M - Freie Universität Berlin

Transcription

Ferromagnetic resonance in nanostructures,
rediscovering its roots in paramagnetic resonance
Klaus Baberschke
Institut für Experimentalphysik
Freie Universität Berlin
Arnimallee 14 D-14195 Berlin-Dahlem Germany
1.
Historical reminiscences
2.
Orbital- and spin-magnetic moments
in ferromagnetic monolayers
3.
Spin-phonon, spin-spin dynamics
4.
Summary and future
 http://www.physik.fu-berlin.de/~bab
Alt100, Kazan
21–25 June 2011
1/21
1. Historical reminiscences
EPR was discovered in 1944. 2004 we celebrated this, here in Kazan.
The resonant microwave absorption in ferromagnetic metals (FMR)
was discovered shortly after (Griffith 1946, Zavoiskii 1947)
Usually the Landau-Lifshitz-Gilbert equation (1935)
is used to analyze and interprete the experimental results
dm
  mHeff  m dm
dt
dt
g 
with  
B

Gilbert damping
|M|=const.
M spirals on a
sphere
into the z-axis
It was difficult to measure g because
of various contributions to the internal anisotropy field Heff.
For itinerant ferromagnets (Fe, Co, Ni) often the g-factor was assumed
to be g~2 and |M|= const (see Section 3) .
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Kazan, Juli 1959
Shortly after it was translated
into German
Kazan, Januar 1962
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Orbital magnetism in second order perturbation theory
H '= µBH•L + L•S
d1
LZ • SZ
+L • S
L± • S _+
 2   ( 2 ) 1 / 2 { 2   2 }  2 
The orbital moment is quenched in cubic
symmetry
2- LZ 2- = 0,
but not for tetragonal symmetry
Are generated by the same
matrix element
Alt100, Kazan
21–25 June 2011
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Magnetic Anisotropy Energy (MAE) and anisotropic µL
1. Magnetic anisotropy energy = f(T)
2. Anisotropic magnetic moment  f(T)
M (G)
500
[111]
300
100
0
0
g|| - g= ge(-||)
anisotropic µL  MAE
D= g g
e
[111]
[100]
L ~~ 0.1 G
LS
MAE  4µ µL
B
[100]
Ni
100
200
B (G)
Bruno (‘89)
300
MAE = ∫ M·dB ≈ ½ ∆M·∆B ≈ ½ 200 · 200 G2
MAE ≈ 2·104 erg / cm3 ≈ 0.2 µeV / atom
 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
K. Baberschke, Lecture Notes in Physics, Springer 580, 27 (2001)
Alt100, Kazan
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2. Orbital- and spin- magnetic moments μL ,μS
in ferromagnetic monolayers
Determination of MAE Ki and g-tensor
2

 , [001]
 H0,  4M 
2K 2  K 4  
M
g  B
with  

l g  2

s
2
C. Kittel, J.Phys. Radiat. 12, 291 (1951 )
f 2(GHz2 ) or f (Ghz)
K 4 || 

K 2 4K 4 || 
K 2 2K 4 || 
2




4M  2
2

 H 0,[100 ]  H 0,[100 ]  4M  2



2
M
M 
M 
M
M 
 ||, [100 ]

0
0
g,[001 ]
g||,[100] / [110]
H0 (kOe)
In FMR a large range of frequencies is needed 1 to >200 GHz
Alt100, Kazan
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In situ UHV-FMR set up 1, 4, 9 GHz
lHe cryostat
thermocouple
-11
pressure: 10 mbar
temperature: 20K - 500K
cavity
sample
UHV
quartzfinger
electromagnet
7.2 ML Ni/Cu(001)
T=297 K
M. Zomak et al.,
Surf. Sci. 178, 618 (1986)
J. Lindner, K.B.
J. Phys.: Cond. Matt 15, R193 (2003)
W. Platow,
Ph.D. thesis
(1999)
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Alt100, Kazan
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Ferromagnetic resonance on Fen/Vm(001) superlattices
[100]Fe/V
[110] MgO
MgO
T/TC
0.2
0.4
0.6
0.8
K2
K4
K 4II 


3
1.0
2
1.2
0 .4
0 .3
0 .2
1
0 .1
0
0 .0
-1
-0.1
-2
-0.2
1
prop. S
prop.  L
L3
L2
0.12
V
Fe
g<2
g>2
S L
S L
0.06
bulk Fe
x5
510 520 530
0
700 720 740
MAE (eV/ atom)
-0.5
bcc (001) Fe2/V5 superlattice
MAE= E[001]-E [110]
g
-1.0
Fe 2 V5
-1.5
-2.0
-2.5
0
50
100
L / S(V) XMCD
40 nm Fe Fe4 / V2 Fe4 / V4 Fe2 / V5
Photon Energy (eV)
b)
0.0
XMC D:  L / S (Fe)
FMR:  L / S (Fe+V)
0
-1
K4 II (eV/atom)
K 2,K 4 (eV/atom)
0 .0
4 a)
2
L / S
Fe
XMCD Integral (arb. units)
a=2. 83Å (-1 .3%)
FMR
X-rayMCD
a=3.05Å (+0.8%)
150
200
T (K)
A.N. Anisimov et al.
J. Phys. C 9, 10581 (1997)
and PRL 82, 2390 (1999)
and Europhys. Lett. 49, 658 (2000)
2.264
g
µ L/µS
2.268 0.133
MAE
µL (µB ) µS (µB ) µeV/atom
0.215
1.62
-2.0
2.13
-1.4
bcc Fe-bulk
2.09
2.09
0.045
0.10
Alt100, Kazan
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Enhancement of Orbital Magnetism at Surfaces: Co on Cu(100)
 ML 
Ae  D ( d 1) /   B nd 3e  D ( n  2 ) /   C

 
d 1  nD / 
M

n 0 e
 S  exp
M. Tischer et al., Phys. Rev. Lett. 75, 1602 (1995)
Alt100, Kazan
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3. spin-phonon, spin-spin dynamics
Alt100, Kazan
21–25 June 2011
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90% of today’s FMR experiments use
Landau-Lifshitz-Gilbert equation(1935)
dm
dm
  m  H eff   m 
dt
dt
Gilbert damping
|M|=const.
M spirals on a sphere into z-axis
Bloch-Bloembergen Equation (1956)
mz  M S
dm z
  ( m  H eff ) z 
dt
T1
dm x , y
dt
  ( m  H eff ) x , y 
mx , y
T2
spin-lattice
relaxation
(longitudinal)
spin-spin relaxation
(transverse)
Mz=const.
Alt100, Kazan
21–25 June 2011
12/21
Gilbert damping versus magnon-magnon scattering.
Mostly an effective damping
(path 1) is modeled/fitted.
In nanoscale
magnetism path 2
has been discussed
very very little.
Path 3:
magnon-phonon scattering,
see Bovensiepen PRL 2008
Alt100, Kazan
21–25 June 2011
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All these processes…do not preserve
the magnitude of the uniform mode…
Longitudinal T1 and
transvers T2 - scattering
…the GLL damping term no
longer applies…
Alt100, Kazan
21–25 June 2011
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FMR Linewidth - Damping
Landau-Lifshitz-Gilbert-Equation
2-magnon-scattering
R. Arias, and D.L. Mills, Phys. Rev. B 60, 7395 (1999);
D.L. Mills and S.M . Rezende in
‘Spin Dynamics in Confined Magnetic Structures ‘,
edt. by B. Hillebrands and K. Ounadjela, Springer Verlag
1  M = _ (M H ) + G (M  M )
eff
 t
MS2
t
 (k|| )
viscous damping,
energy dissipation
k|| > c
k|| < c
FMR
Gilbert-damping ~
G 
H () = 2
 MS
Gil
in conventional FMR
k||
H

() = arcsin
2 Ma g
2+(0/2)2]1/2- 0/2
2
2 1/2
 +(0 /2) ] +  0 /2
0 = (2K2  - 4MS ), =(B /h)g
K2- uniaxial anisotropy constant
MS - saturation magnetization
Which (FMR)-publication has checked (disproved) quantitatively this analytical function?
Alt100, Kazan
21–25 June 2011
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80
200
400
HGilbert
100
0
4
8
200
H*0
H2-magnon
Hinhom
0
0
HPP (Oe)
H (Oe)
H
15 Oe !
40
0
inhomogeneous broadening
20
40
/2 (GHz)
60
80
0
0
50
100
150
200
f (GHz)
J. Lindner et al. PRB 68, 060102(R) (2003)
two-magnon scattering
dominates Gilbert damping
by two orders of magnitude:
T2~ 0.2 n s vs. T1~ 40 n s
  anisotropic spin wave scattering
G  isotropic dissipation
no anisotropic conductivity is need
K. Lenz et al. PRB 73, 144424 (2006)

(kOe)
Fe4V2 ; H||[100]
Fe4V4 ; H||[100]
Fe4V2 ; H||[110]
Fe4V4 ; H||[110]
Fe4V4 ; H||[001]
0.270
0.139
0.150
0.045
0

G
8 -1
8 -1
50.0
26.1
27.9
8.4
0
0.26
0.45
0.22
0.77
0.76
(10 s ) (10 s )
Alt100, Kazan

-3
 H0
(10 )
(Oe)
1.26
2.59
1.06
4.44
4.38
0
0
0
0
5.8
21–25 June 2011
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

Angular- and frequency-dependent
FMR on
Fe3Si binary Heusler structures
epitaxially grown on MgO(001)
d = 40nm
Kh. Zakeri et al.
PRB 76,104416 (2007)
PRB 80, 059901 (2009)
A phenomenological effective
Gilbert damping parameter
gives very little insight into the
microscopic relaxation and scattering .

Angular dependence at 9 and 24 GHz
  (26 –53) • 107 sec-1, anisotropic
G  5 • 107 sec-1, isotropic
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Alt100, Kazan
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4. Summary and future
2 magnon scattering in permalloy = f(ω, l) ,
I. Barsukov, Farle-group, unpublished 2011
FMR using Synchrotron radiation in THz
Alt100, Kazan
21–25 June 2011
20/21
•Todays analysis of spin-wave dynamics should not assume
|M| = const, i. e. T=0 assumption.
•g – tensor and spin wave excitations are ignored in most cases
•Long wavelength spin-waves relax slowly with G ~ nano sec
2-magnon scattering with Γ~ 10-100 pico sec.
r
e
l
u
h
•All spin wave excitations need a second scattering –dephasingconstant. Important for femto sec. relaxation.
s
t
’
l
A
.
u
o
y S. A
k
n
.
a
f
Don’t follow
the
standard
literature
and reasoning.
h
o
r powerful in unexplored areas.
FMRT
can be muchpmore
d
n
a
Alt100, Kazan
21–25 June 2011
21/21
Ferromagnetic resonance in nanostructures,
rediscovering its roots in paramagnetic resonance
Klaus Baberschke
Institut für Experimentalphysik
Arnimallee 14 D-14195 Berlin-Dahlem
e-mail: bab@physik.fu-berlin.de
http://www.physik.fu-berlin.de/~bab
In 1944 Zavoiskii discovered the electron paramagnetic resonance (EPR), here in Kazan. Shortly after the resonant microwave
absorption in ferromagnetic Fe, Co, Ni metals (FMR) was discovered (Griffiths 1946, Zavoiskii and Kittel 1947). Surprisingly both
techniques went different routes: The EPR explored an enormous variety of para-magnets in solids, liquids, and gas phase. Already
one decade later Altshuler and Kosyrew published a comprehensive book – the first “EPR-bible” [1]). The focus was to determine
orbital- and spin-magnetic moments (g-tensor), hyperfine interactions, and from the linewidth the spin dynamics (T1, T2 relaxation).
In FMR most of the experi-ments and theory assumed the total value M to be constant in the equation of motion and used only one
effective damping parameter (Gilbert). This is an enormous, unneces-sary limitation for today’s analysis of magnetism in
nanostructures and ultrathin films. To assume M= const (p.196 in [2]) ignores spin wave excitations, scattering between
longitudinal and transverse components of M. Moreover, in the framework of itinerant ferromagnetism, the magnetic moment/atom μ
was assumed to be isotropic with g = 2! That ignores the anisotropy of μ in nanostructures and the importance of the orbital magnetic
moments with μL/μS = (g-2)/2. Without finite μL we would have no magnetic anisotropy energy (MAE), no hard magnets. Only
recently the “language” of EPR was adapted to FMR in ultrathin films [3]. A g-tensor is discussed and its interrelation with the MAE
is pointed out. Also recent theory points out, that “…there is no reason to assume a fixed magnetization length for
nanoelements…”[4]. This allows a detailed dis-cussion of magnon-magnon scattering, spin-spin, and spin-lattice relaxation – useful,
for example, for fs spin dynamics.
We will discuss recent FMR experiments using frequencies from 1 GHz up to several hundred GHz, which allow measuring the
proper g-factor components and μL, μS. From the frequency dependent linewidth magnon-magnon scattering can be separated from
dissipative spin-lattice damping.
[1] Paramagnetische Elektronenresonanz S.A. Altshuler, B.M. Kosyrew Teubner Verlag Leipzig 1963 (Moskau 1961)
[2]Ultrathin MagneticStructures II B. Heinrich, J:A:C: Bland (Eds.) Springer Verlag Berlin Heidelberg 1994
[3] K. Baberschke in Handbook of Magnetism and Advanced Magnetic Materials, Vol.3 H. Kronmüller and S.S. Parkin (Eds.) John
Wiley, New York 2007, p. 1617 ff
[4] O. Chubykalo-Fesenko et al. Phys. Rev. B 74, 094436 (2006)
Alt100, Kazan
21–25 June 2011
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M - Freie Universität Berlin

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