Transcript New spintronic device concept using spin injection Hall effect: a new

New spintronic device concept using spin injection Hall
effect: a new member of the spintronic Hall family
JAIRO SINOVA
Texas A&M University
Institute of Physics ASCR
Texas A&M L. Zarbo
Hitachi Cambridge
Institute of Physics ASCR
Tomas Jungwirth, Vít Novák, et al Jorg Wunderlich, A. Irvine, et al
Teleconference at Applied Research
Associates, Inc
August 4th , 2009
Stanford University
Shoucheng Zhang, Rundong
Li, Jin Wang
Research fueled by:
Anomalous Hall transport: lots to think about
SHE
AHE
AHE in complex
spin textures
Kato et al
Wunderlich et al
Intrinsic AHE
Inverse SHE
(magnetic monopoles?)
Taguchi et al
Fang et al
Valenzuela et al
Brune et al
2
OUTLINE
• Introduction
• SIHE experiment
–
–
–
–
–
–
Making the device
Basic observation
Analogy to AHE
Photovoltaic and high T operation
The effective Hamiltonian
Spin-charge Dyanmcis
–
–
–
–
AHE basics
Strong and weak spin-orbit couple contributions of AHE
SIHE observations
AHE in SIHE
• AHE in spin injection Hall effect:
• Spin-charge dynamics of SIHE with magnetic field:
– Static magnetic field steady state
– Time varying injection
• AHE general prospective
– Phenomenological regimes
– New challenges
The family of spintronic Hall effects
SHE
         
SHE
B=0
charge current
nonmagnetic
(unpolarized
charge current)
gives
spin current
jq
         
Optical
detection
Electrical
detection
AHE
AHE
B=0
polarized charge
current gives
charge-spin
current
SHE-1
B=0
spin current
gives
charge current
++++++++++
–––––––––––
Ferromagnetic
(polarized charge current)
jqs
iSHE
Electrical
detection
++++++++++
–––––––––––
js 4
Towards a spin-based non-magnetic FET device:
can we electrically measure the spin-polarization?
Can we achieve direct spin polarization detection through an electrical
measurement in an all paramagnetic semiconductor system?
Long standing paradigm: Datta-Das FET
Unfortunately it has not worked:
•no reliable detection of spin-polarization in a diagonal transport configuration
•No long spin-coherence in a Rashba SO coupled system
5
Spin-detection in semiconductors
Crooker et al. JAP’07, others
 Magneto-optical imaging
non-destructive
 lacks nano-scale resolution
and only an optical lab tool
 MR Ferromagnet
 electrical
 destructive and requires
Ohno et al. Nature’99, others
semiconductor/magnet hybrid
design & B-field to orient the FM
 spin-LED
 all-semiconductor
 destructive and requires
further conversion of emitted
light to electrical signal
Spin-injection Hall effect
 non-destructive
 electrical
 100-10nm resolution with current lithography
 in situ directly along the SmC channel
(all-SmC requiring no magnetic elements in the structure or B-field)
Wunderlich et al. Nature Physics 09
Utilize technology developed to detect SHE in 2DHG
and measure polarization via Hall probes
J. Wunderlich, B. Kaestner, J. Sinova and
T. Jungwirth, Phys. Rev. Lett. 94 047204 (2005)
Spin-Hall Effect
B. Kaestner, et al, JPL 02; B. Kaestner, et al Microelec.
J. 03; Xiulai Xu, et al APL 04, Wunderlich et al PRL 05
Proposed experiment/device: Coplanar photocell in
reverse bias with Hall probes along the 2DEG channel
Borunda, Wunderlich, Jungwirth, Sinova et al PRL 07
8
Device schematic - material
ni
p
2DHG
Device schematic - trench
-
ni
p
2DHG
Device schematic – n-etch
p
i
n
2DHG
2DEG
Device schematic – Hall measurement
Vd
Vs
VH
2DHG
2DEG
12
Device schematic – SIHE measurement
Vd
h
h
h h h
h
Vs
e
VH
e
e
e
e
e
2DHG
2DEG
13
Reverse- or zero-biased: Photovoltaic Cell
Red-shift of confined 2D hole  free electron trans.
due to built in field and reverse bias
light excitation with  = 850nm
(well below bulk band-gap energy)
Band bending: stark effect
bulk
-1/2
5m
-1/2
+1/2
-1/2 -3/2
-3/2
+1/2 +3/2
ħω>Eg
Transitions allowed for ħω<E
50
20
R
RHH [ ]
VL
0
σ- σo
σ+
σo
16
14
12
1.00
10
-20
8
-30
6
1.05
4
1.00
-40
2
-50
30
60
90
tm [s]
120
0
150
I/Iav.
1.05
-10
0
(a)
0.95
R
RLL [k[k]]
10
P/Pav.
18
20
Transitions allowed for ħω<Eg
1.00
22
30
+3/2
+1/2
1.05
24
trans. signal
40
-1/2
+1/2
(b)
0.95
Iav. = 525nA
V/Vav.
Vav. = 9.4mV
(c)
0.95
0
30
60
90
tm [s]
120 150
14
Spin injection Hall effect: experimental observation

100
n2
50
R
]
R HH [ 
5m
+
0
-50
n3 (4)
-100
n1 (4)
-4
-2
0
tm [s]
2
4
Local Hall voltage changes sign and magnitude along the stripe
15
Spin injection Hall effect  Anomalous Hall effect
2
n1
0.5
H [ 10 ]
-3
-3
H [ 10 ]
1
p
0
0.0
-1
-0.5
-2
-1.0
-0.5


0.0

0.5
1.0

-1.0
(   ) / (   )

0.0

0.5

1.0
p
0.5
-3
H [ 10 ]
5
-3
H [ 10 ]

(   ) / (   )
n2
10
-0.5
0
0.0
-5
-0.5
-10
-1.0
-0.5


0.0

0.5

(   ) / (   )
1.0
-1.0
-0.5


0.0

0.5

(   ) / (   )
1.0
16
Persistent Spin injection Hall effect
Zero bias-and high temperature operation
n2
VB = 0V
1
+
n2 (2)
]
5
-
+
-3
-3
H [ 10 ]
-
 H [ 10
0
n3 (50)
-5 n1 (10)
-6
-3
0
n1 (2)
0
-1
T = 4K
3
6
tm [s]
T = 230K
n3
VB = -10V
-6
-3
0
3
6
tm [s]
A
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THEORY CONSIDERATIONS
Spin transport in a 2DEG with Rashba+Dresselhaus SO
The 2DEG is well described by the effective Hamiltonian:
H 2DEG


 2k 2
*

  k y x  k x y    k x x  k y y      (k   Vdis (r ))
2m
o2

P 2  1
1
  5.3 A for GaAs,
 

2
2 

3  E g ( E g   so ) 
*
For our 2DEG system:
0
   B k with B  10 eV A 3 for GaAs,
2
z
  * Ez
0
  0.02 eV A , m  0.067me
0
0
  0.01  0.03 eV A (for EZ  0.01  0.03 eV/ A)
Hence
  
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What is special about     ?
H 2DEG
 2k 2

  (k y  k x )( x   y )
2m
Ignoring
 the term

*
   (k   Vdis (r ))
for now
• spin along the [110] direction is conserved
• long lived precessing spin wave for spin perpendicular to [110]
• The nesting property of the Fermi surface:
 

 k   k  Q
Q

4 m
2
19
The long lived spin-excitation: “spin-helix”
• Finite wave-vector spin components
SQ   k ckck Q ,
SQ   k ckQck  ,
 S0z , SQ   2 SQ ,
S0z   k ckck   ckck 
 SQ , SQ   S0z
• Shifting property essential
 

 
 H ReD , c c     k  Q    k c  c  0
k Q k  
k Q k 

An exact SU(2) symmetry
Only Sz, zero wavevector U(1) symmetry previously known:
J. Schliemann, J. C. Egues, and D. Loss, Phys. Rev. Lett. 90, 146801 (2003).
K. C. Hall et. al., Appl. Phys. Lett 83, 2937 (2003).
20
Physical Picture: Persistent Spin Helix    
• Spin configurations do not depend on the particle initial momenta.
• For the same x+ distance traveled, the spin precesses by exactly the same angle.
• After a length xP=h/4mα all the spins return exactly to the original configuration.
21
Thanks to SC Zhang, Stanford University
Persistent state spin helix verified by pump-probe experiments
Similar wafer parameters to ours
22
The Spin-Charge Drift-Diffusion Transport Equations
For arbitrary α,β spin-charge transport equation is obtained for diffusive regime
 t n  D 2 n  B1 x  S x   B2  x  S x 
 t S x   D 2 S x   B2  x  n  C1 x  S z  T1S x 
 t S x   D 2 S x   B1 x  n  C2  x  S z  T2 S x 
 t S z  D 2 S z  C2  x  S x   C2  x  S x   (T1  T2 ) S z
2
2
k

B1/ 2  2(   ) 2 (   )k F2 2 , T1/ 2  (   ) 2 F2
D  v  / 2,
2
F
2
1/ 2
and C
m
 4 DT1/ 2

For propagation on [1-10], the equations decouple in two blocks.
Focus on the one coupling Sx+ and Sz:
 t S x   D 2 S x   C2 x  S z  T2 S x 
 t S z  D 2 S z  C2 x  S x   (T1  T2 ) S z
For Dresselhauss = 0, the equations reduce to Burkov, Nunez and MacDonald, PRB 70, 155308 (2004);
Mishchenko, Shytov, Halperin, PRL 93, 226602 (2004)
23
Steady state spin transport in diffusive regime
Steady state solution for the spin-polarization
component if propagating along the [1-10] orientation
S z / x  ( x[1 1 0] )  S z0/ x  exp[ q x[1 1 0] ]
 L~ 2 L~ 2  L~ 4 4 
~2~ 2 ~ 4 14
 ~
2
q | q | exp( i ) , | q |  ( L1 L2  L2 ) ,   12 arctan  ~1 2 2 ~ 2 1
 L  L 2  L1/ 2  2m |    | 
2
1


Spatial variation scale
consistent with the one
observed in SIHE
24
Understanding the Hall signal of the SIHE:
Anomalous Hall effect
Spin dependent “force” deflects like-spin particles
majority
_
__
FSO
FSO
I
minority
 H  R0 B  4Rs M 
R0  Rs
V
Simple electrical measurement
of out of plane magnetization
 jx    xx  xy  Ex 
 
 
 j   
 

xx  E y 
 y   xy
 xx
1
 xx  2

2
 xx   xy  xx
  xyInMnAs
  xy
2
2
 xy  2







A


B

xy xx
xx
xx
 xx   xy2
 xx2
 xy  B  A xx
25
Anomalous Hall effect (scaling with ρ)
 xy   A xx  B xx2
 xy  B  A xx
Co films
Kotzler and Gil PRB 2005
GaMnAs
Strong SO
coupled regime
Dyck et al PRB 2005
Weak SO
coupled regime
Edmonds et al APL 2003
26
STRONG SPIN-ORBIT COUPLED REGIME (Δso>ħ/τ)
Intrinsic deflection
Electrons deflect to the right or to the
left as they are accelerated by an
electric field ONLY because of the spinorbit coupling in the periodic potential
(electronics structure)
SO coupled quasiparticles
E
~τ0 or independent of impurity density
Electrons have an “anomalous” velocity perpendicular to the
electric field related to their Berry’s phase curvature which is
nonzero when they have spin-orbit coupling.
Side jump scattering
Vimp(r)
independent of impurity density
Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave
the impurity since the field is opposite resulting in a side step. They however come out in a different band so
this gives rise to an anomalous velocity through scattering rates times side jump.
Skew scattering
Asymmetric scattering due to the spinorbit coupling of the electron or the
impurity. This is also known as Mott
scattering used to polarize beams of
particles in accelerators.
~1/ni
Spin Currents 2009
Vimp(r)
WEAK SPIN-ORBIT COUPLED REGIME (Δso<ħ/τ)
Better understood than the strongly SO couple regime
The terms/contributions dominant in the strong SO couple regime are strongly
reduced (quasiparticles not well defined due to strong disorder broadening).
Other terms, originating from the interaction of the quasiparticles with the SOcoupled part of the disorder potential dominate.
Side jump scattering from SO disorder
 λ*Vimp(r)
independent of impurity density
Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave
the impurity since the field is opposite resulting in a side step. They however come out in a different band so
this gives rise to an anomalous velocity through scattering rates times side jump.
Skew scattering from SO disorder
Asymmetric scattering due to the spinorbit coupling of the electron or the
impurity. This is also known as Mott
scattering used to polarize beams of
particles in accelerators.
 λ*Vimp(r)
~1/ni
28
AHE contribution
H 2DEG


 2k 2
*

  k y x  k x y    k x x  k y y      (k   Vdis (r ))
2m
Two types of contributions:
i)
S.O. from band structure interacting with the field (external and internal)
ii) Bloch electrons interacting with S.O. part of the disorder
Type (i) contribution much smaller in the weak SO coupled regime where the
SO-coupled bands are not resolved, dominant contribution from type (ii)
 xy
skew
2e 2*

V0 n (n  n )
2

Crepieux et al PRB 01
Nozier et al J. Phys. 79
 xy
side- jump
H
2e 2 *

(n  n )

side- jump
 5.3 10  4
e
 H ( x[1 1 0] )  2
n pz ( x[1 1 0] )  1.1103 pz
ni 
*
Lower bound
estimate of skew
scatt. contribution
29
Spin injection Hall effect: Theoretical consideration
Local spin polarization  calculation of the Hall signal
Weak SO coupling regime  extrinsic skew-scattering term is dominant
e
 H ( x[1 1 0] )  2
n pz ( x[1 1 0] )
ni 
*
Lower bound
estimate
30
32
Drift-Diffusion eqs. with magnetic field perpendicular to
110 and time varying spin-injection
Jing Wang, Rundong Li, SC Zhang, et al
Similar to steady state B=0 case, solve above equations with appropriate boundary
conditions: resonant behavior around ωL and small shift of oscillation period
σ+(t)
B
Spin Currents 2009
Semiclassical Monte Carlo of SIHE
Numerical solution of
Boltzmann equation
Spin-independent
scattering:
Spin-dependent scattering:
•phonons,
•remote impurities,
•interface roughness, etc.
•side-jump, skew scattering.
AHE
•Realistic system sizes (m).
•Less computationally intensive than
other methods (e.g. NEGF).
Spin Currents 2009
Single Particle Monte Carlo
Spin-Dependent Semiclassical Monte Carlo
Temperature effects, disorder, nonlinear effects, transient regimes.
Transparent inclusion of relevant microscopic mechanisms affecting spin
transport (impurities, phonons, AHE contributions, etc.).
Less computationally intensive than other methods(NEGF).
Realistic size devices.
Spin Currents 2009
Effects of B field: current set-up
Out-of plane magnetic field
In-Plane magnetic field
Spin Currents 2009
SIHE
B=0
Optical injected
polarized current
gives
charge current
Electrical
detection
SHE
B=0
charge current gives
spin current
Optical
detection
HE
++++++++++
–––––––––––
Ferromagnetic
olarized charge current)
AHE
jqs
B=0
polarized charge
current gives
charge-spin
current
Electrical detection
SHE-1
B=0
spin current gives
charge current
Electrical
detection
37
The family of spintronic Hall effects
SHE
         
SHE
B=0
charge current
nonmagnetic
(unpolarized
charge current)
gives
spin current
jq
         
Optical
detection
Electrical
detection
AHE
AHE
B=0
polarized charge
current gives
charge-spin
current
SHE-1
B=0
spin current
gives
charge current
++++++++++
–––––––––––
Ferromagnetic
(polarized charge current)
jqs
iSHE
Electrical
detection
++++++++++
–––––––––––
js38
39
SUMMARY
- electrical detection method for Spin current
- large signal (comparable to AHE in metallic
ferromagnets)
- high spatial resolution (~ < 50nm)
- nondestructive detection of spin WITHOUT
magnetic elements
- linear with degree of spin polarization
- high temperature operation
- first electrical detection of the Spin Helix
(coherently precessing spins)
－6－
- all electrical polarimeter (transfers degree of
light polarization into an electrical signal) 40