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SPINHALL EFFECT a new adventure in condensed matter physics. JAIRO SINOVA. San Houston State University, January 22 th 2008. Research fueled by:. NERC. Mario Borunda Texas A&M U. Sergio Rodriguez Texas A&M U. Xin Liu Texas A&M U. Alexey Kovalev Texas A&M U. Nikolai Sinitsyn
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SPINHALL EFFECT a new adventure in condensed matter physics
JAIRO SINOVA
San Houston State University, January 22th 2008
Research fueled by:
NERC
Texas A&M U.
Sergio Rodriguez
Texas A&M U.
Xin Liu
Texas A&M U.
Alexey Kovalev
Texas A&M U.
Nikolai Sinitsyn
Texas A&M U.
U. of Texas
Ewelina Hankiewicz
U. of Missouri
Texas A&M U.
Laurens Molenkamp
Wuerzburg
Kentaro Nomura
U. Of Texas
Branislav Nikolic
U. of Delaware
Tomas Jungwirth
Inst. of Phys. ASCR
U. of Nottingham
Joerg Wunderlich
CambridgeHitachi
Allan MacDonald
U of Texas
Other collaborators: Bernd Kästner, Satofumi Souma, Liviu Zarbo, Dimitri Culcer , Qian Niu, SQ Shen, Brian Gallagher, Tom Fox, Richard Campton, Winfried Teizer, Artem Abanov
Two parts to his
personality !
SPIN
What is spintronics?
ELECTRONICSMr. Electron
UP TO NOW: all electronics are mostly based
on the manipulation of the charge of the electron so perhaps we should say “charge electronics”
SPINTRONICS: manipulate spin and charge simultaneously
>0
gate
S
D






thin free charge carrier
channel induced by electric field from gate
Using the chargethe field effect transistor:work horse of information processing
ALL computers have these
transistors in one form or another
insulator
semiconductor
substrate
HIGH tunablity of electronic transport
properties the key to FET success in
processing technology
High mobility 2DEG: IQHE, FQHE, MIT, etc.
ferromagnetism:work horse of information storing
GMR allowed readout heads in hard drives to be MUCH smaller
1st generation spintronic devices based on ferromagnetic metals: GMR– already in every computerMagnetic tunneling junction (MTJ) or “spin valve” Nonvolatile MRAM: “Microchips that never forget”
Compatibility with Si and GaAs next phase:semiconductor spintronics, a marriage of convenience!!!
A brighter future with semiconductor spintronics
MORE KNOBS = MORE PHYSICS
Necessities in performing spintronics in semiconductors
Spingeneration: “spin battery”
 injection (conventional)
 optical, via selection rules (excitation with circular polarized light)
 via SO coupling (e.g., occupationasymmetry in kspace, Spin Hall effect)
Spinmanipulation
 external magnetic field
 via SO coupling (e.g. Datta Das Spintransistor)
Spindetection: “spin meter”
 Magnetoresistive measurement (conventional)
 optical, via selection rules (Spin LED)
 via SO coupling(e.g., anomalous Hall effect)
an electric field
Ingredients: “Impurity” potential V(r)
 Motion of an electron
In the rest frame of an electron
the electric field generates and
effective magnetic field
This gives an effective interaction with the electron’s magnetic moment
Spinorbit coupling interaction(one of the few echoes of relativistic physics in the solid state)Movie created by Mario Borunda
References:
N. A. Sinitsyn, J.E. Hill, Hongki Ming, Jairo Sinova, and A. H. MacDonald, Phys. Rev. Lett. 97, 106804 (2006)Jairo Sinova, Shuichi Murakami, S.Q. Shen, MahnSoo Choi, Solid State Comm. 138, 214 (2006).K. Nomura, J. Wunderlich, Jairo Sinova, B. Kaestner, A.H. MacDonald, T. Jungwirth, Phys. Rev. B 96, 076804 (2006).B. Kaestner, J. Wunderlich, Jairo Sinova, T. Jungwirth, Appl. Phys. Lett. 88, 091106 (2006).K. Nomura, Jairo Sinova, N.A. Sinitsyn, and A. H. MacDonald,Phys. Rev. B. 72, 165316 (2005).E. M. Hankiewicz, Tomas Jungwirth, Qian Niu, ShunQing Shen, and Jairo Sinova, Phys. Rev. B.72, 155305 (2005).N.A. Sinitsyn, Qian Niu, Jairo Sinova, K. Nomura, Phys. Rev. B 72, 045346 (2005).Branislav K. Nikolic, Satofumi Souma, Liviu P. Zarbo, Jairo Sinova,Phys. Rev. Lett. 95, 046601 (2005). Joerg Wunderlich, Bernd Kaestner, Jairo Sinova, Tomas Jungwirth, Phys. Rev. Lett. 94, 047204 (2005).K. Nomura, Jairo Sinova, T. Jungwirth, Q. Niu, A. H. MacDonald, Phys. Rev. B 71, 041304(R) (2005).E. M. Hankiewicz, L.W. Molenkamp, T. Jungwirth, and Jairo Sinova, Phys. Rev. B 70, 241301 (2004)N. A. Sinitsyn, E. H. Hankiewicz, Winfried Teizer, Jairo Sinova,Phys. Rev. B 70, 081212 (R), (2004).D. Culcer, Jairo Sinova, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Qian Niu, Phys. Rev. Lett 93, 046602 (2004).Jairo Sinova, Dimitrie Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Phys. Rev. Lett. 92, 126603 (2004).
_
_
_
FSO
_
FSO
I
minority
V
Anomalous Hall effect: where things started, the unresolved problem
Spinorbit coupling “force” deflects likespin particles
Simple electrical measurement
of magnetization
InMnAs
controversial theoretically: three contributions to the AHE (intrinsic deflection, skew scattering, side jump scattering)
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)
Movie created by Mario Borunda
Electrons have an “anomalous” velocity perpendicular to the electric field related to their Berry’s phase curvature which is nonzero when they have spinorbit coupling.
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.
Movie created by Mario Borunda
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.
Related to the intrinsic effect: analogy to refraction from an imbedded medium
Movie created by Mario Borunda
(thanks to P. Bruno– CESAM talk)
n, q
m, p
m, p
n, q
n, q
n’n, q
THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACHSkew
σHSkew (skew)1 2~σ0 S where
S = Q(k,p)/Q(p,k) – 1~
V0 Im[<kq><qp><pk>]
Skew scattering
Sidejump scattering
Vertex Corrections
σIntrinsic
Intrinsic AHE: accelerating between scatterings
Intrinsic
σ0 /εF
n’n, q
FOCUS ON INTRINSIC AHE: semiclassical and KuboSTRATEGY: compute this contribution in strongly SO coupled ferromagnets and compare to experimental results, does it work?
Kubo:
Semiclassical approach in the “clean limit”
K. Ohgushi, et al PRB 62, R6065 (2000); T. Jungwirth et al PRL 88, 7208 (2002);
T. Jungwirth et al. Appl. Phys. Lett. 83, 320 (2003); M. Onoda et al J. Phys. Soc. Jpn. 71, 19 (2002); Z. Fang, et al, Science 302, 92 (2003).
Experiment
sAH 1000 (W cm)1
Theroy
sAH 750 (W cm)1
Berry’s phase based AHE effect is quantitativesuccessful in many instances BUT still not a theory that treats systematically intrinsic and extrinsic contribution in an equal footing AND supposedly equivalent theories give different results when disorder is incorporated.
_
_
FSO
_
nonmagnetic
FSO
I
V=0
Spin Hall effect
Take now a PARAMAGNET instead of a FERROMAGNET: Spinorbit coupling “force” deflects likespin particles
Carriers with same charge but opposite spin are deflected by the spinorbit coupling to opposite sides.
Spincurrent generation in nonmagnetic systems
without applying external magnetic fields
Spin accumulation without charge accumulation
excludes simple electrical detection
(Dyaknov and Perel)
Interband
Coherent Response
(EF) 0
X `Skewness’
[Hirsch, S.F. Zhang]
[Murakami et al, Sinova et al]
Influence of Disorder
`Side Jump’’
[Inoue et al, Misckenko et al, Chalaev et al…]
Paramagnets
n’n, q
INTRINSIC SPINHALL EFFECT: Murakami et al Science 2003 (condmat/0308167)Sinova et al PRL 2004 (contmat/0307663)as there is an intrinsic AHE (e.g. Diluted magnetic semiconductors), there should be an intrinsic spinHall effect!!!
(differences: spin is a nonconserved quantity, define spin current as the gradient term of the continuity equation. SpinHall conductivity: linear response of this operator)
Inversion symmetry
no RSO
Broken inversion symmetry
RSO
Bychkov and Rashba (1984)
n’n, q
= j = e v
= jz = {v,sz}
SHE conductivity: all contributions– Kubo formalism perturbation theory
Skew
σ0 S
Intrinsic
σ0 /εF
Vertex Corrections
σIntrinsic
n’n, q
Disorder effects: beyond the finite lifetime approximation for Rashba 2DEGQuestion: Are there any other major effects beyond the finite life time broadening? Does side jump contribute significantly?
+…=0
+
For the Rashba example the side jump contribution cancels the intrinsic contribution!!
Inoue et al PRB 04
Raimondi et al PRB 04
Mishchenko et al PRL 04
Loss et al, PRB 05
Ladder partial sum vertex correction:
the vertex corrections are zero for 3D hole systems (Murakami 04) and 2DHG (Bernevig and Zhang 05)
For these models one can do the exact calculations numerically: testing the perturbation theory
k1 Rashba: g=constant α = 1
k3 Rashba: g=constant α = 3
2DEG+Rahsba
2DHG+Rahsba
Nomura et al. PRB 06
Nomura et al PRB 05
k^1 Rashba model
k^3 Rashba model
2D electron+Rashba
2D holes+Rashba
Prediction: one should observe strong intrinsic SHE in 2D hole systems
First experimentalobservations at the end of 2004
Wunderlich, Kästner, Sinova, Jungwirth, condmat/0410295
PRL 05
Experimental observation of the spinHall effect in a two
dimensional spinorbit coupled semiconductor system
Coplanar spin LED in GaAs 2D hole gas: ~1% polarization
CP [%]
1.505
1.52
Light frequency (eV)
Kato, Myars, Gossard, Awschalom, Science Nov 04
Observation of the spin Hall effect bulk in semiconductors
Local Kerr effect in ntype GaAs and InGaAs:
~0.03% polarization (weaker SOcoupling, stronger disorder)
How our experiment worked: creating a spinmeter at edges
Conventionalvertical spinLED
Novel dual coplanar spinLED
Y. Ohno: Nature 402, 790 (1999)
R. Fiederling: Nature 402, 787 (1999)
● SHE in 2DHG with strong and tunable SO
● SHE detected directly in the 2DHG
● Light emission near edge of the 2DHG
● No heterointerface along the LED current
2DHG
2DEG
Spin polarization detected through circular polarization of emitted light
LED 1
CP [%]
Ip
a
Experiment “B”
+Ip
LED 1
CP [%]
LED 2
b
a
+Ip
E [eV]
Opposite perpendicular polarization for opposite Ip currents
or opposite edges SPIN HALL EFFECT
Transport observation of the SHE by spin injection!!
Valenzuela and Tinkham condmat/0605423, Nature 06
Saitoh et al APL 06
Sih et al, Nature 05, PRL 05
“demonstrate that the observed spin accumulation is due to a transverse bulk electron spin current”
A COMMUNITY WILLING TO WORK TOGETHER
APCTP Workshop on Semiconductor NanoSpintronics: SpinHall Effect and Related IssuesAugust 811, 2005 APCTP, Pohang, Korea
http://faculty.physics.tamu.edu/sinova/SHE_workshop_APCTP_05.html
Semantics agreement:The intrinsic contribution to the spin Hall conductivity is the spin Hall conductivity in the limit of strong spin orbit coupling and >>1. This is equivalent to the single bubble contribution to the Hall conductivity in the weakly scattering regime.
The new challenge: understanding spin accumulation
Spin is not conserved; analogy with eh system
Spin Accumulation – Weak SO
Quasiequilibrium
Parallel conduction
Spin diffusion length
Burkov et al. PRB 70 (2004)
SPIN ACCUMULATION IN 2DHG: EXACT DIAGONALIZATION STUDIES
so>>ħ/
Width>>mean free path
Nomura, Wundrelich et al PRB 06
Key length: spin precession length!!
Independent of !!
LED
1
p
y
m
1.5
m
x
n
channel
LED
2
z
SHE experiment in GaAs/AlGaAs 2DHG
Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. \'05
10m channel
 shows the basic SHE symmetries
 edge polarizations can be separated
over large distances with no significant
effect on the magnitude
 12% 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
Theoretical achievements:
Intrinsic SHE
back to the beginning on a higher level
2003
2006
Theoretical challenges:
GUT the bulk (beyond simple graphene)
intrinsic + extrinsic SHE+AHE+AMR
Obtain the same results for different equivalent approaches (Keldysh and Kubo must agree)
Others
materials and defects
coupling with the lattice
effects of interactions (spin Coulomb drag)
spin accumulation > SHE conductivity
WHERE WE ARE GOING (EXPERIMENTS)
Experimental achievements
Optical detection of currentinduced polarization
photoluminescence (bulk and edge 2DHG)
Kerr/Faraday rotation (3D bulk and edge, 2DEG)
Transport detection of the SHE
Experimental (and experiment modeling) challenges:
General
edge electric field (Edelstein) vs. SHE induced spin accumulation
Photoluminescence cross section
edge electric field vs. SHE induced spin accumulation
free vs. defect bound recombination
spin accumulation vs. repopulation
angledependent luminescence (top vs. side emission)
hot electron theory of extrinsic experiments
SHE detection at finite frequencies
detection of the effect in the “clean” limit
Texas A&M U.
Sergio Rodriguez
Texas A&M U.
Xin Liu
Texas A&M U.
Alexey Kovalev
Texas A&M U.
Nikolai Sinitsyn
Texas A&M U.
U. of Texas
Ewelina Hankiewicz
U. of Missouri
Texas A&M U.
Laurens Molenkamp
Wuerzburg
Kentaro Nomura
U. Of Texas
Branislav Nikolic
U. of Delaware
Tomas Jungwirth
Inst. of Phys. ASCR
U. of Nottingham
Joerg Wunderlich
CambridgeHitachi
Allan MacDonald
U of Texas
Other collaborators: Bernd Kästner, Satofumi Souma, Liviu Zarbo, Dimitri Culcer , Qian Niu, SQ Shen, Brian Gallagher, Tom Fox, Richard Campton, Winfried Teizer, Artem Abanov
NERC
VT
2DHG
2DEG
2DHG
VD
2D spinLED
SpinHall effect measrement
Measurement of 2DHG Rashba splitting
Light emitted comes from Type II recombination processes: 3D electrons with 2D holes. 3D electrons have an asymmetric momentum space population (e.g. ky>0)
c
B
Wafer 1
a
I
8
EL
A
PL
6
4
B
A
X
2
Int [a.u.]
0
10
I
d
b
8
p
AlGaAs
C
Wafer 2
E [eV]
6
GaAs
A
4
B
X
2
B
C
A
0
z [nm]
1.48
1.49
1.50
1.51
1.52
E [eV]
Sub GaAs gap spectra analysis: EL vs PL
X :
bulk GaAs
excitons
I :
recombination
with impurity
states
B (A,C):
3D electron –
2D hole
recombination
HH+ and HH subbands
3D electron2D hole
Recombination
20
a
<sz>HH
0
+

<sx>HH+
E [meV]
HH+
<S>
<sx>HH
HH
LH
<sz>HH+
0.2 0.0 0,2
ky [nm1]
ky [nm1]
Light polarization due to recombination with SOsplit holesubband in a pn LED under forward bias
Microscopic bandstructure calculations of the 2DHG:
s=1/2 electrons to j=3/2 holes plus selection rules
circular polarization of emitted light
spin operators of holes: j=3s
inplanepolarization
p
y
y
x
x
n
n
Junction
Junction
z
z
m
m
20
20
m
m
Inplane
detection angle/polarization
Perp.to plane
detection angle/polarization
NO perp.toplane component of polarization at B=0
B≠0 behavior consistent with SOsplit HH subband