1. Electric-field controlled semiconductor spintronic devices
University of Nottingham
Bryan Gallagher, Tom Foxon,
Richard Campion, Kevin Edmonds,
Andrew Rushforth, Devin Giddings et al.
Institute of Physics ASCR
Alexander Shick
Tomas Jungwirth
Hitachi Cambridge University of Texas and Texas A&M
Jorg Wunderlich, Bernd Kaestner Allan MacDonald, Jairo Sinova
David Williams

2. e- Spintronics Beff s Beff Bex + Beff spin coupled to macroscopicV
Beff p s
Spin-orbit coupling
Dirac eq. in external field V(r) & 2nd-order
in v /c around non-relativistic limit
Beff
Bex + Beff
Ferromagnetism
Coulomb repulsion & Pauli exclusion principle ky ky
spin coupled to
momentum and
crystal fields
macroscopic
moment kx kx
e.g. GaAs valence band
As p-orbitals  large SO
e.g. GaMnAs valence band
FM & large SO

3. Current spintronics - two terminal AMR or GMR devicesAu Au
[010] F
Magnetization
[110]
[100] 
Current

4. Yamanouchi et al., Nature (2004)
Electrical control of spintronic devices
1. Current driven magnetization reversal
2. Spintronic transistor
3. Electric-field induced spin-polarization in non-magnetic systems
2 orders of magnitude lower critical
currents in dilute moment (Ga,Mn)As
than in conventional metal FMs
Sinova, Jungwirth et al., PRB (2004)
Magnetic race track memory
Parkin, US
Patent (2004)
Yamanouchi et al., Nature (2004)
Coulomb blockade AMR
spintronic SET
in thin-film GaMnAs
Spin Hall effect induced
edge spin polarization
in GaAs 2DHG

5. Coulomb blockade AMR
Spintronic transistor - magnetoresistance controlled by gate voltage
Bptp
B90 B0 I
Strong dependence
on field angle
hints to AMR origin
Huge hysteretic
low-field MR
Sign & magnitude
tunable by small
gate valtages
Wunderlich, Jungwirth,
Kaestner et al.,
cond-mat/

6. AMR nature of the effect
normal AMR
Coulomb blockade AMR

7. 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

8. 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)

9. Coulomb blockade AMR Q0 e2/2C SO-coupling  (M) electric & magnetic
[010] F M
[110]
[100]
SO-coupling 
(M)
electric &
magnetic
control of Coulomb blockade oscillations

10. Calculated doping dependence of
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 change of |(M)|~100Kelvin
CBAMR works with dot both ferro
or paramegnetic
Calculated doping dependence of
(M1)-(M2)

11. 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

12. Spin Hall effect Spin-orbit only & electric fields only
applied electrical
current
Detection through circularly
polarized electroluminescence x z
induced transverse
spin accummulation
spin (magnetization)
component y
Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05
Nomura, Wunderlich, Sinova, Kaestner, MacDonald,
Jungwirth, Phys. Rev. B '05

13. Testing the co-planar spin LED only first
2DHG
2DEG
p-n junction current only
(no SHE driving current)
-10
-20 10 20
Circ. polarization [%] EL EL
peak
Bz=0
Can detect spin polarization
due to Zeemen effect
Zero perp-to-plane component
of polarization at Bz=0 and Ip=0

14. In-plane HH spin-splitting due to SO-coupling
Non-zero in-plane component
of EL polarization at Bx=0 and Ip=0 -5
-10 5 10
Circ. polarization [%]

15. SHE experiments - show the SHE symmetries
1.5m channel
SHE experiments n p y x z
LED 1 2
applied electrical
current x z
10m channel
induced transverse
spin accummulation
spin (magnetization)
component y
- show the SHE symmetries
- edge polarizations can be separated
over large distances with no significant
effect on the magnitude

16. =0 Szedge Lso ~ jzbulk tso jyz (y)/Ex Ex Sz (y)/Ex x y [kF-1]10 20 30 40 50
jyz (y)/Ex
Sz (y)/Ex =0 y x Ex
Szedge Lso ~ jzbulk tso
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, ...

17. skew scattering 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

19. Q VD Source Drain Gate VG Microscopic origin Vg = 0  Coulomb blockade
e2/2C
Q=ne - discrete
Q0=CgVg - continuous
Q0=-ne  blocked
Q0=-(n+1/2)e  open

20. ++ -- Sub GaAs gap spectra analysis: PL vs EL X : bulk GaAs excitons
recombination
with impurity
states
B (A,C):
3D electron –
2D hole
Bias dependent emission wavelength for 3D electron – 2D hole recombination [A. Y. Silov et al., APL 85, 5929 (2004)]

21.  NO perp.-to-plane component of polarization at B=0
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

23. 1. Introduction e- Non-relativistic many-body
Pauli exclusion principle & Coulomb repulsion  Ferromagnetism
total wf antisymmetric =
orbital wf antisymmetric
* spin wf symmetric
(aligned)
FERO
MAG
NET
Robust (can be as strong as bonding in solids)
Strong coupling to magnetic field
(weak fields = anisotropy fields needed
only to reorient macroscopic moment)

24. AMR (anisotropic magnetoresistance)
Ferromagnetism: sensitivity to magnetic field
SO-coupling: anisotropies in Ohmic transport
characteristics
M || <100>
M || <010>
GaMnAs ky kx
Band structure depends on M 

25. TMR (tunneling magnetoresistance)
Based on ferromagnetism only
spin-valve
no (few) spin-up DOS available at EF
large spin-up DOS available at EF

26. Tunneling AMR: anisotropic tunneling DOS due to SO-coupling
MRAM
(Ga,Mn)As Au Au
[100]
[010]
[010] F
Magnetization
[110]
[100] 
Current
- no exchange-bias needed
- spin-valve with ritcher phenomenology than TMR
Gould, Ruster, Jungwirth,
et al., PRL '04, '05

27. Wavevector dependent tunnelling probabilityT (ky, kz) in GaMnAs
Red high T; blue low T. y x jt z
thin film
Magnetisation in plane
Magnetization perp. to plane
Magnetization in-plane x z y jt
constriction
Giddings, Khalid, Jungwirth,
Wunderlich et al., PRL '05

28. TAMR in metals TAMR TMR NiFe ab-initio calculations
Shick, Maca, Masek,
Jungwirth, PRB '06
NiFe
TAMR
TMR
Bolotin,Kemmeth, Ralph,
cond-mat/
TMR ~TAMR >>AMR
Viret et al.,
cond-mat/
Fe, Co break junctions TAMR >TMR

29. EXPERIMENT
Spin Hall Effect
2DHG
2DEG VT VD

30. Q VD Source Drain Gate VG Single Electron Transistor Vg = 0
 Coulomb blockade
Vg  0 Q0
e2/2C
Q=ne - discrete
Q0=CgVg - continuous
Q0=-ne  blocked
Q0=-(n+1/2)e  open

31. Coulomb blockade anisotropic magnetoresistance
Spin-orbit coupling
Band structure (group velocities,
scattering rates, chemical potential) depend on
If lead and dot different
(different carrier concentrations in our (Ga,Mn)As SET)
electric &
magnetic
control of Coulomb blockade oscillations

32. CBAMR if change of |(M)| ~ e2/2C
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

33. CBAMR  new device concepts

34. Electrically generated spin polarization in normal semiconductors
SPIN HALL EFFECT

35. Ordinary Hall effect B I V
Lorentz force deflect charged-particles towards the edge B
_ _ _ _ _ _ _ _ _ _ _ FL I V
Detected by measuring transverse voltage

36. Spin-orbit coupling “force” deflects like-spin particles
Spin Hall effect
Spin-orbit coupling “force” deflects like-spin particles
V=0 _ _ _ _
FSO
non-magnetic
FSO I
Spin-current generation in non-magnetic systems
without applying external magnetic fields
Spin accumulation without charge accumulation
excludes simple electrical detection

37. Szedge Lso ~ jzbulk tso tso=h/so : (intrinsic) spin-precession time
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

38. SHE experiment in GaAs/AlGaAs 2DHG
1.5 m
channel n p y x z
LED 1 2
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

39. 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
1.5 m
channel n p y x z
SHE microchip,
100A
high-field lab. equipment,
100 A

40. I Spin and Anomalous Hall effects V Simple electrical measurement
Spin-orbit coupling “force” deflects like-spin particles I _
FSO
majority
minority V
InMnAs
Simple electrical measurement
of magnetization

41. Skew scattering off impurity potential (Extrinsic SHE/AHE)

42. SO-coupling from host atoms (Intrinsic SHE/AHE)
bands from l=0 atomic orbitals  weak SO
(electrons in GaAs)
bands from l>0 atomic orbitals  strong SO
(holes in GaAs)
Since I am the first talk and the topic of spin-orbit coupling will come up often let me introduce its basic notion. The spin orbit coupling interactions is nothing but an effective magnetic field interaction felt by a moving charge due to a changing electric field due to its relative motion in a potential generating such an electric field. Maxwell’s equations show us that this relative motion of the charge and the electric field induces an effective magnetic field proportional to the orbital momentum of the quasiparticle.
As illustrated in the equation shown the spin quantization axis for such a

43. 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]
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]
Experiment
sAH  1000 (W cm)-1
Theroy
sAH  750 (W cm)-1

44. Hall effects family
Ordinary: carrier density and charge; magnetic field sensing
Quantum: text-book example a strongly correlated many-electron 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

46. e- Spintronics Beff s Beff Bex + Beff Bex Ferromagnetism
Coulomb repulsion & Pauli exclusion principle V
Beff p s
Spin-orbit coupling
Dirac eq. in external field V(r) & 2nd-order
in v /c around non-relativistic limit
Beff
Bex + Beff
Bex
FM without SO-coupling
GaAs valence band
As p-orbitals  large SO
GaMnAs valence band
FM & large SO