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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.
Hitachi Cambridge, Univ. Cambridge Jorg Wunderlich, Andrew Irvine, Elisa de Ranieri,
Byonguk Park, et al.
Institute of Physics ASCRJan Mašek, František Máca, Josef Kudrnovský,
Alexandr Shick,Karel Výborný, Jan Zemen, Vít Novák, Kamil Olejník, et al.
University of Texas Allan MaDonald, et al.
Texas A&MJairo Sinova, et al.Charles University, Prague
Petr Němec, Petra Horodyská, Naďa Tesařová, Eva Rozkotová, et al.
H. Ohno,T. Dietl, M. Sawicki, C. Gould, L. Molenkamp, et al.
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Outline
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h+
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
3) Revisiting experimental characteristics of (Ga,Mn)As epilayers with Tc up to ~190K and high uniformity
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Outline
h+
h+
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
3) Revisiting experimental characteristics of (Ga,Mn)As epilayers with Tc up to ~190K and high uniformity
![Page 4: Theory of ferromagnetic semiconductor (Ga,Mn)As Tomas Jungwirth University of Nottingham Bryan Gallagher, Richard Campion, Tom Foxon, Kevin Edmonds, Andrew](https://reader030.vdocument.in/reader030/viewer/2022032802/56649e155503460f94b00323/html5/thumbnails/4.jpg)
x=0.07%
1%
2.5%
7%
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 <<0.1% Mn
>1% Mn~
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x=0.07%
1%
2.5%
7%
Conventional semiconductor picture of MIT reminiscent of p-GaAs:Zn
Jungwirth et al. PRB ’07
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
~0.1% Mn
>1% Mn~
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(Ga,Mn)As
(Ga,Mn)As
Novak et al. PRL ’08
FM (Ga,Mn)As: conventional valence-band picture of a doped semiconductor
>1% Mn~
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(Ga,Mn)As
(Ga,Mn)As
Ni
d/d
T~c
v
T
h+
h+
Ferromagnetically split itinerant bands reminiscent of conventional FMs Fe, Co, Ni,..
Novak et al. PRL ’08
FM (Ga,Mn)As: conventional valence-band picture of a doped semiconductor
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Tunable by doping
and by gating
Novak et al. PRL ’08
Owen et al. NJP ’09 3%Mn8%
(Ga,Mn)As: combined FM and SC properties in one system
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Microscopics of the conventional semiconductor valence-band picture
long-range Coulomb
MnGa- acceptor
~30 meV
Ga
As
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Microscopics of the conventional semiconductor valence-band picture
short-range central cell
long-range Coulomb
MnGa- acceptor
Ga
AsMn p
Ga p
~30 meV
~1.5 eV
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Microscopics of the conventional semiconductor valence-band picture
short-range central cell
short-range p-d hybridization
As p Mn d
Mn d
~0.1eV MnGa acceptor state
long-range Coulomb
MnGa- acceptor
Ga
AsMn p
Ga p
~30 meV
Linnarsson PRB’97
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Microscopics of the conventional semiconductor valence-band picture
short-range p-d hybridization
As p
Mn d
long-range Coulomb
MnGa- acceptor
Ga
AsMn d
Mn p
Ga p
short-range central cellno bound-state above V.B.
broad resonance in V.B.
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Microscopics of the conventional semiconductor valence-band picture
short-range p-d hybridization
As p
Mn d
long-range Coulomb
MnGa- acceptor
Ga
AsMn d
Mn p
Ga p
<<0.1% Mn
h+
h+
short-range central cell
>1% Mn~
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Consistent valence-band pictures from full-potential density-functional in LDA+U and spd tight-binding approximation (tabulated atomic levels and overlaps)
6%
Ga As
Mn
Harrison ‘80
Disorder-averaged band-structures
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Consistent valence-band pictures from LDA+U, TBA, kinetic-exchange k . p
Consistent with experiment where:
Mn d-level at ~4 eV
N0 = /Sx ~ 1- 3 eV (S=5/2)
Energy (eV)
DO
S
LDA+U
x=
k . p: N0 1.2 eV
Top VB with similar orbital character and DOS as in host GaAs(dominant As(Ga)-p with smaller admixture of Mn-d)
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Consistent valence-band pictures from LDA+U, TBA, kinetic-exchange k . p
Energy (eV)
DO
S
LDA+U
x=
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
h+
h+
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
3) Revisiting experimental characteristics of (Ga,Mn)As epilayers with Tc up to ~190K and high uniformity
![Page 18: Theory of ferromagnetic semiconductor (Ga,Mn)As Tomas Jungwirth University of Nottingham Bryan Gallagher, Richard Campion, Tom Foxon, Kevin Edmonds, Andrew](https://reader030.vdocument.in/reader030/viewer/2022032802/56649e155503460f94b00323/html5/thumbnails/18.jpg)
Mn-p Impurity band picture #1
Impurity band picture #2Mn-d
As-p Impurity band picture #3
<<0.1% Mn >1% Mn~
microscopic realizations of single MnGa bound state
microscopic band-structuresat dopings of FM (Ga,Mn)As
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Impurity-band picture: binding primarily due to short-range potentials (screening and IB broadening play minor role)
short-range p-d hybridization
As p
0.1eV
long-range Coulomb
MnGa- acceptor
Ga
As
short-range central cell
Mn d
Mn p
Ga p
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short-range central cell
Mn p
Ga p
0.1eV Mn-p Microscopic realization of IB picture #1cannot use DFT (too much ab initio) TBA ideal tool
TBAp : no bound-state even for Mn p-level shifts > 10’s eV
Ga
see also Tang, Flatté et al. PRL’04
Mn
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0.1eV Mn-d Microscopic realization of IB picture #2
short-range p-d hybridization
As p Mn d
Mn
As
||
||||~
2
dE
pVd
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0.1eV Mn-d
TBAd : no detached narrow (<0.1eV) IB at >0.2% Mn
Shifted by 1.5eV
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0.1eV Mn-d
Similarity between TBAd and LDA:both shift Mn-d upwards and enhance p-d hybridization
TBAd
LDA
3 eV
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0.1eV Mn-dd
TBAd : not dominant Mn d but still mixed with As(Ga) p Exchange splitting N0 > then experimental limits (1-3 eV)
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0.1eV Microscopic realization of IB picture #3
short-range p-d hybridization
As p Mn d
As-p
Mn d
As
As
||
||||~
2
dE
dVp
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0.1eV As-p
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 (<0.1eV) IB at >0.2% Mn
Exchange splitting N0 > then experimental limits (1-3 eV)
Enhanced ~2.5x
Tang, Flatté et al. PRL’04,’05
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short-range p-d hybridization
As p
long-range Coulomb
MnGa- acceptor
Ga
As
short-range central cell
Mn d
Mn p
Ga p
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 (<0.1eV) IB at >0.2% Mn in any of the microscopic band-structure realizations (spd-TBAd, spd-TBApd)
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Outline
h+
h+
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
3) Revisiting experimental characteristics of (Ga,Mn)As epilayers with Tc up to ~190K and high uniformity
![Page 29: Theory of ferromagnetic semiconductor (Ga,Mn)As Tomas Jungwirth University of Nottingham Bryan Gallagher, Richard Campion, Tom Foxon, Kevin Edmonds, Andrew](https://reader030.vdocument.in/reader030/viewer/2022032802/56649e155503460f94b00323/html5/thumbnails/29.jpg)
Ordered magnetic semiconductors Disordered DMSs
Sharp critical behavior of resistivity at Tc Broad peak near Tc which disappeares in annealed (presumably more uniform) materials
Euchalcogenides
Tc
as-grown
annealed
Tc
6
4
2
0 100 300
(1
03
cm)
T (K)
Tc
Critical behavior of resistivity near Tc
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~)( dFsingular
Nickel
Carrier scattering off correlated spin-fluctuations
UdF ~)~(
vcdTdUdTd /~/singular
Eu0.95Gd0.05S
Strongest scattering (resonance) for correlated fluctuations of length-scale
comparable to Fermi wavelength
00~)( SSSST ii
Fisher&Langer, PRL‘68
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00~)( SSSST ii
Fisher&Langer, PRL‘68 ~)( dFsingular
Nickel
UdF ~)~(
vcdTdUdTd /~/singular
Eu0.95Gd0.05S
Carrier scattering off correlated spin-fluctuations
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00~)( SSSST ii
Fisher&Langer, PRL‘68 ~)( dFsingular
Nickel
UdF ~)~(
vcdTdUdTd /~/singular
GaMnAsEu0.95Gd0.05S
Novak et al., PRL‘08
Carrier scattering off correlated spin-fluctuations
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Materials prepared to minimize unintentional impurities and non-uniformity
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Annealing sequence ofone (Ga,Mn)As material
Materials prepared to minimize unintentional impurities and non-uniformity
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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
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1) Ab initio (LDA+U), 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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