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

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

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

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)

4K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005

in-situ UHV-FMR

5K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005

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

7K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005

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

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)

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)

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

12K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005

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)

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)

15K. Baberschke FU Berlin „Lectures on magnetism“ #4, Fudan Univ. Shanghai, Oct. 2005

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