M.Czapkiewicz

Department of Electronics, AGH University of Science and Technology, POLAND

Calculations of interplay between anizotropy and

coupling energy in magnetic multilayers systems

• Schedule • one-domain S-W model• MAGEN2 - program for simulation of magnetization process of multilayers systems• examples of calculations and experiments

– PSV– SV– Biased FP– TMR SV – SV AAF

• To-do tasks

Definitions

• Magnetization:

monolayer

bilayer

• AMR (ML)

• GMR (BL)

Task to compute: how depend on H ?

cos)( SMHM

)/()coscos()( 21222111 ttMtMtHM SS

2cos RRRRx

21cos12

RRRR

Stoner-Wohlfarth model• Surface energy density (example for 2 layers with

planar UA anisotropy):

where• Numerical gradient seeking of local minimum for

each H field

,..., 21 E )cos( 1212 J

)(

cos

11

12

11

ZE

tK

)(

cos

22

22

22

ZE

tK

0id

dE

0

2

iid

Ed

0

22

2

2

2

2

ijji

EEE

)sincos()( 0 iYiXSiiiZi HHMtE

Program interface• Input:

– Saturation magnetization– Effective anisotropy

energy– Anisotropy axis definition– Interlayer coupling energy– Field range

• Output: angles for each layer– Total magnetization M(H)– Total energy– To do: GMR, TMR…

1. example – PSV-type bilayer

Measured example:Py2.8nm/Co2.1nm/Cu2nm/Co3nm

Fit for: Ku1/Ku2 = 31

GMR only in non-parallel state

Influence of ferromagnetic coupling on PSV switching

AF-state only if JFF weak

2. example – SV with AF layer

Measured sample: Co4.4nm/Cu2.3nm/Co4.4nm/FeMn10nm

exchange coupling energy JFP-FF= 7.9 10-6 J/m2

interface coupling energy JEB = 94 10-6 J/m2

anisotropy energy KFF = 580 J/m3,

effective AF anizotropy KAF = 80·103  J/m3

Influence of FP-FF ferromagnetic coupling on GMR of SV structure• Analytical simulation for

FFAF

FFFP

J

Jj

3. Influence of effective anisotropy of AF layer on SV biased field

Energy density model of AF-FP system:

2

20

cos

coscos

)cos(

AFAFAF

FPFPFPFPFPFP

FPAFEB

tK

tKHMt

JE

M.Tsunoda model: ordering of AF layer grains (during deposition for top-type SV or during field cooling for bottom-type SV) lead to increase total eff. anisotropy

Example of AF-FP system (after f.c.)

Courtesy of Prof. C.G. Kim Chungnam University RECAMM, Taejon, Korea

MnIr – 100Å

CoFe – 25 Å

Si/Ta5nm/Cu10nm/Ta5nm/NiFe2nm/Cu5nm/MnIr10nm/CoFe2,5nm

annealed: 200oC/1h, field cooling 1kOe

fit for: JEB= 200 10-6 J/m2 , KAF = 40000 J/m3.

4. Influence of KAF to JEB ratio of FF/S/FF/AF structure on M(H) switching

symulacja - ma³e KAF - PSV

H [kA/m]

-2e+2 -1e+2 0 1e+2 2e+2

Y D

ata

-1

0

1

J1= 1.1E-0005 Eeb= 5.2E-0004 K1=2.1E+0002 K2= 5.2E+0003 Kaf= 2.6E+0004

H [kA/m]

-2e+2 -1e+2 0 1e+2 2e+2

Y D

ata

-540

-360

-180

0

180

360

540

symulacja - du¿e KAF - SV

H [kA/m]

-2e+2 -1e+2 0 1e+2 2e+2

Y D

ata

-1

0

1

J1= 1.1E-0005 Eeb= 5.2E-0004 K1=2.1E+0002 K2= 5.2E+0003 Kaf= 10.4E+0004

H [kA/m]

-2e+2 -1e+2 0 1e+2 2e+2

Y D

ata

-540

-360

-180

0

180

360

540

Dependence of HEB on KAF

4. MTJ example

Fit for: anizotropy energy of FF layer K1 = 210 J/m3,

0 Ms1 = 0.85 T,

exchange coupling energy FF-FP

J12= 1.04 10-6 J/m2 (FF).

effective anizotropy energy of FP layer

K2 = 95000 J/m3,

0 Ms2 = 1.5 T,

interface coupling energy FP-AF

JEB= 470 10-6 J/m2.

effective anizotropy energy of AF layer

KAF = 50000 J/m3

wide range of field

H [kA/m]-400 -200 0 200 400

M/M

s-1.0

-0.5

0.0

0.5

1.0

Buffer:Si/Ta5nm/Cu10nm/Ta5nm/Ni80Fe202nm/Cu5nm

AF layer: Ir25Mn75 (10nm), FP layer Co70Fe30 (2.5nm),

isolator spacer and FF layer AlOx(1.5nm)/Co70Fe30(2.5nm)/Ni80Fe20 (10nm)

5. SV with Artificial AF – before annealing

FFFFFFFFFFFF

FPFPFPFPFPFP

FPFPFPFPFPFP

AFAFAFFPFPFPAFEB

tKHMt

tKHMt

tKHMt

tKJJE

20

22

212022

12

111011

221231

coscos

coscos

coscos

cos)cos()cos(

AFF-SV: AF/FP1/S1/FP2/S2/FF

Example:

Si(111)/Ta10.5nm/PtMn19.8nm/

CoFe2nm/Ru0.77nm/CoFe2nm/

Cu2.2nm/CoFe0.8nm/NiFe3.8nm/

Ta5nm/Cu0.5nm

• “To do” list for MAGEN2 program • bugs fixing experimental data in background more layers• 3D axis of anisotropy and field definition animation of magnetisation vector of each

ferromagnetic layer during simulation process• GMR/TMR characteristics

END

S-W model for monolayer

• Total energy E = EH + EU + ED

• Zeeman energy

• Anisotropy energy

• Demagnetizing energy

2'nn UU KE

MH 021 DDE

HM 0HE

MNH 0D

Field in plane (Nx=Ny0, Nz1):

)(cos)cos( 20 Us KHME

4. Example of Magnetic Tunneling Junction

Substrate Si (100)

Ta – 50 Å

Cu – 100 Å

Ta – 50 Å

NiFe – 20 Å

Cu – 50 Å

MnIr – 100Å

CoFe – 25 ÅAl2O3 – 15 ÅCoFe – 25 Å

NiFe – 100 Å

Ta – 50Å

Energy density model:

)(coscos 332

333033

tKHMt

E

)(cos2 AFAFAFAFtK )cos( 2 AFEBJ

)(coscos 222

222022 tKHMt

)(coscos 112

111011 tKHMt)cos( 1212 J