Lectue 4 Trilayers a prototype of...
Transcript of Lectue 4 Trilayers a prototype of...
![Page 1: Lectue 4 Trilayers a prototype of multilayersusers.physik.fu-berlin.de/~bab/teaching/Fudan2005/Fudan2005-4.pdf · 1250 1.57x108 110 1.38x107 125 1.57x107 220 1.57x107 200 J inter](https://reader035.fdocuments.in/reader035/viewer/2022070109/6044441b54b65554ff7f2d3d/html5/thumbnails/1.jpg)
1K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
Lectue 4 Trilayers a prototype of multilayers
Important parameters: K – anisotropy, ∆Eband for FM1 and FM2
interlayer exchange coupling IEC, Jinter
Ni8Cun
Ni9
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2K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
Landau-Lifshitz-Gilbert-Equation 1 = _∂ M
γM H (J ,K)× eff inter∂ t +γ∂ M∂ tMS
G2 (M × )
J. Lindner, K. B. Topical Rev., J. Phys. Condens. Matter 15, R193-R232 (2003)
in-situUHV-experiment
theory
FMR
4a Optical and acoustic modes in the spin wave spectrum
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3K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
in-situ UHV-FMR measures FM and AFMand determines Jinter in absolute units, e.g. µeV/atom
Ferromagnetically coupled system
H (kOe)0
0 2 4 60
10
20
30
2HexθH=90°
f (G
Hz)
(a)
2Hex
0 2 4 6 8 10 12
0
5
10
15
20
H =4 MA π
θH=0°
H (kOe)0
f (G
Hz)
(b)
Antiferromagnetically coupled system2Hex
2Hex
1 2 3 40
5
10
15
20θH=90°
H (kOe)0
f (G
Hz)
(c)f (
GH
z)
2Hex
2 4 6 80
2
4
6
4 M+2Hπ ex
θH=0°
H (kOe)0
(d)
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4K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
in-situ UHV-FMR
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5K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
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6K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
a) J. Lindner, K. B., J. Phys. Condens. Matter 15, S465 (2003)b) A. Ney et al., Phys. Rev. B 59, R3938 (1999)c) J. Lindner et al., Phys. Rev. B 63, 094413 (2001)d) P. Bruno, Phys. Rev. B 52, 441 (1995)
J (
eV
/ato
m)
inte
rµ
Theoried
-20 -60
-40
-20
20
40
60
0
2 3 4 5 6 7 8 9
-10
10
20
0
d (ML)Cu
J (
eV
/atom)
inte
rµ
FMR : / / / /FMR : / / /
a
c
XMCD : / / /b
Cu Cu Cu(001)Cu Cu(001)
Cu Cu(001)
Ni NiNi
8 9
NiCo
Co }
more in lecture 5
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7K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
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8K. Baberschke FU Berlin „Lectures on magnetism“ #4, 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 in 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)
2 4 6 8 10 12 14 16 18-0.3
-0.2
-0.1
0.0
0.1
vacu
um12 ML Ni
Cu(
100)
subs
trate
unrelaxed relaxed -2.5 % relaxed -5.5 %
∆Eb(m
eV)
layer
layer resolved ∆Eb=ΣKi at T=0
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9K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
“volume”, “surface” and “interface” MAE
t=T/TC(d)
Full trilayer grows in fct structure
K.B. JMMM, 272-276, 1130 (2004)
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10K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
Are the calculated IEC and the measured Jinter identical?
22
i=1
2E M = (2Σ π i ,i i i inter K d J− θ −2⊥ ) cos M M1 2⋅M M1 2
Experiment measures ∆ free energy and projects it on a macroscopic Heisenberg model
Theory uses microscopic magnetic moments mi with site selectic Jij
⟨ ⟩ = ∑E J ij ⟨ ⟩JJ ∑ ∑ m mi j⋅ m mi j⋅ m mi j⋅m mi j m mi j m mi ji,j i,j i,j
Jinter
M M1 2⋅M M1 2⟨ ⟨ ⟨⟨ ⟨ ⟨∼ ⇔
They are related only via the approximations Jij → ⟨ J ⟩
Conclusion: IEC ∝ Jinterbut necessarily not identical
4b Interlayer exchange coupling (IEC)
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11K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
Temperature dependence of Jinter ⇔ ∆ free energy
J =J [ ]inter inter,0 1-(T/T )C 3/2
P. Bruno, PRB 52, 411 (1995) N.S. Almeida et al. PRL 75, 733 (1995)
J =J inter inter,0 [ ]T/T0
sinh(T/T )0
T = hv / 2 k d0 F Bπ
J. Lindner et al.PRL 88, 167206 (2002)
Ni7Cu9Co2/Cu(001)
T=55K - 332K
(Fe2V5)50
T=15K - 252K, TC=305K
0 2000 4000 6000 80000
10
20
T3/2
T3/2
T5/2
J (
µeV
/ato
m)
inte
r
v =2.8 10 cm/sF
8
v =2.8 10cm/sF 7
T=294K
0 0.2 0.4 0.6 0.80
50
100
150
J (
µeV
/ato
m)
inte
r
(T/T )C3/2
(T/T )C3/2
(T/T )C5/2
v =5.3 10 cm/sF6
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12K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
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13K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
On the origin of temperature dependence of interlayer exchange coupling in metallic trilayers
S. Schwieger and W. Nolting PRB 69, 224413 (2004)
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14K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
59
125220
≈
T0 (K) vF (cm/s)1250 1.57x108
110 1.38x107
125 1.57x107
220 1.57x107
200 Jinter=45.8µeV/atom1250 Jinter=-24µeV/atom
0 2000 4000 6000 80000
5
10
15
20
25
30
35
T3/2
J (
µeV
/ato
m)
inte
r
Ni Cu Co7 5 2
Ni Cu Co7 9 2
K. Lenz et al. unpublished
Jinter (T) for different dCu
Σ
TC (≈370K)
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15K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
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16K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005
1. Trilayer is a prototype to study multilayer coupling2. UHV-FMR is a useful method to measure in situ
MAE and IEC in trilayer - step by step3. Both parameter are measured in absolute energy units (e.g. eV/atom)
for the FM and the AFM coupling4. The IEC energy is a T-dependent quantity, vanishing at TC.
Note when comparing with T=0 calculations5. The linewidth of optical and acoustical modes will be discussed
again in lecture 6
Summary