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1
MINT Seminar
How to measure Magnetic Anisotropy Constants
Takao SuzukiMINT Center
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama March 8, 2013 ([email protected])
2
Contents
1. Magnetic Anisotropy
2. Stoner-Wohlfarth Model
3. Torque Measurements
3.1 Rotational hysteresis loss
3.2 Torque analysis
3.3 45 Torque method
4. Our new torque magnetometer
5. Users Guideline
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama March 8, 2013 ([email protected])
3MINT Center, Univ.Alabama
1 kA/m= 1 emu/cm3
1 kA/m = 12.57 Oe
1. Magnetic Anisotropy
Magnetic anisotropy K = Ms x Hs = (1,400 emu/cc x 6.5kOe) = 5 x 106 erg/cc
E.A.
E.A. E.A.
H.A.
H.A. H.A.
1. Example
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4
1. Magnetic Anisotropy
2. Magnitude
K1 (Ni): 4 x 104 erg/cc (0.2 eV/atom)K1 (Fe): 5 x 105 erg/cc (2 eV/atom) Ku1 (Co): 5 x 106 erg/cc (20 eV/atom)
MINT Center, Univ.Alabama 5
200 400 600 800 1000 1200 1400
106
107
108 CoPt
Fe3Pt
Co
NdFeBFePt
SmCo5
Co3Pt
FePdMnAl
CoPtCr
K U
(erg/
cc)
MS (emu/cc)
MnBi MnAlMnBi
Hk (= 2Ku/Ms) : 4 20 T
3. Materials1. Magnetic Anisotropy
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6
1. Magnetic Anisotropy
4. Origin4.1 Magneto-crystalline anisotropy (Intrinsic)
4.2 Induced magnetic anisotropy (Extrinsic)- Pair-ordering- Shape anisotropy- Stress induced anisotropy- Surface/interface anisotropy
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama March 8, 2013 ([email protected])
7
Magneto-crystalline Anisotropy
Spin Angular Moment
Orbital Angular
MomentumLattice
Spin Angular Moment
Orbital Angular
MomentumLattice
3d elementsFe, Ni, Co
RE elementsTb, Dy, Nd
S CouplingCrystalline field
S L
MINT Center, Univ.Alabama
1. Magnetic Anisotropy
March 8, 2013 ([email protected])
8MINT Center, Univ.Alabama
1. Magnetic Anisotropy
4. Origin
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9MINT Center, Univ.Alabama Hiroaki Yamamoto and Takao Suzuki: Unexpectedly Large Magnetic Anisotropy of Fe3Pt Alloy Thin Films with Various Crystallographical Orientations IEEE Trans.Mag., 44, No.11, 2868 (2008).
1. Magnetic Anisotropy
March 8, 2013 ([email protected])
10
4. Origin4.2 Induced magnetic anisotropy (Extrinsic)
- Surface/interface anisotropy
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama
1. Magnetic Anisotropy
March 8, 2013 ([email protected])
11MINT Center, Univ.Alabama
1. Magnetic Anisotropy
5. Phenomenological expression
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-6 -4 -2 0 2 4 6
-5
0
5
-6 -4 -2 0 2 4 6
-5
0
5
E=K1(122232)+K2(1222+ 2232 + 3212)+.
Magnetic anisotropy constants of Fe3Pt/MgO
K1= 4106 erg/cc
K2= 2107 erg/cc
Magnetic anisotropy energy in Cubic
is the easy axis, since those K1 and K2 fulfill the condition
K2 > 9/4K1
K2=9K1
K2=9/4K1
K1
K2
H(kOe)
M (1
0-3 e
mu)
Substrate : MgO(100)Deposition temperature : 400 Thickness : 500
0 15 30 45 60 75 901.2
1.4
1.6
1.8
angle,
Hc
(kO
e)Magnetic Anisotropy
MINT Center, Univ.Alabama 12Hiroaki Yamamoto and Takao Suzuki: Unexpectedly Large Magnetic Anisotropy of Fe3Pt Alloy Thin Films with Various Crystallographical Orientations IEEE Trans.Mag., 44, No.11, 2868 (2008).
March 8, 2013 ([email protected])
13
Ku1 and Ku2 vs T for h.c.p. Co
M.Takahashi and T.Suzuki; Jap. J.Apply.Phys.18, No6, 1071-1078 (1979).
MINT Center, Univ.Alabama March 8, 2013 ([email protected])
14
2. Stoner Wolfarth Model
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama
Note: In reality, unless H > Hk
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15
2. Stoner-Wohlfarth Model
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation Technology
h//2/3 + h 2/3 = 1
MINT Center, Univ.Alabama
Two angles ( = ,) for stable M direction when h (= H/Hk) < 1.
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16
3. Torque Magnetometer
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama
L = M x H
0 90 180 270 360
-5
0
515kOe
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17
Torque Analysis -1-Rotational hysteresis-
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama
Calculation Experimental0.489
0.415
0.369
0.738
0.553
0.0.521
5.45
1.20
0.922
0.5+
0.5-
0.3
0.8
0.7
0.6
>>
1.0
0.9
March 8, 2013 ([email protected])
Floyd.B. Humphrey: JPL Research summary No.36-13 (1962)
Torque Analysis -1-Rotational hysteresis-
William D. Doyle Torque and Rotational Hysteresis in fcc Single Crystal Cobalt Films J. Appl. Phys. 35, 929 (1964).
MINT Center, Univ.Alabama 18
Bi-axial anisotropy of fcc Co film
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MINT Center, Univ.Alabama 19March 8, 2013 ([email protected])
20
Torque Analysis -245 Torque Method
E = KV sin2 MVH cos ( )L = MVH sin ( )
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation Technology
M
H
E.A.
H.A.(L/H)2 = - (M2V/2K)L + (MV)2
(L/H)2
L
(M2V/2K)
(MV)2
K and Ms can be estimated directly !
For = 45,
H.Miyajima, K.Sato and T. Mizoguchi: Simple analysis of torque measurement of magnetic thin films J.Appl.Phys. 47, No10, 4669-4671 (1976).
MINT Center, Univ.Alabama
K
March 8, 2013 ([email protected])
0 90 180 270 360-20
-10
0
10
20 15kOe
0 90 180 270 360
-5
0
515kOe
() ()
Fe3Pt (001)/MgO(100) Fe3Pt (111)/MgO(111)
Easy Axis Easy Axis
Lin=(1/18)K2sin6Torque, Lin=(1/2)K1sin4
Torque curves of different crystallographycal orientationTo
rque
, L(d
yne-
cm)
Lin=L1sin+L2sin2+L4sin4+..+L6sin6+...
TS:4000C
sample
Mirror DL
N S
Torque Analysis -3Fourier Analysis Method
L() (H) Lin()Hiroaki Yamamoto and Takao Suzuki: Unexpectedly Large Magnetic Anisotropy of Fe3Pt Alloy Thin Films with Various Crystallographical Orientations IEEE Trans.Mag., 44, No.11, 2868 (2008).MINT Center, Univ.Alabama 21March 8, 2013 ([email protected])
22THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation Technology
Torque Analysis - 3Fourier Analysis Method
Experimental torque curves;
L(,Ho) = L1sin + L2sin2 + L3sin 3 +L4sin 4 + . ,Where L1, L2, L3, L4 .. can be obtained from the Fourier Decomposition of the torque curves as a function of Ho.
Two-fold component K1 or Ku1
Four-fold component K2 or Ku2
L2L4
1/Ho
Torq
ue A
mpl
itude Ku1
Ku2
MINT Center, Univ.Alabama March 8, 2013 ([email protected])
MINT Center, Univ.Alabama 23
90 kOe (9T)10-7 emu2 ~400 KTorque mag
4. Our new Torque magnetometer
March 8, 2013 ([email protected])
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama 24March 8, 2013 ([email protected])
MINT Center, Univ.Alabama 25March 8, 2013 ([email protected])
26
Magnetic Anisotropy - 1
1. Header (36)1.1 sub header (32)
Text font (24)
1.1.1 sub sub header (28)
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama March 8, 2013 ([email protected])
27
Magnetic Anisotropy - 1
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama March 8, 2013 ([email protected])
28THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation Technology
300 K 2 K
MINT Center, Univ.Alabama 28March 8, 2013 ([email protected])
29
Users Guideline
Users must have- Understanding of basic principle of
operation- Training for how to operate- Report each time in logbook- Report any problems to Mr. John
Hawkins and Mr. Jason Foster, as well as your adviser
THE UNIVERSITY OF ALABAMA MINT
Center for Materials for INformation TechnologyMINT Center, Univ.Alabama March 8, 2013 ([email protected])
MINT Center, Univ.Alabama 30March 8, 2013 ([email protected])
Slide Number 1Slide Number 21. Magnetic Anisotropy Slide Number 4Slide Number 5Slide Number 6Magneto-crystalline Anisotropy1. Magnetic Anisotropy1. Magnetic AnisotropySlide Number 10Slide Number 11Slide Number 12Ku1 and Ku2 vs T for h.c.p. CoSlide Number 14Slide Number 15Slide Number 16Slide Number 17Torque Analysis -1-Rotational hysteresis-Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30