How to measure Magnetic Anisotropy Constants · 1 MINT Seminar How to measure Magnetic Anisotropy...

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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])

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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



3MINT Center, Univ.Alabama

1 kA/m= 1 emu/cm3

1 kA/m = 12.57 Oe


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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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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4. Origin4.1 Magneto-crystalline anisotropy (Intrinsic)

4.2 Induced magnetic anisotropy (Extrinsic)- Pair-ordering- Shape anisotropy- Stress induced anisotropy- Surface/interface anisotropy



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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





4. Origin


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).



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4. Origin4.2 Induced magnetic anisotropy (Extrinsic)

- Surface/interface anisotropy


Center for Materials for INformation TechnologyMINT Center, Univ.Alabama





5. Phenomenological expression


-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).


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Ku1 and Ku2 vs T for h.c.p. Co

M.Takahashi and T.Suzuki; Jap. J.Apply.Phys.18, No6, 1071-1078 (1979).

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2. Stoner Wolfarth Model



Note: In reality, unless H > Hk


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2. Stoner-Wohlfarth Model


Center for Materials for INformation Technology

h//2/3 + h 2/3 = 1


Two angles ( = ,) for stable M direction when h (= H/Hk) < 1.


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3. Torque Magnetometer



L = M x H

0 90 180 270 360

-5

0

515kOe


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Torque Analysis -1-Rotational hysteresis-



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


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).


Bi-axial anisotropy of fcc Co film


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Torque Analysis -245 Torque Method

E = KV sin2 MVH cos ( )L = MVH sin ( )



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).


K


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


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])


90 kOe (9T)10-7 emu2 ~400 KTorque mag

4. Our new Torque magnetometer



Center for Materials for INformation TechnologyMINT Center, Univ.Alabama 24March 8, 2013 ([email protected])

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Magnetic Anisotropy - 1

1. Header (36)1.1 sub header (32)

Text font (24)

1.1.1 sub sub header (28)



27

Magnetic Anisotropy - 1



28THE UNIVERSITY OF ALABAMA MINT


300 K 2 K


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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




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

How to measure Magnetic Anisotropy Constants · 1 MINT Seminar How to measure Magnetic Anisotropy...

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