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Report
Anisotropic magnetoresistance effects in ferromagnetic
semiconductor and metal devices
Tomas Jungwirth
Institute of Physics ASCR
Alexander Shick, Jan Mašek, Josef Kudrnovský,
František Máca, Karel Výborný, Jan Zemen,
Vít Novák, Kamil Olejník, et al.
Hitachi Labs., UK & Japan
Jorg Wunderlich, Byong-Guk Park, Andrew Irvine,
David Williams, Akira, Sugawara, et al.
University of Nottingham
Bryan Gallagher, Tom Foxon,
Richard Campion, Kevin Edmonds,
Andrew Rushforth, Chris King et al.
University of Texas and Texas A&M
Allan MacDonald, Jairo Sinova
University of Wuerzburg
Polish Academy of Sciences
Laurens Molenkamp, Charles Gould
Tomasz Dietl, et al.
Tohoku University
Hideo Ohno, et al.
Outline
1. Intro - basic micromagnetics in DMSs
2. DMS materials science
3. AMR effects in DMSs and metals – devices and physics
(Ga,Mn)As: an archetypical dilute moment FM semiconductor
Ga
SW-transf.  Jpd SMn . shole
As-p-like holes
Mn
As
Mn
Mn-d-like local
moments
Dilute Mn-doped SC:
sensitive to doping; 100smaller Ms than in conventional metal FMs
Mn-Mn coupling mediated by holes in SO-coupled SC valence bands:
sensitive to gating, comparable magnetocrystalline anisotropy energy and stiffness to metal FMs
For not too strong p-d hybridization:
kinetic-exchange (Jpd) & host SC bands provides simple yet often semiquantitative description
MF-like M(T);
square hysteresis loops
1 mm
500 nm
Macro (100’s m) domains;
8K
10-100 nm domain walls (~A/K)
reflecting combined T-dependent
uniaxial and cubic anisotropies
22 K
One
Strain controlled micromagnetics and
current induced DW dynamics 
tunable 100x smaller critical currents
than in metals
Huge hysteretic MR tunable by gate
due to CBAMR  spintronic transistor
(b)
0.1-1 m
… plus weak dipolar crosslinks 
prospect for dense integration
of magnetic microelements
One
Outline
1. Intro - basic micromagnetics in DMSs
2. DMS materials science
3. AMR effects in DMSs and metals – devices and physics
coupling strength / Fermi energy
Magnetism in systems with coupled dilute moments
and delocalized band electrons
band-electron density / local-moment density
(Ga,Mn)As
GaAs VB
GaAs:Mn extrinsic semiconductor
Mn-acceptor level (IB)
GaMnAs disordered VB
2.2x1020 cm-3
VB-IB
VB-CB

Short-range ~ M . 
s potential
- additional Mn-hole binding
- ferromagnetism
- scattering
MIT in GaAs:Mn at order of magnitude higher doping than quoted in text books
MIT in p-type GaAs:
- shallow acc. (30meV) ~ 1018 cm-3
- Mn (110meV) ~1020 cm-3
Mobilities:
- 3-10x larger in GaAs:C
- similar in GaAs:Mg or InAs:Mn
> 2% Mn: metallic but strongly disordered
  Mn spacing
Model:
SO-coupled, exch.-split Bloch VB & disorder
- conveniently simple and increasingly
meaningful as metallicity increases
- no better than semi-quantitative
MnGa solubility limit
Covalent SCs do not like doping
 self-compensation by interstitial Mn
Interstitial MnInt is detrimental to magnetic order
charge and moment compensation defect
+
Mnsub
As
MnInt
Mnsub
Can be annealed out
MnInt
Tc 95K in as-grown (9% Mn)
theory & exp.
to 173 in annealed (6% Mnsub)
Ga
but MnGa < nominal Mn
Weak hybrid.
Delocalized holes
long-range coupl.
Search for optimal III-V host:
optimal combination of hole delocalization,
InSb, InAs, GaAs
d5
p-d coupling strength, low self-compensation
Strong hybrid.
Impurity-band holes
short-range coupl.
GaP, AlAs
d5d4
no holes
d
GaN
d4
I-II-Mn-V ferromgantic semiconductors
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 doping by Li-Zn
stoichiometry adjustment
Outline
1. Intro - basic micromagnetics in DMSs
2. DMS materials science
3. AMR effects in DMSs and metals – devices and physics
Anisotropic, SO-coupled,
exchange-split hole bands
M || <100>
M || <111>
Chemical potential 
CBAMR
M
Tunneling DOS 
TAMR
M
I
Impurity scattering rates 
AMR
I
Coulomb blockade AMR – anisotropic chemical potential
Source
Q VD
Drain
Gate
VG

Q( M )
U   dQ'VD ( Q' ) 
e
0
[110]
[010] M
F
Q
[100]
[110]
[010]


( Q  Q0 )2
( M ) C
U
& Q0  CG [ VG  VM ( M )] &VM 
2C
e
CG
electric
& magnetic
control of Coulomb blockade oscillations
Worth trying to look for CBAMR in SO-coupled room-Tc metal FMs
• 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
Tunneling AMR – anisotropic TDOS
TAMR in GaMnAs
Au
GaMnAs
Au
Anisotropc tunneling amplitudes
M perp.
Resistance
AlOx
Magnetisation in plane
~ 1-10% in metallic GaMnAs
M in-plane
Huge when approaching MIT in GaMnAs
TAMR in metals
theory
experiment
Anisotropic magnetoresistance
EXPERIMENT
THEORY
Semiquantitative numerical understanding in GaMnAs
Qualitative physical (analytical) picture
SO & polarized scatterers
anisotropic scattering

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