Transcript Prezentacja programu PowerPoint

Calculations of interplay
between anizotropy and
coupling energy in magnetic
multilayers systems
M.Czapkiewicz
Department of Electronics, AGH University of
Science and Technology, POLAND
• 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:
M ( H )  MS cos
monolayer
M ( H )  (t1MS1 cos 1  t 2 MS 2 cos 2) /(t1  t 2)
bilayer
Rx  R  R  R cos2 
• AMR (ML)
R  R
• GMR (BL)
1  cos   
RR 

2
1
2
Task to compute: how  depend on H ?
Stoner-Wohlfarth model
• Surface energy density (example for 2 layers with
planar UA anisotropy):
E1 , 2 ,...   J12 cos( 2 1 )
 K1t1 cos2 1  K 2t2 cos2  2
 EZ 1 (1 )
 EZ 2 ( 2 )
where EZi (i )  ti 0 M Si (H X cosi  HY sini )
• Numerical gradient seeking of local minimum for
each H field
2
2
2
2
2
dE
d E
 E  E   E 
0
0

0
2
2


d i
 i  j   j i 
d ii
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
M1
M2
1.5
1.0
M [T]
0.5
M1
M2
0.0
M1
M2
-0.5
-1.0
M1
M2
-1.5
-15
-10
-5
0
Field [kA/m]
5
10
15
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
simulation sv4206
2.0
1.5
J=0
J>>0
1.0
Ms
0.5
0.0
-0.5
-1.0
AF-state only if JFF weak
-1.5
-2.0
-20
-10
0
H [kA/m]
10
20
2. example – SV with AF layer
1.5
M1
M2
1.0
M [T]
0.5
0.0
M1
M2
-0.5
Measured sample:
Co4.4nm/Cu2.3nm/Co4.4nm/FeMn10nm
-1.0
M1
M2
-1.5
exchange coupling energy JFP-FF= 7.9 10-6 J/m2
-30
-20
-10
Field [kA/m]
0
10
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
J FP FF
J AF  FF
• Analytical simulation for j 
j = -0.1
R+R
j = 0.25
j = 0.2
j = 0.1
Rezystancja [a.u.]
3
j=0.25 j=0.2
k¹ t 1i2
j=0.4
j = 0.4
2
1

R
2
0
-1.00
-0.75
h1
-0.50
Pole h [a.u.]
-0.25
0.00
h2
-1.00
-0.75
-0.50
Pole h
-0.25
0.00
3. Influence of effective anisotropy of AF
layer on SV biased field
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
Energy density model of AF-FP system:
E   J EB cos( AF   FP )
 t FP M FP  0 H cos FP  K FPt FP cos2  FP
 K AF t AF cos2  AF
Example of AF-FP system (after f.c.)
Si/Ta5nm/Cu10nm/Ta5nm/NiFe2nm/Cu5nm/MnIr10nm/CoFe2,5nm
annealed: 200oC/1h, field cooling 1kOe
CoFe – 25 Å
1.0
MnIr – 100Å
fit for:
10-6
J/m2
JEB= 200
,
KAF = 40000 J/m3.
Courtesy of Prof. C.G. Kim
Chungnam University RECAMM,
Taejon, Korea
M/MS
0.5
0.0
-0.5
-1.0
-200
-100
0
H [kA/m]
100
200
4. Influence of KAF to JEB ratio of
FF/S/FF/AF structure on M(H) switching
symulacja - du¿e KAF - SV
symulacja - ma³e KAF - PSV
1
Y Data
Y Data
1
0
-1
0
-1
-2e+2
-1e+2
0
1e+2
2e+2
-2e+2
-1e+2
H [kA/m]
J1= 1.1E-0005 Eeb= 5.2E-0004 K1=2.1E+0002 K2= 5.2E+0003 Kaf= 10.4E+0004
1e+2
2e+2
J1= 1.1E-0005 Eeb= 5.2E-0004 K1=2.1E+0002 K2= 5.2E+0003 Kaf= 2.6E+0004
540
540
360
360
180
180
Y Data
Y Data
0
H [kA/m]
0
0
-180
-180
-360
-360
-540
-540
-2e+2
-1e+2
0
H [kA/m]
1e+2
2e+2
-2e+2
-1e+2
0
H [kA/m]
1e+2
2e+2
Dependence of HEB on KAF
140
120
160
Kaf vs Hex2
Kaf vs Hc2
140
120
100
80
80
60
60
40
40
20
0
1e+3
20
1e+4
1e+5
KAF [J/m2]
0
1e+6
HC2 [kA/m]
HEX2 [kA/m]
100
4. MTJ example
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)
Fit for:
wide range of field
1.0
0.5
M/Ms
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
0.0
-0.5
-1.0
-400
-200
0
H [kA/m]
200
400
5. SV with Artificial AF – before annealing
E   J EB cos( AF   FP1 )  J 23 cos( FP1   FP 2 )  K AF t AF cos2  AF
 t FP1M FP1 0 H cos FP1  K FP1t FP1 cos2  FP1
 t FP 2 M FP 2  0 H cos FP 2  K FP1t FP 2 cos2  FP 2
 t FF M FF  0 H cos FF  K FF t FF cos2  FF
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
•
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
•
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•
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
EH  0M H
• Zeeman energy
• Anisotropy energy EU  KU n n'2
1
E


• Demagnetizing energy D 2 H D   0 M
Field in plane
(Nx=Ny0, Nz1):
E  0 M s H cos( )  KU  cos2 (  )
H D  N0M
4. Example of Magnetic Tunneling Junction
Energy density model:
Ta – 50Å
NiFe – 100 Å
CoFe – 25 Å
Al2O3 – 15 Å
CoFe – 25 Å
MnIr – 100Å
Cu – 50 Å
NiFe – 20 Å
Ta – 50 Å
Cu – 100 Å
Ta – 50 Å
Substrate Si (100)
E
 J12 cos( 2 1 )
 t1M10 H cos1  K1t1 cos2 (1 1 )
 t2 M 2 0 H cos 2  K2t2 cos2 ( 2 2 )
 J EB cos( AF  2 )  K AFt AF cos2 ( AF   AF )
 t3 M 3  0 H cos 3  K 3t3 cos2 ( 3   3 )