Ferromagnetic semiconductors for spintronics Theory concepts and experimental overview

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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 AM
• Jairo Sinova, et al.

University of Texas Allan MaDonald, et al.

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Electric field controlled spintronics
From storage to logic
HDD, MRAM controlled by Magnetic field
Spintronic Transistor control by electric gates
STT MRAM spin-polarized charge current
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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
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Hard disk drive
First hard disc (1956) - classical electromagnet
for read-out
1 bit 1mm x 1mm
MBs
From PC hard drives ('90) to micro-discs -
spintronic read-heads
1 bit 10-3mm x 10-3mm
10s-100s GBs
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Dawn of spintronics
Magnetoresistive read element
Inductive read/write element
Anisotropic magnetoresistance (AMR) 1850s ?
1990s Giant magnetoresistance (GMR) 1988 ?
1997
Fert Grunberg, Nobel Prize 07
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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
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Spin-orbit coupling
nucleus rest frame
electron rest frame
2
2
Lorentz transformation ? Thomas precession
Spintronics its all about spin and charge of
electron communicating
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SO coupling from relativistic QM
quantum mechanics special relativity ? Dirac
equation


Ep2/2m E? ih d/dt p? -ih d/dr
E2/c2p2m2c2 (Emc2 for p0)
Spin
HSO (2nd order in v/c around the
non-relativistic limit)
Anisotropic Magneto-Resistance
1 MR effect
Current sensitive to magnetization direction
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Ferromagnetism Pauli exclusion principle
Coulomb repulsion
DOS
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)

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Giant Magneto-Resistance
DOS
SO-coupling not utilized
?? ? ??
?AP
gt
?P
10 MR effect
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Tunneling Magneto-Resistance
More direct link between transport and spin-split
bands
DOS? ? DOS?
100 MR effect
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Spin Transfer Torque writing
Slonczewski JMMM 96
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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
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Dilute moment ferromagnetic semiconductors
More tricky than just hammering an iron nail in a
silicon wafer
GaAs - standard III-V semiconductor Group-II Mn
- dilute magnetic moments
holes (Ga,Mn)As - ferromagnetic
semiconductor
Ohno et al. Science 98
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Strongly spin-split and spin-orbit coupled
carriers in a semiconductor
As-p-like holes
Mn-d-like local moments
Strong SO due to the As p-shell (L1) character
of the top of the valence band
Dietl et al., Abolfath et al. PRB 01
Beff
Bex Beff
AMR, TMR,
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Dilute moment nature of ferromagnetic
semiconductors

• Key problems with increasing MRAM capacity (bit
  density)
• Unintentional dipolar cross-links
• External field addressing neighboring bits

10-100x weaker dipolar fields
10-100x smaller Ms
10-100x smaller currents for switching
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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. arXiv0807.0906
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Tc below room-temperature issue
increasing Mn-doping
Wang, et al. arXiv0808.1464 Olejnik et al., PRB
08

• Low-Tc inherent feature of dilute moments but Tc
  ? 200K for 10 (Ga,Mn)As compared to Tc300K in
  the 100 MnAs, i.e., Tcs are already remarkable
  and the quest is still on
• New spintronics paradigms applicable to
  conventional ferromagnets or semiconductors

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AMR
TMR
FM exchange int.
Spin-orbit int.
TAMR
FM exchange int.
Discovered in GaMnAs Gould et al. PRL04
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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
ab intio theory
TAMR is generic to SO-coupled systems including
room-Tc FMs
experiment
Park et al PRL '08
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Optimizing TAMR in transition-metal structures
Consider uncommon TM combinations e.g. Mn/W ?
voltage-dependent upto 100 TAMR
Shick, et al PRB 08
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Devices utilizing M-dependent electro-chemical
potentials FM SET
SO-coupling ? ??(M)
magnetic
electric
control of CB oscillations
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(Ga,Mn)As nano-constriction SET
SO-coupling ? ??(M)
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
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Complexity of the relation between SO
exchange-split bands and transport
Complexity of the device design
Magnitude and sensitivity to electric fields of
the MR
Chemical potential ? CBAMR
SET
Tunneling DOS ? TAMR
Tunneling device
Group velocity lifetime ? AMR
Resistor
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Spintronics in conventional semiconductors
Datta-Das transistor
Datta and Das, APL 99
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Anomalous Hall effect
KarplusLuttinger intrinsic AHE mechanism revived
in Ga1-xMnxAs
KarplusLuttinger 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
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Spin Hall effect spin-dependent deflection ?
transverse edge spin polarization
Anomalous Hall effect
Spin Hall effect
_
_
FSO
M
_
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
SHE mikrocip, 100?A
supercondicting magnet, 100 A
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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
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(Ga,Mn)As material
5 d-electrons with L0 ? S5/2 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
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Ferromagnetic semiconductor GaAsMn
Exchange-split, SO-coupled, itinerant holes
EF
spin ?
1 Mn
ltlt 1 Mn
gt2 Mn
DOS
Energy
spin ?
onset of ferromagnetism near MIT
As-p-like holes localized on Mn acceptors
valence band As-p-like holes
As-p-like holes
Mn-d-like local moments
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Mnhole spin-spin interaction
As-p
Mn-d
hybridization
Hybridization ? like-spin level repulsion ? Jpd S
? shole AF interaction
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Equivalence between microscopic hybridization
(weak) picture and kinetic-exchange model
Microscopic (Anderson) Hamiltonian
Schrieffer-Wolf transformation
k0 approx.
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Mean-field ferromagnetic Mn-Mn coupling mediated
by holes
heff Jpd ltSgt x
Hole Fermi surfaces
Heff Jpd ltsholegt -x
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Fluctuations around the MF state
eMF - Jpd Ss
H Jpd S . s Jpd /2 ( S2TOT - S2 - s2)
STOT S - s
Antiferromagnetic coupling (Jpd gt 0)
eGS Jpd /2 (S-s)(S-s1) - S(S1) -s(s1)
- Jpd (Sss)
e GS lt eMF
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Magnetism in systems with coupled dilute moments
and delocalized band electrons
Jungwirth et al, RMP '06
(Ga,Mn)As
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Delocalized holes long-range coupl.
Weak hybrid.
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
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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
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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 GaAsC - similar in
GaAsMg or InAsMn
gt 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
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(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
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Optimized (Ga,Mn)As materials
MnGa doping
1.5
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Wang, et al. arXiv0808.1464 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 gt6 MnGa
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• 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
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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)
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MIT in GaAsMn at order of magnitude higher
doping than quoted in text books
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Curie point transport anomaly
Ordered magnetic semiconductors
Disordered DMSs
Eu? - chalcogenides
Broad peak near Tc and disappeares with annealing
(higher uniformity)???
Sharp critical contribution to resistivity at Tc
magnetic susceptibility
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Scattering off correlated spin-fluctuations
FisherLanger, PRL68
singular
singular
Ni, Fe
Eu0.95Cd0.05S
Tc
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In GaMnAs ?Fd?-? ? sharp singularity at Tc in
d?/dT
Annealing sequence
T/Tc-1
Optimized GaMnAs materials with x4-12 and
Tc80-185K very well behaved FMs
Novak et al., PRL 08
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Conclusions
(Ga,Mn)As and related FS

• Spintronic field-effect transistors

CBAMR

• New paradigms for spintronics applicable to
  conventional FM and SC

• Well behaved ferromagnet compatible with
  standard SC technologies