Theory of ferromagnetic semiconductor Ga,MnAs

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Theory of ferromagnetic semiconductor (Ga,Mn)As
Tomas Jungwirth
University of Nottingham
Bryan Gallagher, Richard Campion, Tom Foxon,
Kevin Edmonds, Andrew Rushforth, et al.

Institute of Physics ASCR Jan Maek, Frantiek
Máca, Josef Kudrnovský, Alexandr Shick,Karel
Výborný, Jan Zemen, Vít Novák, Kamil Olejník, et
al.

• Texas AM
• Jairo Sinova, et al.

Charles University, Prague Petr Nemec, Petra
Horodyská, Nada Tesarová, Eva Rozkotová, et al.

University of Texas Allan MaDonald, et al.
Hitachi Cambridge, Univ. Cambridge Jorg
Wunderlich, Andrew Irvine, Elisa de Ranieri,
Byonguk Park, et al.
H. Ohno,T. Dietl, M. Sawicki, C. Gould, L.
Molenkamp, et al.

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Outline
1a) Phenomenology of the conventional
semiconductor valence band picture of
(Ga,Mn)As 1b) Microscopics of the valence band
picture
2a) Phenomenology of the narrow detached impurity
band pictures 2b) Search for microscopic
realization of the impurity band pictures

• Revisiting experimental characteristics of
  (Ga,Mn)As epilayers with Tc up to 190K and high
  uniformity

3
Outline
1a) Phenomenology of the conventional
semiconductor valence band picture of
(Ga,Mn)As 1b) Microscopics of the valence band
picture
2a) Phenomenology of the narrow detached impurity
band pictures 2b) Search for microscopic
realization of the impurity band pictures

• Revisiting experimental characteristics of
  (Ga,Mn)As epilayers with Tc up to 190K and high
  uniformity

4
FM (Ga,Mn)As conventional valence-band picture
of a doped semiconductor
Ohno, Dietl et al. Science 98,00 Jungwirth et
al. PRB 99
Jungwirth et al. PRB 07
ltlt0.1 Mn
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FM (Ga,Mn)As conventional valence-band picture
of a doped semiconductor
Ohno, Dietl et al. Science 98,00 Jungwirth et
al. PRB 99
0.1 Mn
Jungwirth et al. PRB 07
ltlt0.1 Mn
Conventional semiconductor picture of MIT
reminiscent of p-GaAsZn
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FM (Ga,Mn)As conventional valence-band picture
of a doped semiconductor
Novak et al. PRL 08
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FM (Ga,Mn)As conventional valence-band picture
of a doped semiconductor
Ferromagnetically split itinerant bands
reminiscent of conventional FMs Fe, Co, Ni,..
Novak et al. PRL 08
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(Ga,Mn)As combined FM and SC properties in one
system
Tunable by doping
Owen et al. NJP 09
and by gating
Novak et al. PRL 08
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Microscopics of the conventional semiconductor
valence-band picture
long-range Coulomb
30 meV
Ga
As
MnGa- acceptor
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Microscopics of the conventional semiconductor
valence-band picture
short-range central cell
long-range Coulomb
30 meV
Ga
As
Mn p
1.5 eV
Ga p
MnGa- acceptor
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Microscopics of the conventional semiconductor
valence-band picture
short-range p-d hybridization
0.1eV MnGa acceptor state
short-range central cell
?
30 meV
long-range Coulomb
Ga
As p ?
Mn d ?
As
Linnarsson PRB97
Mn d ?
MnGa- acceptor
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Microscopics of the conventional semiconductor
valence-band picture
short-range p-d hybridization
no bound-state above V.B.
short-range central cell
As p ?
Mn d ?
broad resonance in V.B.
Mn d ?
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Microscopics of the conventional semiconductor
valence-band picture
ltlt0.1 Mn
short-range p-d hybridization
short-range central cell
As p ?
Mn d ?
Mn d ?
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Consistent valence-band pictures from
full-potential density-functional in LDAU and
spd tight-binding approximation (tabulated atomic
levels and overlaps)
Harrison 80
Disorder-averaged band-structures
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Consistent valence-band pictures from LDAU, TBA,
kinetic-exchange k . p
Top VB with similar orbital character and DOS as
in host GaAs (dominant As(Ga)-p with smaller
admixture of Mn-d)

• Consistent with experiment where
• Mn d-level at 4 eV
• ? N0? ?/Sx 1- 3 eV (S5/2)

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Consistent valence-band pictures from LDAU, TBA,
kinetic-exchange k . p
Top VB with similar orbital character and DOS as
in host GaAs (dominant As(Ga)-p with smaller
admixture of Mn-d)

• Plausible one-electron band structure
• (overall DOS, character and strength
• of exchange-splitting and spin-orbit
• coupling
• Much simpler than e.g. in Fe, Co, Ni,..
• Physics still potentially very complex
• (strong disorder, band-tail localization,
• vicinity of MIT, thermal fluctuations of
• magnetization, electron-electron
• interaction effects, ..) ? often not
• sufficiently discussed in VB based
• theories

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Outline
1a) Phenomenology of the conventional
semiconductor valence band picture of
(Ga,Mn)As 1b) Microscopics of the valence band
picture
2a) Phenomenology of the narrow detached impurity
band pictures 2b) Search for microscopic
realization of the impurity band pictures

• Revisiting experimental characteristics of
  (Ga,Mn)As epilayers with Tc up to 190K and high
  uniformity

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Impurity band picture 1
Mn-p
Impurity band picture 2
Mn-d
Impurity band picture 3
As-p
microscopic realizations of single MnGa bound
state
microscopic band-structures at dopings of FM
(Ga,Mn)As
ltlt0.1 Mn
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Impurity-band picture binding primarily due to
short-range potentials
(screening and IB broadening play
minor role)
0.1eV
short-range p-d hybridization
short-range central cell
As p ?
Mn d ?
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Microscopic realization of IB picture 1 cannot
use DFT (too much ab initio) ? TBA ideal tool
0.1eV
Mn-p
short-range central cell
Ga
Mn
TBAp no bound-state even for Mn p-level shifts
gt 10s eV
see also Tang, Flatté et al. PRL04
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Microscopic realization of IB picture 2
0.1eV
Mn-d
short-range p-d hybridization
As
Mn
As p ?
Mn d ?
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0.1eV
Mn-d
Shifted by 1.5eV
TBAd no detached narrow (lt0.1eV) IB at gt0.2 Mn
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0.1eV
Mn-d
Similarity between TBAd and LDA both shift Mn-d
upwards and enhance p-d hybridization
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0.1eV
Mn-d
TBAd not dominant Mn d but still mixed
with As(Ga) p Exchange
splitting N0? gt then experimental limits (1-3 eV)
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As-p
Microscopic realization of IB picture 3
0.1eV
short-range p-d hybridization
As
As
Mn d ?
As p ?
Mn d ?
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As-p
0.1eV
Enhanced 2.5x
Mn d ?
spd-TBApd bound-state indeed dominated by
As(Ga)p ( spatial extent determined by fitted
binding energy) ? practical model for single or
few Mn no detached narrow (lt0.1eV) IB at gt0.2
Mn Exchange splitting N0? gt then experimental
limits (1-3 eV)
Tang, Flatté et al. PRL04,05
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Bound state without long-range Coulomb potential
? likely overestimated exchange splitting
(distortion) of one-electron DOS in FM
(Ga,Mn)As 0.1eV acceptor level is too shallow
for having narrow (lt0.1eV) IB at gt0.2 Mn in any
of the microscopic band-structure realizations
(spd-TBAd, spd-TBApd)
short-range p-d hybridization
short-range central cell
As p ?
Mn d ?
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Outline
1a) Phenomenology of the conventional
semiconductor valence band picture of
(Ga,Mn)As 1b) Microscopics of the valence band
picture
2a) Phenomenology of the narrow detached impurity
band pictures 2b) Search for microscopic
realization of the impurity band pictures

• Revisiting experimental characteristics of
  (Ga,Mn)As epilayers with Tc up to 190K and high
  uniformity

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Critical behavior of resistivity near Tc
Ordered magnetic semiconductors
Disordered DMSs
as-grown
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Eu? chalcogenides
Tc
4
? (103 ?cm)
2
annealed
Tc
Tc
0
100
300
T (K)
Broad peak near Tc which disappeares in annealed
(presumably more uniform) materials
Sharp critical behavior of resistivity at Tc
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Carrier scattering off correlated
spin-fluctuations
FisherLanger, PRL68
Strongest scattering (resonance) for correlated
fluctuations of length-scale comparable to Fermi
wavelength
Eu0.95Gd0.05S
Nickel
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Carrier scattering off correlated
spin-fluctuations
FisherLanger, PRL68
Eu0.95Gd0.05S
Nickel
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Carrier scattering off correlated
spin-fluctuations
FisherLanger, PRL68
GaMnAs
Eu0.95Gd0.05S
Nickel
Novak et al., PRL08
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Materials prepared to minimize unintentional
impurities and non-uniformity
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Materials prepared to minimize unintentional
impurities and non-uniformity
Annealing sequence of one (Ga,Mn)As material
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5nm, 7 Mn
100nm, 1.7 Mn
Non-universal behavior seen in thick, ultra-thin
or low-doped materials (latter most often used
for gating)
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Summary
1) Ab initio (LDAU), spd-TBA, and
kinetic-exchange k.p realizations of the
valence band picture capture similar
microscopic physics consistent with conventional
description of doped semiconductors
2) No microscopic realization has been
found for one-particle DOS with a narrow
detached impurity band in FM (Ga,Mn)As
3) Revisiting experimental material properties of
(Ga,Mn)As may resolve some of the
outstanding open problems in the field
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