lecture 2: magnetic anisotropy...
TRANSCRIPT
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 ~~
2K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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)
4K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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)
5K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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
6K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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
10K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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
11K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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)
12K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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)
14K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
O. Hjortstam, K. B. et al. PRB 55, 15026 (’97)
2b ab initio calculations
anisotropic µL ↔ MAE
ξLSMAE ∝ ∆µL4µB
15K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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
16K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
(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)
17K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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
18K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
C. Sorg et al., Surf. Sci. 565, 197-205 (2004)M. Farle, Surf. Sci. Perspectives 575, 1-2 (2005)
Improved growth by oxygen surfactant
19K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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]
20K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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
21K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
NEXAFS ⇒ no bulklike NiO is formed
Ni L2,3-edge O K-edge
Electronic structure from X-ray absorption spectroscopy
2pz3d
2pxy4sp
22K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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
24K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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
25K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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)
26K. Baberschke FU Berlin „Lectures on magnetism“ #2, Fudan Univ. Shanghai, Oct. 2005
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