W(110) Ni(001)/Cu(001)

||

⊥

4 π K

⊥ /2 M 2

/2 π K 2

M 2 a)

b)

M. Farle et al., PRB 55, 3708 (1997)

A. Berghaus, M. Farle, Yi Li, K. BaberschkeAbsolute determ. of the mag. anisotropy of ultrathinGd and Ni/W(110).Second Intern. Workshop on the Magnetic Properties of Low-Dimensional Systems.San Luis Potosi, Mexico, Proc. in Physics 50, 61 (1989)

Only with K4 ≠ 0a continues SRT is possible!

Do not use Keff = 2πM2 – Ki …because f(T) and f’(T) are different.Use the ratio Ki / 2πM2 ⇒ f(T) / f’(T)


Oxygen surfactant assisted growth: a new procedure to prepare ferromagnetic ultrathin films

• oxygen acts as surfactant for Fe, Co and Ni films on Cu(100)

• change of magnetic anisotropy by surfactant

• induced magnetic moment of surfactant


C. Sorg et al., Surf. Sci. 565, 197-205 (2004)M. Farle, Surf. Sci. Perspectives 575, 1-2 (2005)

Improved growth by oxygen surfactant


evaporate 5.5 ML Ni

O(√2 × 2√2)R45°/Cu(100)missing row reconstruction

47 eV

0 2 40

2

4

nm

nm[0

10]

[100]

top layer

bottom layermiddle layer

oxygen

0 2 4nm

0

1.5

3

nm

U = 0.110 VI = 1.55 nA

[010

]

[100]

oxygentop layerbottom layer

0 2.5 5nm

0

2

4

nm

U = 0.110 VI = 0.65 nA

c(2 × 2)O/Ni/Cu(100)

R. Nünthel et al., Surf. Sci. 531, 53-67 (2003)

from AES ⇒ oxygen floats on top of Ni film

[010

]

[001]


Local structure: Surface EXAFS Ni on O/Cu(100)

Rnn= (1.85±0.03) Å

h = 0.41 Å

Comparison to theory(T.S. Rahman):

Rnn= 1.87 Å

h = 0.44 Å

R. Nünthel et al., Surf. Sci. 531, 53-67 (2003)

oxygen K-edge SEXAFS

300 K hν


NEXAFS ⇒ no bulklike NiO is formed

Ni L2,3-edge O K-edge

Electronic structure from X-ray absorption spectroscopy

2pz3d

2pxy4sp


K filmV

0 0.05 0.10

10d(ML) 57

0.15 0.20-20

-15

-10

-5

0

5

10

15

20

25

Ni/Cu(001)

Ni vacuum

Ni + Cu capNi + O surfactant

t=0.75

2 Mπ 2

1/d (1/ML)

K (

µeV

/ato

m)

2

K bulkV

≈ 0

10.8

7.6

7.3

6.8

4.9

-107

-59

-81

-70

-17

Ni/vacuum

Ni/Cu

Ni/CO (van Dijken et al.)

(van Dijken et al.)

(surfactant)Ni/O

Ni/H2

Interface KS ( eV/atom)µ d C (ML)

ExperimentTheory

Jisang Hong et al., Phys. Rev. Lett. 92, 147202-1 (2004)

( ) θπ 22

2 cos2~ ⊥− KMFd

KKKK

SSV

21 ++=

23K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005Jisang Hong et al., Phys. Rev. Lett. 92, 147202-1 (2004)

E (eV)

Γ X

MAE along ΓX axisDensity of states

Results of ab initio calculations

clean Ni

O/Ni

• DOS shows that topmost Ni moment is basically unchanged

• O-induced surface state seen in the vicinity of X-point is responsible for change in MAE

• theory reveals induced moment in surfactant oxygen

DO

S (

stat

es/e

V⋅a

tom

⋅spi

n)

clean Ni film

surfactant grown Ni film


530 540 550

-2

0

2

-0.02

0.00

0.02

XA

S (

arb.

uni

ts)

Photon Energy (eV)

Experiment Theory

XM

CD

(ar

b.

units)

Induced magnetism in oxygen: Ni on O/Cu(100)

theory: Ruqian Wu (UC Irvine):

induced moments in oxygen:

µS=0.053 µBµL=0.0021 µB

oxygen K-edge XMCD → orbital moment µL

BESSY: UE56/2-PGM2

15 ML Ni on O/Cu(100)300K

2pz3d

2pxy4sp


Induced magnetism in oxygen: Co and Fe films Co on O/Cu(100)

540 5600

1

2 grazing normal

Nor

m. X

AS

(ar

b. u

nits

)

Photon Energy (eV)

Fe on O/Cu(100)

540 560 5800

1

grazing normal

norm

. XA

S (

arb.

uni

ts)

photon energy (eV)

530 540 550

-0.08

-0.04

0.00

0.04

norm

. XM

CD

(arb

. uni

ts)

photon energy (eV)

4 ML Co on O/Cu(100)300K

3 ML Fe on O/Cu(100)300K

hν

hνM

M

BESSY: UE56/2-PGM2

2pz3d

2pxy4sp

norm

. XA

S (

arb.

uni

ts)

norm

. XA

S (

arb.

uni

ts)

530 540 550

-0.08

-0.04

0.00

norm

. XM

CD

(ar

b. u

nits

)

photon energy (eV)


Conclusion

• spin reorientation transition changes dramatically with surfactant→ surface anisotropy is strongly reduced in magnitude

• Fe, Co and Ni induce magnetic moment in surfactant

• fair agreement with ab initio calculations

Lecture 2: Magnetic Anisotropy...

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