Calculations of i nterplay between anizotropy and coupling energy in magnetic multilayers systems

M.CzapkiewiczDepartment 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

ZEtK

)(cos

22

22

22

ZEtK

0id

dE

02

iidEd

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 = 31GMR 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

JJj

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 layerKAF = 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 ÅNiFe – 20 ÅCu – 50 Å

MnIr – 100Å

CoFe – 25 ÅAl2O3 – 15 ÅCoFe – 25 ÅNiFe – 100 ÅTa – 50Å

Energy density model:

)(coscos 332

333033

tKHMt

E

)(cos2 AFAFAFAFtK )cos( 2 AFEBJ

)(coscos 222

222022 tKHMt)(coscos 11

2111011 tKHMt

)cos( 1212 J