1. Institute of Physics ASCR Hitachi Cambridge, Univ. Cambridge
Ferromagnetic semiconductors for spintronics Theory concepts and experimental overview
Tomas Jungwirth
University of Nottingham
Bryan Gallagher, Tom Foxon,
Richard Campion, Kevin Edmonds,
Andrew Rushforth, Chris King et al.
Institute of Physics ASCR
Jan Mašek, Josef Kudrnovský, František Máca, Alexander Shick, Karel Výborný, Jan Zemen,
Vít Novák, Kamil Olejník, et al.
Hitachi Cambridge, Univ. Cambridge
Jorg Wunderlich, Andrew Irvine, David Williams, Elisa de Ranieri, Byonguk Park, Sam Owen, et al.
Texas A&M
Jairo Sinova, et al.
University of Texas
Allan MaDonald, et al.

2. Electric field controlled spintronics Spintronic Transistor
From storage to logic
HDD, MRAM
controlled by
Magnetic field
STT MRAM
spin-polarized
charge current
Spintronic Transistor
control by
electric gates
Magnetic race track memory
I think you can remove the history of spintronics devices. You have also too much symbol in your up graph 2

3. Current spintronics with FM metals
FM semiconductors: all features of current spintronics plus much more
Basic magnetic and magnetotransport properties of (Ga,Mn)As and related FS

4. First hard disc (1956) - classical electromagnet for read-out
Hard disk drive
First hard disc (1956) - classical electromagnet for read-out
1 bit: 1mm x 1mm
MB’s
From PC hard drives ('90)
to micro-discs - spintronic read-heads
1 bit: 10-3mm x 10-3mm
10’s-100’s GB’s

5. Anisotropic magnetoresistance (AMR) – 1850’s  1990’s
Dawn of spintronics
Magnetoresistive read element
Inductive read/write element
Anisotropic magnetoresistance (AMR) – 1850’s  1990’s
Giant magnetoresistance (GMR) – 1988  1997
Fert & Grunberg, Nobel Prize 07

6. MRAM – universal memory
fast, small, low-power, durable, and non-volatile
2006- First commercial 4Mb MRAM
RAM chip that actually won't forget  instant on-and-off computers

8. 2 2 e- Spin-orbit coupling nucleus rest frame electron rest frame
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
Lorentz transformation  Thomas precession e-
Spintronics: it’s all about spin and charge
of electron communicating

9. Anisotropic Magneto-Resistance
SO coupling from relativistic QM
quantum mechanics & special relativity  Dirac equation
E=p2/2m
E ih d/dt
p -ih d/dr
E2/c2=p2+m2c2
(E=mc2 for p=0)
Spin
& HSO (2nd order in v/c around
the non-relativistic limit)
Anisotropic Magneto-Resistance
~ 1% MR effect
Current sensitive to magnetization direction

10. Ferromagnetism = Pauli exclusion principle & Coulomb repulsion
total wf antisymmetric =
orbital wf antisymmetric
* spin wf symmetric
(aligned) e-
DOS e-
DOS
Robust (can be as strong as bonding in solids)
Strong coupling to magnetic field
(weak fields = anisotropy fields needed
only to reorient macroscopic moment)

11. Giant Magneto-Resistance
DOS
SO-coupling not utilized
  
AP
> P
~ 10% MR effect

12. Tunneling Magneto-Resistance
More direct link between transport and spin-split bands
DOS  DOS
~ 100% MR effect

13. Spin Transfer Torque writing
Slonczewski JMMM 96

14. Current spintronics with FM metals
FM semiconductors: all features of current spintronics plus much more
Basic magnetic and magnetotransport properties of (Ga,Mn)As and related FS

15. Ga As Mn Dilute moment ferromagnetic semiconductors
More tricky than just hammering an iron nail in a silicon wafer Mn Ga As
GaAs - standard III-V semiconductor
Group-II Mn - dilute magnetic moments
& holes
(Ga,Mn)As - ferromagnetic
semiconductor
Ohno et al. Science 98

16. Mn Ga As As-p-like holes Mn-d-like local moments Beff s Beff
Strongly spin-split and spin-orbit coupled carriers in a semiconductor Mn Ga As
As-p-like holes
Mn-d-like local
moments V
Beff p s
Strong SO due to the As p-shell (L=1) character of the top of the valence band
Dietl et al., Abolfath et al. PRB 01
Beff
Bex + Beff
AMR, TMR, …

17. Ga Mn As Dilute moment nature of ferromagnetic semiconductors
Key problems with increasing MRAM capacity (bit density):
Unintentional dipolar cross-links
External field addressing neighboring bits
One
10-100x weaker dipolar fields
10-100x smaller Ms Ga As Mn
10-100x smaller currents for switching

18. Low-voltage gating (charge depletion) of ferromagnetic semiconductors
Low-voltage dependent R & MR
(Ga,Mn)As p-n junction FET
Switching by short low-voltage pulses
Magnetization
Owen, et al. arXiv:

19. Ga Mn As Tc below room-temperature issue
increasing Mn-doping
Wang, et al. arXiv:
Olejnik et al., PRB 08
Low-Tc inherent feature of dilute moments but Tc  200K for 10% (Ga,Mn)As compared to Tc~300K in the 100% MnAs, i.e., Tc’s are already remarkable and the quest is still on
New spintronics paradigms applicable to conventional ferromagnets or semiconductors

20. AMR TMR TAMR FM exchange int.: Spin-orbit int.: FM exchange int.: Au
Discovered in GaMnAs Gould et al. PRL’04

21. Bias-dependent magnitude and sign of TAMR
Shick et al PRB ’06, Moser et al. PRL 07,Parkin et al PRL ‘07, Park et al PRL '08
TAMR is generic to SO-coupled systems including room-Tc FMs
ab intio theory
Park et al PRL '08
experiment 21

22. Optimizing TAMR in transition-metal structures
spontaneous moment
magnetic susceptibility
spin-orbit coupling
Consider uncommon TM combinations
e.g. Mn/W  voltage-dependent upto ~100% TAMR
Shick, et al PRB ‘08

23. Devices utilizing M-dependent electro-chemical potentials: FM SET
[010] M
[110]
[100]
Source
Drain
Gate VG VD Q
SO-coupling  (M)
electric &
magnetic
control of CB oscillations

24. (Ga,Mn)As nano-constriction SET
SO-coupling  (M)
(Ga,Mn)As nano-constriction SET
[010] M
[110]
[100]
~ 1mV in GaMnAs
~ 10mV in FePt
Low-gate-voltage controlled huge magnitude and sign of MR  very sensitive spintronic transistor
Wunderlich et al, PRL '06

25. Group velocity & lifetime
Magnitude and sensitivity to electric fields of the MR
Complexity of the device design
Complexity of the relation between SO & exchange-split bands and transport
Chemical potential
 CBAMR
SET
Tunneling DOS
 TAMR
Tunneling device
Group velocity & lifetime
 AMR
Resistor

26. Spintronics in conventional semiconductors
Datta-Das transistor
Datta and Das, APL ‘99

27. I V _ Anomalous Hall effect
FSO V
Anomalous Hall effect
Karplus&Luttinger intrinsic AHE mechanism revived in Ga1-xMnxAs
Karplus&Luttinger PR ‘54
Jungwirth et al. PRL ‘02,APL ’03
Experiment
sAH  1000 (W cm)-1
Theory
sAH  750 (W cm)-1
intrinsic AHE in pure Fe:
Yao et al. PRL ‘04

28. spin-dependent deflection  transverse edge spin polarization
Spin Hall effect
spin-dependent deflection  transverse edge spin polarization
Anomalous Hall effect
Spin Hall effect V _ _ I _
FSO M _
FSO I
Murakami et al Science 04, SInova et al. PRL 04,
Wunderlich et al. PRL ‘05
Same magnetization achieved
by external field generated by
a superconducting magnet
with 106 x larger dimensions &
106 x larger currents
Spin Hall effect detected optically
in GaAs-based structures n p
SHE mikročip, 100A
supercondicting magnet, 100 A

29. Current spintronics with FM metals
FM semiconductors: all features of current spintronics plus much more
Basic magnetic and magnetotransport properties of (Ga,Mn)As and related FS

30. Ga As Mn (Ga,Mn)As material 5 d-electrons with L=0
 S=5/2 local moment
moderately shallow
acceptor (110 meV)
 hole
- Mn local moments too dilute
(near-neighbors couple AF)
- Holes do not polarize
in pure GaAs
- Hole mediated Mn-Mn
FM coupling

31. EF DOS Energy Ga As-p-like holes As Mn Mn-d-like local moments
Ferromagnetic semiconductor GaAs:Mn
Exchange-split, SO-coupled, & itinerant holes
spin  EF
<< 1% Mn
~1% Mn
>2% Mn
DOS
Energy
spin 
onset of ferromagnetism near MIT
As-p-like holes localized on Mn acceptors
valence band As-p-like holes Mn Ga As
As-p-like holes
Mn-d-like local
moments

32. Ga As Mn As-p Mn-d hybridization Mn–hole spin-spin interaction
Hybridization  like-spin level repulsion  Jpd S  shole AF interaction

33. Equivalence between microscopic hybridization (weak) picture
and kinetic-exchange model
Microscopic (Anderson) Hamiltonian
Schrieffer-Wolf transformation
k=0 approx.

34. heff = Jpd <S> || x
Mean-field ferromagnetic Mn-Mn coupling mediated by holes
heff = Jpd <S> || x
Hole Fermi surfaces Mn As Ga
Heff = Jpd <shole> || -x
holes

35. e GS < eMF eMF = - Jpd Ss H = Jpd S . s = Jpd /2 ( S2TOT - S2 - s2)
Fluctuations around the MF state
eMF = - Jpd Ss
H = Jpd S . s = Jpd /2 ( S2TOT - S2 - s2)
Antiferromagnetic coupling (Jpd > 0)
STOT = S - s
eGS = Jpd /2 [ (S-s)(S-s+1) - S(S+1) -s(s+1) ] = - Jpd (Ss+s)
e GS < eMF

36. Magnetism in systems with coupled dilute moments
and delocalized band electrons
coupling strength / Fermi energy
band-electron density / local-moment density
Jungwirth et al, RMP '06
(Ga,Mn)As

37. d5 d d4 Nature of Mn-impurity in III-V host
Weak hybrid.
Delocalized holes
long-range coupl.
Nature of Mn-impurity in III-V host
Kudrnovsky et al. PRB 07
InSb,
GaAs d5
GaP
More localized holes
shorter-range coupl.
Strong hybrid.
no holes d
hole-Mn exchange = hybridization & splitting between Mn d-level and valence band edge
GaN d4

38. Hole-mediated Mn-Mn exchange in III-V host
Weak hybrid.
Mean-field but
low TcMF
InSb d5
Strong hybrid.
Large TcMF but
low stiffness
GaP
GaAs seems close to the optimal III-V host

39. Random Mn  disorder MIT in p-type GaAs:
- shallow acc. (30meV) ~ 1018 cm-3
- Mn (110meV) ~1020 cm-3
Short-range ~ M . s potential
Together with central-cell
shifts MIT to ~1% Mn (1020 cm-3)
Mobilities:
- 3-10x larger in GaAs:C
- similar in GaAs:Mg or InAs:Mn
> 1-2% Mn: metallic but strongly disordered
Model:
SO-coupled, exch.-split Bloch VB & disorder
- conveniently simple and increasingly
meaningful as metallicity increases
- no better than semi-quantitative

40. (Ga,Mn)As growth
high-T growth
optimal-T growth
Low-T MBE to avoid precipitation & high enough T to maintain 2D growth
need to optimize T & stoichiometry for each Mn-doping
Detrimental interstitial AF-coupled Mn-donors
 need to anneal out (Tc can increase by more than 100K)
Annealing also needs to be optimized for each Mn-doping

41. Optimized (Ga,Mn)As materials
MnGa doping
1.5% 8%
Wang, et al. arXiv:
Olejnik et al., PRB 08, Novak et al. PRL 08
t=(Tc-T)/Tc
Tc in (Ga,Mn)As semiquantitative theory understanding (within a factor of ~2)
No saturation seen in theory and in optimized (Ga,Mn)As samples yet
Material synthesis becomes increasingly tedious for >6% MnGa

42. I-II-Mn-V ferromgantic semiconductors (so far in theory only)
III = I + II  Ga = Li + Zn
GaAs and LiZnAs are twin semiconductors
Prediction that Mn-doped are also twin ferromagnetic semiconductors
No limit for Mn-Zn (II-II) substitution
Independent carrier (holes or
electrons) doping by Li-Zn
stoichiometry adjustment
Masek, et al. PRL 07

43. Transport in (Ga,Mn)As: MIT
GaAs VB
Mn-acceptor level (IB)
Transport in (Ga,Mn)As: MIT
GaMnAs disordered VB
Jungwirth et al, PRB '07
2.2x1020 cm-3
VB-IB
VB-CB  
Short-range ~ M . s potential
Together with central-cell
shifts MIT to ~1% Mn (1020 cm-3)

44. MIT in GaAs:Mn at order of magnitude higher doping than quoted in text books

45. Ordered magnetic semiconductors
Curie point transport anomaly
Ordered magnetic semiconductors
Disordered DMSs
Eu - chalcogenides
Sharp critical contribution to resistivity at Tc ~ magnetic susceptibility
Broad peak near Tc and disappeares with annealing (higher uniformity)???

46. Scattering off correlated spin-fluctuations
Fisher&Langer, PRL‘68
singular
singular
Ni, Fe
Eu0.95Cd0.05S Tc

47. In GaMnAs F~d-  sharp singularity at Tc in d/dT
Annealing sequence
T/Tc-1
Optimized GaMnAs materials with x~4-12% and Tc~80-185K: very well behaved FMs
Novak et al., PRL ‚08

48. (Ga,Mn)As and related FS:
Conclusions
(Ga,Mn)As and related FS:
Spintronic field-effect transistors
[010] M
[110]
[100]
CBAMR
New paradigms for spintronics applicable to conventional FM and SC
Well behaved ferromagnet compatible with standard SC technologies