theory of diluted ferromagnetic iii-v compound semiconductor materials of spintronics
DESCRIPTION
Theory of Diluted Ferromagnetic III-V compound semiconductor materials of Spintronics. Spintronics = Spin + Electronics The most interesting material is Diluted Ferromagnetic semiconductor III-V based with Mn impurity i.e. (In,Mn)As, (Ga,Mn)As. III-V DMSs : - PowerPoint PPT PresentationTRANSCRIPT
Theory of Diluted FerromagTheory of Diluted Ferromagnetic III-V compound semicnetic III-V compound semiconductor materials of Spintonductor materials of Spintronicsronics
• Spintronics = Spin + Electronics• The most interesting material is Diluted Ferromagnetic semiconductor III-V based with Mn impurity i.e. (In,Mn)As, (Ga,Mn)As
• III-V DMSs : S = 5/2 (Mn 2+) hole concs. ~ 10% impurities concs. (compensated doping) hole spins couple with Mn AF (p-d coupling)
Compensated doping
Carrier mediated ferromagetismDilute electrons
Local moments
RKKY indirect interaction
Kondo Lattice model
iii
jiji SJcctH
,,,,
With Zeeman energies i
ZiB
i
ZiB hgShg
1)()();()( nj
njiij SStStG
HtAdttdAi ),()(
Arbitrary S local moment Green’s function
Equation of motion
1, )()(;,)( n
jn
jinji SSHStGdtdi
The time derivative of local spin greens function
.)()(;)()(;2
)()(;)(
11
1,
nj
njiz
nj
nji
Z
nj
nji
Znji
SSSSSSJ
SSSJtGdtdi
izZiii
Zii SJSJSHS , Where hg Bz
Then
Through RPA mean field
1
1
1,
)()(;
)()(;2
)()(;)(
nj
njiz
nj
nji
Z
nj
nji
Znji
SSS
SSSJ
SSSJtGdtdi
1)()(; nj
nji SSIncluding spin flip
Greens function of conducting electrons
equal to
1)()(; nj
njii SScc
),(121)( )(
,
qGdeeN
tG ti
q
RRiqji
ji
)(
,2
)(
,
1,,2
1
);,(1
)()(;1
)()(;
ji
ji
RRiq
qk
RRiq
qK
nj
njkqk
nj
njii
ekqkN
eSSccN
SScc
Through the Fourier transformation
Local spin Greens function
spin flip Greens function
);()2
(
);,(1);(
qGJ
kqkN
SJqG
zZ
k
Zn
);,()(
);()(2
);,()22();,(
kqkSJ
qGccccJ
kqkkqk
ZZ
qkqkkk
kqk
Combined together
kn
ZZ
kqk
kkqkqk
ZZ
Z
qGSJ
cccc
N
SJJ
);()1
22(
2
k ZZ
kqk
kkqkqk
Z
iSJ
cccc
N
SJq
1
2),(
2Self-energy
Dyson’s general formula of magnetization
1212
1212
)()(1)()(1)(1)(
SS
SSZ
SSSSSSSS
S
where 1)1(1
)( q
qeN
S
22ZZ
k SJ
22ZZ
k SJ
RPA first order approx. for electrons
k
take the dilute limit by conversing the kinetic energy to free electrons like
*
22
2mk
k
0
2 sin21 ddkkN k
The summation becomes
dk
mkq
mqSJ
mkq
mqSJ
nqfkm
VSJ
dk
mkq
mqSJ
mkq
mqSJ
nqfkm
VSJJ
Zq
Zq
k
C
Z
Zq
Zq
k
C
ZZq
)
2
2( 22
)
2
2( 22
*
2
*
22
*
2
*
22
0 2
*2
*
2
*
22
*
2
*
22
0 2
*2
Spinwave Spectrum
where
k
BZZ
k
kk
f
TKSJcc
1/)22
(exp
1
ak
BZZ
qk
qkqk
f
TKSJ
cc
1/)22
(exp
1
0qfor
By L’Hospital rule
dkSJ
fkV
SJ
dkSJ
fkV
SJ
J
Zq
kC
Z
Zq
kC
ZZq
0
2
2
0
2
2
122
2
122
2
Imaginary part of self energy will cause the spin waves spread
)()(
cos22
)()(12
),(Im
0
1
1
22
2
kqkZ
kqk
C
Z
kqkZ
kkqk
Z
SJff
ddkkV
SJ
SJffN
SJq
02
cos *
22
*
2
mq
mkq
SJ Z
The delta function made a constraint
the existing region for the imaginary part
kppZ
kppZ
SJ
SJ
2
2
q
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0
2e-4
4e-4
6e-4
8e-4
1e-3
)2
(2
)2
(2
Zpp
Z
Zpp
Z
SJSJ
SJSJ
Considering the zero temperature situation
the existing region for the imaginary part
Temperature(K)
0 10 20 30 40 50 60 70 80 90 100
Mag
netiz
atio
n
-0.6-0.4-0.20.00.20.40.60.81.01.21.41.61.82.02.22.42.62.83.0
SZ (C*=1.0E-3)
(C*=1.0E-3)
SZ (C*=1.0E-2)Z (C*=1.0E-2)
From Dyson’s general formula of magnetization Magnetization profile is comparable for Monte Carlo result for Ising interaction(Osamu Sakai, Physica E 10,148(2001)
20.1 En
30.1 En
Temperature
0 10 20 30 40 50 60 70 80
Susc
eptib
ility
0.0
1.0e-5
2.0e-5
3.0e-5
4.0e-5
5.0e-5
6.0e-5
7.0e-5
8.0e-5
9.0e-5
1.0e-4
To evaluate the temperature dependence of static susceptibility,
hSS
Sdhdstatic
Zh
Z
hZ 0)(
are expectation values of local spin with magnetic field turned on and off
hZS 0 ZSan
dWhere
• Kondo lattice model utilizes the equation of motion method with RPA approximation in dilute limitation to obtain a local spin greens function of self consistent solution can well describe the magnetic properties of diluted ferromagnetic semiconductors
Conclusions:
• From examining the imaginary part of self energy reveals that the spin excitations are well established in this model • The temperature dependence of magnetization is qualitatively consistent with Monte Carlo result • the significant peak of susceptibility appearing before Tc agrees with experimental result