Spin currents, spin-Hall spin accumulation, and anomalous Hall transport in strongly spin-orbit coupled systems Diluted Magnetic Semiconductors and Magnetization Dynamics ONR N00014-06-1-0122. JAIRO SINOVA. Denver March 9 th 2007. Research fueled by:. Alexey Kovalev. Nikolai Sinitsyn.
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Spin currents, spin-Hall spin accumulation, and anomalous Hall transport in strongly spin-orbit coupled systemsDiluted Magnetic Semiconductors and Magnetization DynamicsONR N00014-06-1-0122
Denver March 9th 2007
Research fueled by:
Allan MacDonald, Qian Niu, Ken Nomura from U. of Texas
Marco Polini from Scuola Normale Superiore, Pisa
Rembert Duine from Utretch Univeristy, The Netherlands
Joerg Wunderlich from Cambridge-Hitachi
Laurens Molenkamp et al from Wuerzburg
Brian Gallager, Richard Campton, and Tom Fox from U. of Nottingham
Mario Borunda and Xin Liu from TAMU
Ewelina Hankiewicz from U. Missouri and TAMU
Branislav Nikolic, S. Souma, and L. Zarbo from U. of Delaware
Circuit heat generation is the main limiting factor for scaling device speed
Did we solve it: Yes (but temporarily)
EMERGING RESEARCH DEVICES
charge current gives
polarized charge current gives
spin current gives
Anomalous Hall effect: where things started, the long debate
Spin-orbit coupling “force” deflects like-spin particles
Simple electrical measurement
controversial theoretically: semiclassical theory identifies three contributions (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 spin-orbit coupling in the periodic potential (electronics structure)
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
Related to the intrinsic effect: analogy to refraction from an imbedded medium
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.
Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. This is also known as Mott scattering used to polarize beams of particles in accelerators.
n’n, qTHE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACH
σHSkew (skew)-1 2~σ0 S where
S = Q(k,p)/Q(p,k) – 1~
sAH 1000 (W cm)-1
sAH 750 (W cm)-1
Berry’s phase based AHE effect is quantitative-successful in many instances BUT still not a theory that treats systematically intrinsic and extrinsic contribution in an equal footing.
Spin Hall effect
Take now a PARAMAGNET instead of a FERROMAGNET: Spin-orbit coupling “force” deflects like-spin particles
Carriers with same charge but opposite spin are deflected by the spin-orbit coupling to opposite sides.
Spin-current generation in non-magnetic systems
without applying external magnetic fields
Spin accumulation without charge accumulation
excludes simple electrical detection
(Dyaknov and Perel)
[Hirsch, S.F. Zhang]
[Murakami et al, Sinova et al]
Influence of Disorder
[Inoue et al, Misckenko et al, Chalaev et al.]
Kato, Myars, Gossard, Awschalom, Science Nov 04
Observation of the spin Hall effect bulk in semiconductors
Local Kerr effect in n-type GaAs and InGaAs:
(weaker SO-coupling, stronger disorder)
Wunderlich, Kästner, Sinova, Jungwirth, PRL 05
Experimental observation of the spin-Hall effect in a two
dimensional spin-orbit coupled semiconductor system
Light frequency (eV)
Transport observation of the SHE by spin injection!!
Valenzuela and Tinkham cond-mat/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”
SHE at room temperature in HgTe systems Stern et al PRL 06 !!!
Intrinsic + Extrinsic:Connecting Microscopic and Semiclassical approach
Sinitsyn et al PRL 06, PRB 07
AHE in Rashba systems with disorder:
Dugaev et al PRB 05
Sinitsyn et al PRB 05
Inoue et al (PRL 06)
Onoda et al (PRL 06)
Borunda et al (cond-mat 07)
All are done using same or equivalent linear response formulation–different or not obviously equivalent answers!!!
Semiclassical Boltzmann equation
In metallic regime:
J. Smit (1956):
Sinitsyn et al PRL 06, PRB 06
In metallic regime:
Sinitsyn et al PRL 06, PRB 06
SAME RESULT OBTAINED USING BOLTMANN!!!
Non-equilibrium Green’s function formalism (Keldysh-LB)
B.K. Nicolić, et al PRL.95.046601, Mario Borunda and J. Sinova unpublished
5 d-electrons with L=0
S=5/2 local moment
acceptor (110 meV)
-Mn local moments too dilute
(near-neghbors cople AF)
- Holes do not polarize
in pure GaAs
- Hole mediated Mn-Mn
FERROMAGNETISM MEDIATED BY THE CARRIERS!!!
Jungwirth, Sinova, Mašek, Kučera, MacDonald, Rev. Mod. Phys. (2006), http://unix12.fzu.cz/ms
As anti-site deffect: Q=+2e
acceptor +Local 5/2 moment
BUT THINGS ARE NOT THAT SIMPLE
courtesy of D. Basov
Problems for GaMnAs (late 2002)
“110K could be a fundamental limit on TC”
But are these intrinsic properties of GaMnAs ??
Can a dilute moment ferromagnet have a high Curie temperature ?
and delocalized band electrons
coupling strength / Fermi energy
band-electron density / local-moment density
PROS: No initial assumptions, effective Heisenberg model can be extracted, good for determining chemical trends
CONS: Size limitation, difficulty dealing with long range interactions, lack of quantitative predictability, neglects SO coupling (usually)
PROS: “Unbiased” microscopic approach, correct capture of band structure and hybridization, treats disorder microscopically (combined with CPA), good agreement with LDA+U calculations
CONS: difficult to capture non-tabulated chemical trends, hard to reach large system sizes
PROS: simplicity of description, lots of computational ability, SO coupling can be incorporated,
CONS: applicable only for metallic weakly hybridized systems (e.g. optimally doped GaMnAs), over simplicity (e.g. constant Jpd), no good for deep impurity levels (e.g. GaMnN)
Intrinsic properties of (Ga,Mn)As
Jungwirth, Wang, et al. Phys. Rev. B 72, 165204 (2005)
Tc linear in MnGa local moment concentration; falls rapidly with decreasing hole density in more than 50% compensated samples; nearly independent of hole density for compensation < 50%.
Tc as grown and annealed samples
Open symbols as grown. Closed symbols annealed
- Effective concentration of uncompensated MnGa moments has to increase
beyond 6% of the current record Tc=173K sample. A factor of 2 needed
12% Mn would still be a DMS
- Low solubility of group-II Mn in III-V-host GaAs makes growth difficult
Strategy A: stick to (Ga,Mn)As
- alternative growth modes (i.e. with proper
substrate/interface material) allowing for larger
and still uniform incorporation of Mn in zincblende GaAs
More Mn - problem with solubility
(Al,Ga)As & Ga(As,P) hosts
lattice constant (A)
conc. of wide gap component
local moment - hole spin-spin coupling Jpd S . s
Mn d - As(P) poverlap
Mn d level - valence band splitting
GaAs & (Al,Ga)As
(Al,Ga)As & Ga(As,P)
p-d coupling and Tc in mixed
(Al,Ga)As and Ga(As,P)
Smaller lattice const. more important
for enhancing p-d coupling than larger gap
Mixing P in GaAs more favorable
for increasing mean-field Tc than Al
Factor of ~1.5 Tc enhancement
Mašek, et al. PRB (2006)
Microscopic TBA/CPA or LDA+U/CPA
Using DEEP mathematics to find a new material
GaAs and LiZnAs are twin SC
Wei, Zunger '86;
Bacewicz, Ciszek '88;
Kuriyama, et al. '87,'94;
Wood, Strohmayer '05
LDA+U says that Mn-doped are also twin DMSs
Masek, et al. PRB (2006)
substituting for group-II Zn
Additional interstitial Li in
Ga tetrahedral position - donors
Electronmediated Mn-Mn coupling n-type Li(Zn,Mn)As -
similar to hole mediated coupling in p-type (Ga,Mn)As
Comparable Tc's at comparable Mn and carrier doping and
Li(Mn,Zn)As lifts all the limitations of Mn solubility, correlated local-moment and carrier densities, and p-type only in (Ga,Mn)As
Li(Mn,Zn)As just one candidate of the whole I(Mn,II)V family
1st benefit of this meeting (UCSD+TAMU)
corollary of Aharonov-Bohm effect with electric fields instead
Control of conductance through a novel Berry’s phase effect induced by gate voltages instead of magnetic fields
Three phase factors:
m> 3 x 105 cm2/Vsec
8 x 8 k×p band structure model
Rashba splitting energy
A. Novik et al., PRB 72, 035321 (2005).
Y.S. Gui et al., PRB 70, 115328 (2004).
Modeling E. Hankiewicz, J. Sinova,
Concentric Tight Binding Model + B-field
Semiconductor nano-spintronics (TAMU): ONR AWARD N00014-06-1-0122
Rationale and motivation
Task 1- Develop quantitative theories of spin transport and accumulation in spin-orbit coupled systems: spin-Hall and anomalous Hall effect and spin-transport phenomena
Task 2- Develop quantitative theories for novel spintronics materials that couple semiconducting properties and ferromagnetic properties
Task 3- Develop a theory of spin Coulomb drag in systems with spin-orbit coupling
Task 1- Possibility of manipulating spin and spin currents by solely electrical means in a controlled fashion. New switching devices.
Task 2- Allows control of new transport phenomena such as anisotropic tunneling magneto-resistance by gates. New memory devices.
Task 3- Allows for longer spin coherence times in spin transport and makes larger spin based devices more likely to impact the IT field.
Task 1- Possibility to create new logical switching devices with lower dissipative heat consumption, increasing reliability and speed.
Task 2- Novel MRAM devices for larger memory density capabilities and reliability (no mechanical parts)
Task 3- Allows for larger size devices in the mesoscopic range.
The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V shallow acceptor metallic DMSs very well in the regime that is valid:
BUT it is only a peace of the theoretical mosaic with many remaining challenges!!
TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity formation energies, lattice constant variations upon doping
Contributions due to impurity states: Flatte’s approach of starting from isolated impurities
Systematic p and xeff study (need more than 2 meff data points)
Possible issues regarding IR absorption