Transcript talk-regensburg-07

Spin-orbit coupling based spintronics: Extraordinary
magnetoresistance studies in semiconductors
Tomas Jungwirth
Institute of Physics ASCR
Alexander Shick, Jan Mašek, Josef Kudrnovský,
František Máca, Karel Výborný, Jan Zemen,
Vít Novák, Miroslav Cukr, Kamil Olejník, et al.
University of Nottingham
Bryan Gallagher, Tom Foxon,
Richard Campion, Kevin Edmonds,
Andrew Rushforth, Devin Giddings et al.
Hitachi Cambridge
University of Texas and Texas A&M
Jorg Wunderlich, Bernd Kaestner
David Williams, et a.
Allan MacDonald, Jairo Sinova, et al.
Extraordinary magnetoresistance
V
s
p
Ordinary magnetoresistance:
Extraordinary magnetoresistance:
Beff
response to external magnetic field
via classical Lorentz force
response to internal spin-polarization
via quantum-relativistic spin-orbit coupling
 
H SO  s  Beff

Beff 
_ _ _ _ _ _ _ _ _ _
M
B
__
FSO
+++++++++++++
I
anomalous Hall effect
_ _ _ _ _ _ _ _ _ _
_

1
(

V
)

p
2m 2 c 2
FL
+++++++++++++
I
V
anisotropic magnetoresistance
V
e.g. ordinary (quantum)
Hall effect
Discovered in the 19th century in TM ferromagnets
– classical unsettled CMP field
- now accessible in semiconductors
Conventional ferromagnetic metals
Mott’s model of transport
ss
sd
ss
sd
itinerant 4s:
no exch.-split
no SO
Ab initio Kubo (CPA) formula for
AMR and AHE in FeNi alloys
AMR
Mott&Wills ‘36
AHE
Khmelevskyi ‘PRB 03 Banhart&Ebert EPL‘95
localized 3d:
exch. split
SO coupled
difficult to match models and microscopics
Ferromagnetic semiconductors
insulating GaMnAs
Ga
As-p-like holes
Mn
As
Mn
metallic GaMnAs
Mn-d-like local
moments
- carriers
with both strong
SO coupling and
exchange splitting
- simpler band structure
- SO topology of holes dominated by As
p-orbitals as in hosts (Mn on Ga sublattice)
favorable for exploring physical origins
Origin of R[M  I]> R[M || I] non-crystalline AMR in GaMnAs
1st order Born approximation
Boltzmann eq. in relax. time approximation
4-band spherical Kohn-Luttinger model
SO-coupling – spherical model
FM exchange spiitting
M
ky
~(k . s)2
kx
~Mx . sx
M
hot spots for scattering for states moving  M
 R[M  I]> R[M || I] (opposite to most metal FMs)
1/k (M)
M
current
M
spherical model:
non-crystalline AMR only
full 6-band Hamiltonian:
non-crystalline and
crystalline AMR
current

[110]
theory
In metallic GaMnAs:
also magnitudes and relative strengths
of non-crystalline and crystalline AMR
terms consistent with experiment
Rushforth et al. ‘07
exp.
Family of new AMR effects: TAMR – anisotropic TDOS
TAMR – discovered in GaMnAs
Au
GaMnAs
AlOx

predicted and observed in metals
Au Au
[100]
[100]
[010]
[100]
[010]
[110]
[010] M
F
[100]
[110]
[010]
[010]
Gould, et al., PRL'04, Brey et al. APL’04,
Ruster et al.PRL’05, Giraud et al. APL’05,
Saito et al. PRB’05,
Shick et al.PRB'06, Bolotin et al. PRL'06,
Viret et al. EJP’06, Moser et al. 06,
Grigorenko et al. ‘06
Coulomb blockade AMR – anisotropic chemical potential
Source
Q VD
Drain
Gate
VG

Q( M )
U   dQ'VD ( Q' ) 
e
0
[110]
[010] M
F
Q
[100]
[110]
[010]


( Q  Q0 )2
( M ) C
U
& Q0  CG [ VG  VM ( M )] &VM 
2C
e
CG
electric
& magnetic
control of Coulomb blockade oscillations
Wunderlich et al. ‘06
Predicted stronger
CBAMR for metals
_
AHE mechanisms
FSO
Karplus&Luttinger intrinsic AHE mechanism revived in GaMnAs
Karplus&Luttinger PR ‘54
__
FSO
I
V
Jungwirth et al. PRL ‘02,APL ’03,
Edmonds et al. APL ’03, Chun et al. PRL ‘07
 intrinsic AHE in pure Fe: ab initio Kubo eq.
Yao et al. PRL ‘04
Co [Kotzler&Gil PRB ‘05]
SrRuO3 and pyrochlore ferromagnets [Onoda and
Experiment
sAH  1000 (W cm)-1
Theroy
sAH  750 (W cm)-1
Nagaosa, J. Phys. Soc. Jap. 01,Taguchi et al., Science 01, Fang
et al Science 03, Shindou and Nagaosa, PRL 01]
Ferromagnetic spinel CuCrSeBr [Lee et al. Science 04]
- AHE  SHE
_
__
FSO
FSO
_
I
FSO
V
__
FSO
non-magnetic
I
V=0
- All Semiconductor systems including 2D with “model” SO
Cubic (2DHG) and linear (2DEG) in k Rashba model
Kato Sci ’04, Wunderlich et al PRL’05, PRB’06,
Sih et al. NatPhys ‘05
- Optical methods: polarized EL
Solvable analytically
p-AlGaAs
etched
2DHG
i-GaAs
2DEG
n--doped AlGaAs
Exploring SHE & AHE fenomenologies in 2D non-magnetic SC
+
p-AlGaAs
etched
z
-
p-AlGaAs
2DHG
2DHG
i-GaAs
i-GaAs
2DEG
2DEG
n--doped AlGaAs
n--doped AlGaAs
Gate
Gate
SHE
2DHG 2DEG
AHE
x
etched
+
2D “model” systems ideal to explore intrinsic vs. extrinsic AHE/SHE
intrinsic
semicalssical Boltzmann eq.
skew scattering
side jump
distribution function
group velocity
quantum Kubo formula
int.
skew
sc.
side
jump
Extrinsic skew scattering term:
- absent in 2DEG for two-band occupation
- absent in 2DHG for any band occupation
Borunda et al. ‘07
Optical means of exploring EMR fundamentals on systems with simple
yet topologically distinct SO-bands
SO-coupling and electric field controlled spintronics:
1. Coulomb-blockade anisotropic magnetoresistance
Spintronic SET
in thin-film GaMnAs
2. Spin-Hall effect
Electric-field induced
edge spin polarization
in GaAs 2DHG
1. Coulomb blockade AMR
Spintronic transistor - magnetoresistance controlled by gate voltage
Bptp
B90
Huge hysteretic
low-field MR
I
B0
Strong dependence
on field angle
hints to AMR origin
Sign & magnitude
tunable by small
gate valtages
Wunderlich, Jungwirth,
Kaestner et al.,
cond-mat/0602608
AMR nature of the effect
normal AMR
Coulomb blockade AMR
Single electron transistor
Narrow channel SET
dots due to disorder potential fluctuations
(similar to non-magnetic narrow-channel GaAs or Si SETs)
CB oscillations
low Vsd  blocked
due to SE charging
CB oscillation shifts by magnetication rotations
magnetization angle 
At fixed Vg peak  valley
or valley  peak

MR comparable to CB
negative or positive MR(Vg)
Coulomb blockade AMR
QQind0 = (n+1/2)e
QQ0ind = ne
eE2/2C
C 
n-1
n
n+1
n+2
[110]
F
[100]
[110]

Q( M )
U   dQ'VD ( Q' ) 
e
0
Q


( Q  Q0 )
( M ) C
U
& Q0  CG [ VG  VM ( M )] &VM 
2C
e
CG
2
electric
& magnetic
control of Coulomb blockade oscillations
[010] M
[010]
SO-coupling 
(M)
Different doping expected in leads an dots in narrow channel GaMnAs SETs
• CBAMR if change of
|(M)| ~ e2/2C ~ 10Kelvin from exp.
 consistent
• In room-T ferromagnet
|(M)|~100Kelvin
change
• CBAMR works with dot both ferro
or paramegnetic
Calculated doping dependence of
(M1)-(M2)
of
CBAMR SET
• Huge, hysteretic, low-field MR tunable
by small gate voltage changes
• Combines electrical transistor action
with permanent storage
Other FERRO SETs
• Non-hysteretic MR and large B chemical potential shifts due to Zeeman effect
Ono et al. '97, Deshmukh et al. '02
• Small MR - subtle effects of spin-coherent and
resonant tunneling through quantum dots
Ono et al. '97, Sahoo '05
SPIN HALL EFFECT
no ferromagnetism, spin-orbit coupling only
all-electric spintronics
_
FSO
__
FSO
non-magnetic
I
V=0
lateral LED
CP photon
emission
I
Spin-current generation in non-magnetic systems
without applying external magnetic fields
Spin accumulation without charge accumulation
excludes simple electrical detection
lateral LED
2. Spin Hall effect
Spin-orbit only & electric fields only
induced transverse
spin accummulation
x
y applied electrical
current
z
spin (magnetization)
component
Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05
Nomura, Wunderlich, Sinova, Kaestner, MacDonald,
Jungwirth, Phys. Rev. B '05
Detection through circularly
polarized electroluminescence
Testing the co-planar spin LED only first
p-n junction current only
(no SHE driving current)
p-AlGaAs
etched
2DHG
i-GaAs
2DEG
n--doped AlGaAs
Circ. polarization [%]
20
EL
10
0
-10
-20
Bz=0
EL
peak
• Can detect edge polarization
• Zero perp-to-plane component
of polarization at Bz=0 and Ip=0
SHE experiments
1
p
0
LED 1
-1
y
z
x
1
n LED 2
0
-1
1.505
10m channel
- show the SHE symmetries
- edge polarizations can be separated
over large distances with no significant
effect on the magnitude
1.510
1.515
Energy in eV
1.520
Polarization in %
n
Polarization in %
1.5m channel
Sz (y)/Ex
jyz (y)/Ex
=0
Ex
Szedge Lso ~ jzbulk tso
x
0
10
20
30
40
50
y [kF-1]
y
H SO

Beff 
 
 s  Beff

1
(

V
)

p
2m 2 c 2
Theory: 8% over 10nm accum. length
for the GaAs 2DHG
Consistent with experimental
1-2% polarization over detection
length of ~100nm
Murakami et al. '03, Sinova et al.'04, Nomura et al. '05, ...
Other SHE experiments:
Spin injection from SHE GaAs channel
Electrical measurement of SHE in Al
Valenzuela, Tinkham '06
Kato et al. '04, Sih et al. '06
100's of theory papers: transport with SO-coupling
intrinsic
vs.
extrinsic
=0
skew
scattering
Microscopic origin
Source
Q VD
Drain
• Vg = 0
Q
Q2
U   dQ VD ( Q ) & VD  Q / C  U 
2C
0
'
Gate
VG
e2
 k BT
2C
'
 Coulomb blockade
• Vg  0
( Q  Q0 )2
U
& Q0  CGVG
2C
QQind0 = (n+1/2)e
Q=ne - discrete
Q0=CgVg - continuous
QQ0ind = ne
eE2/2C
C 
n-1
n
n+1
n+2
Q0=-ne  blocked
Q0=-(n+1/2)e  open
Sub GaAs gap spectra analysis: PL vs EL
++
y
X:
bulk GaAs
excitons
--
z
GaAs
p-AlGaAs
etched
6
i-GaAs
4
n-AlGaAs
B
A
X
GaAs/AlGaAs superlattice
GaAs substrate
E [eV]
010
8
p1 AlGaAs
Wafer 2 C
GaAs
0
A
B
-1
-2
0
2
I
2
B (A,C):
3D electron –
2D hole
recombination
-50
8
-100
z [nm]
-150
1.48
A
1.49
B
1.50
6
4
X
2
C
1.51
[eV]
E–
Bias dependent emission wavelength for 3D electron
2D hole
recombination [A. Y. Silov et al., APL 85, 5929 (2004)]
1.52
0
Int [a.u.]
I:
recombination
with impurity
states
EL
A
PL
2DHG
2DEG
B Wafer 1
I
10
Circularly polarized EL
In-plane
detection angle
Perp.-to plane
detection angle
 NO perp.-to-plane component of polarization at B=0
 B≠0 behavior consistent with SO-split HH subband
Light polarization due to recombination with SO-split
hole-subband in a p-n LED under forward bias
Microscopic band-structure calculations of the 2DHG:
3D electron-2D hole
Recombination
0.50
a
0
s+
s20
HH+
0
0.25
<S>
E [meV]
20
spin-polarization of
HH+ and HH- subbands
<sz>HH<sx>HH+
0.00
<sx>HH-
-0.25
HH-
LH
-20
-0.2
0.0
0,2
-0.50
ky [nm-1]
s=1/2 electrons to j=3/2 holes plus selection rules
<sz>HH+
-0.2
0.0
0.2
ky [nm-1]
spin operators of holes: j=3s
 circular polarization of emitted light
 in-plane polarization
1. Introduction
Non-relativistic many-body
e-
Pauli exclusion principle & Coulomb repulsion  Ferromagnetism
total wf antisymmetric
FERO
= orbital wf antisymmetric * spin wf symmetric
(aligned)
MAG
• Robust (can be as strong as bonding in solids)
• Strong coupling to magnetic field
(weak fields = anisotropy fields needed
only to reorient macroscopic moment)
NET
e-
Spin-orbit coupling
(Dirac eq. in external field V(r) & 2nd-order
in v /c around non-relativistic limit)
Bex
V
Beff
Beff
s
p
 
H SO  s  Beff

Beff 

1
(

V
)

p
2m 2 c 2
Bex + Beff
FM without SO-coupling
GaAs valence band
As p-orbitals  large SO
GaMnAs valence band
tunable FM & large SO
AMR (anisotropic magnetoresistance)
Ferromagnetism: sensitivity to magnetic field
SO-coupling: anisotropies in Ohmic transport
characteristics
GaMnAs
M || <010>
M || <100>
ky
kx
Band structure depends on

M
TMR (tunneling magnetoresistance)
Based on ferromagnetism only
spin-valve
no (few) spin-up DOS available at EF
large spin-up DOS available at EF
Tunneling AMR: anisotropic tunneling DOS due to SO-coupling
MRAM
(Ga,Mn)As
Au
Au
[100]
[110]
[100]
[010] Magnetization
F
[010]
[100]
[100]
Current
[110]
[010]

[010]
[010]
- no exchange-bias needed
- spin-valve with ritcher phenomenology than TMR
Gould, Ruster, Jungwirth,
et al., PRL '04, '05
Wavevector dependent tunnelling probabilityT (ky, kz) in GaMnAs
Red high T; blue low T.
y
thin film
Magnetisation in plane
jt
z
Magnetization
perp. to plane
x
y
constriction
jt
Magnetization
in-plane
z
x
Giddings, Khalid, Jungwirth,
Wunderlich et al., PRL '05
TAMR in metals
ab-initio calculations
Shick, Maca, Masek,
Jungwirth, PRB '06
NiFe
TAMR
Bolotin,Kemmeth, Ralph,
cond-mat/0602251
TMR ~TAMR >>AMR
Viret et al.,
cond-mat/0602298 Fe, Co break junctions TAMR >TMR
TMR
EXPERIMENT
Spin Hall Effect
2DEG
2DHG
VD
VT
Single Electron Transistor
Source
Q VD
Drain
• Vg = 0
Q
Q2
U   dQ VD ( Q ) & VD  Q / C  U 
2C
0
'
Gate
VG
e2
 k BT
2C
'
 Coulomb blockade
• Vg  0
( Q  Q0 )2
U
& Q0  CGVG
2C
QQind0 = (n+1/2)e
Q=ne - discrete
Q0=CgVg - continuous
QQ0ind = ne
eE2/2C
C 
n-1
n
n+1
n+2
Q0=-ne  blocked
Q0=-(n+1/2)e  open
Coulomb blockade anisotropic magnetoresistance
Spin-orbit coupling
Band structure (group velocities,
scattering rates, chemical potential) depend on

M
If lead and dot different
(different carrier concentrations in our (Ga,Mn)As SET)




Q( M )
'
'
U   dQ VD ( Q ) 
& ( M )   L ( M )   D ( M )
e
0
Q


( Q  Q0 )
( M ) C
U
& Q0  CG [ VG  VM ( M )] &VM 
2C
e
CG
2
electric
& magnetic
control of Coulomb blockade oscillations
Wunderlich, Jungwirth, Kaestner, Shick, et al., preprint
• CBAMR if change of |(M)| ~ e2/2C
• In our (Ga,Mn)As ~ meV (~ 10 Kelvin)
• In room-T ferromagnet change of
|(M)|~100K
• Room-T conventional SET
(e2/2C >300K) possible
CBAMR  new device concepts
(a)
“0”
(c)
50
RC [ MW ]
20
18
25
RC [ MW ]
16
M1
0
0.6
M0
0.8
1.0
VG [ V ]
14
12
magnetic
non-volatile
mode
10
Electrical
operation mode
“READ”:
measure RC
at VG = VG1
“1” (M1)
“0” (M0)
POWER
“ON”
“WRITE”
permanently
POWER
“OFF”
8
“1”
6
1.00
1.01
VG0
RC [ MW ]
(b)
electric mode
1.02
1.03
1.04
VG1
VG [ V ]
Magnetic non-volatile mode
M0
20
M1
0
-0.08 -BC2
-M1
-BC1 0.00 BC1
B [ T ]
M = M1 : VG0 (“0”)  VG1 (“1”)
[Inverse: M = M0 : VG0 (“1”)  VG1 (“0”)]
VG = VG1 = 1.04V
M0
(d) Electric mode
BC2 0.08
VG = VG1 : M0 (“0”)  M1 (“1”)
[Inverse: VG = VG0 : M0 (“1”)  M1 (“0”)]
M0 : B  B0  0
BC1 < B0 < BC2
M1 : B  B1  0
B1 < -BC2
Electrically generated spin polarization in normal semiconductors
SPIN HALL EFFECT
Ordinary Hall effect
Lorentz force deflect charged-particles towards the edge
B
_ _ _ _ _ _ _ _ _ _
_
FL
+++++++++++++
I
V
Detected by measuring transverse voltage
Spin Hall effect
Spin-orbit coupling “force” deflects like-spin particles
_
FSO
__
FSO
non-magnetic
I
V=0
Spin-current generation in non-magnetic systems
without applying external magnetic fields
Spin accumulation without charge accumulation
excludes simple electrical detection
Microscopic theory and some interpretation
experimentally detected
spin * velocity
non-conserving (ambiguous)
theoretical quantity
- weak dependence on impurity scattering time
- Szedge
~ jzbulk / vF
tso=h/so : (intrinsic) spin-precession time
Lso=vF tso : spin-precession length
Szedge Lso ~ jzbulk tso
Nomura, Wunderlich, Sinova, Kaestner, MacDonald,
Jungwirth, Phys. Rev. B '05
n
p
1.5 m
channel
LED1
0
y
-1
z
n LED2
x
1
0
-1
1.505
1.510
1.515
1.520
Energy in eV
Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05
10m channel
- shows the basic SHE symmetries
- edge polarizations can be separated
over large distances with no significant
effect on the magnitude
- 1-2% polarization over detection
length of ~100nm consistent with
theory prediction (8% over 10nm
accumulation length)
Nomura, Wunderlich, Sinova, Kaestner, MacDonald,
Jungwirth, Phys. Rev. B '05
Polarization in %
1
Polarization in %
SHE experiment in
GaAs/AlGaAs 2DHG
Conventionally generated spin polarization in non-magnetic semiconductors:
spin injection from ferromagnets, circular polarized light sources,
external magnetic fields
SHE: small electrical currents in simple semiconductor microchips
n
p
1.5  m
channel
y
z
n
x
SHE microchip,
100A
high-field lab. equipment,
100 A
Spin and Anomalous Hall effects
Spin-orbit coupling “force” deflects like-spin particles
majority
__ FSO
_
 H  R0 B  4πRs M
FSO
I
minority
V
InMnAs
Simple electrical measurement
of magnetization
Skew scattering off impurity potential (Extrinsic SHE/AHE)
H SO

skew
scattering

 2s   
  2 2   k  Vimp(r)
m c 


SO-coupling from host atoms (Intrinsic SHE/AHE)
H SO

E





 
 es   k  1 dV (r ) 
    Beff  
 r
   s  l
 m c   m c  er dr 

bands from l=0 atomic orbitals  weak SO
(electrons in GaAs)
bands from l>0 atomic orbitals  strong SO
(holes in GaAs)
Intrinsic AHE approach explains many experiments
• (Ga,Mn)As systems [Jungwirth et al. PRL 02, APL 03]
• Fe [Yao, Kleinman, Macdonald, Sinova,
Jungwirth et al PRL 04]
• Co [Kotzler and Gil PRB 05]
Experiment
sAH  1000 (W cm)-1
Theroy
sAH  750 (W cm)-1
• Layered 2D ferromagnets such as SrRuO3 and
pyrochlore ferromagnets [Onoda and Nagaosa, J. Phys. Soc.
Jap. 01,Taguchi et al., Science 01, Fang et al Science 03, Shindou and
Nagaosa, PRL 01]
• Ferromagnetic spinel CuCrSeBr [Lee et al. Science 04]
Hall effects family
• Ordinary: carrier density and charge; magnetic field sensing
• Quantum: text-book example a strongly correlated manyelectron system with e.g. fractionally charged quasiparticles;
universal, material independent resistance
• Spin and Anomalous: relativistic effects in solid state;
spin and magnetization generation and detection