Download (Ga,Mn)As

Theory of ferromagnetic semiconductor (Ga,Mn)As
Tomas Jungwirth
Institute of Physics ASCR
Jan Mašek, František Máca, Josef Kudrnovský,
Alexandr Shick,Karel Výborný, Jan Zemen,
Vít Novák, Kamil Olejník, et al.
University of Nottingham
Bryan Gallagher, Richard Campion,
Tom Foxon, Kevin Edmonds, Andrew
Rushforth, et al.
Charles University, Prague
Petr Němec, Petra Horodyská, Naďa Tesařová, Eva
Rozkotová, et al.
Hitachi Cambridge, Univ. Cambridge
Jorg Wunderlich, Andrew Irvine, Elisa de Ranieri,
Byonguk Park, et al.
Texas A&M
Jairo Sinova, et al.
University of Texas
Allan MaDonald, et al.
H. Ohno,T. Dietl, M. Sawicki, C.
Gould, L. Molenkamp, et al.
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
3)
Revisiting experimental characteristics of
(Ga,Mn)As epilayers with Tc up to ~190K and high
uniformity
 h+
 h+
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
3)
Revisiting experimental characteristics of
(Ga,Mn)As epilayers with Tc up to ~190K and high
uniformity
 h+
 h+
FM (Ga,Mn)As: conventional valence-band picture of a doped semiconductor
Ohno, Dietl et al. Science ’98,’00; Jungwirth et al. PRB ’99
>1% Mn
~
7%
2.5%
1%
x=0.07%
Jungwirth et al. PRB ’07
<<0.1% Mn
FM (Ga,Mn)As: conventional valence-band picture of a doped semiconductor
Ohno, Dietl et al. Science ’98,’00; Jungwirth et al. PRB ’99
7%
>1% Mn
~
2.5%
1%
~0.1% Mn
x=0.07%
Jungwirth et al. PRB ’07
<<0.1% Mn
Conventional semiconductor picture
of MIT reminiscent of p-GaAs:Zn
FM (Ga,Mn)As: conventional valence-band picture of a doped semiconductor
(Ga,Mn)As
>1% Mn
~
(Ga,Mn)As
Novak et al. PRL ’08
FM (Ga,Mn)As: conventional valence-band picture of a doped semiconductor
d/dT~cv
(Ga,Mn)As
Ferromagnetically split itinerant bands
reminiscent of conventional FMs Fe, Co, Ni,..
 h+
Ni
T
 h+
(Ga,Mn)As
Novak et al. PRL ’08
(Ga,Mn)As: combined FM and SC properties in one system
Tunable by doping
3%Mn
Owen et al. NJP ’09
8%
and by gating
Novak et al. PRL ’08
Microscopics of the conventional semiconductor valence-band picture
long-range Coulomb
~30 meV
Ga
As
MnGa- acceptor
Microscopics of the conventional semiconductor valence-band picture
short-range central cell
~30 meV
long-range Coulomb
Ga
As
Mn p
~1.5 eV
Ga p
MnGa- acceptor
Microscopics of the conventional semiconductor valence-band picture
short-range p-d hybridization
~0.1eV MnGa acceptor state

~30 meV
short-range central cell
long-range Coulomb
Ga
Mn d  As p 
As
Linnarsson PRB’97
Mn p
Ga p
Mn d 
MnGa- acceptor
Microscopics of the conventional semiconductor valence-band picture
short-range p-d hybridization
no bound-state above V.B.
short-range central cell
long-range Coulomb
Ga
Mn d  As p 
As
Mn p
broad resonance in V.B.
Ga p
Mn d 
MnGa- acceptor
Microscopics of the conventional semiconductor valence-band picture
<<0.1% Mn
>1% Mn
~
short-range p-d hybridization
 h+

h+
short-range central cell
long-range Coulomb
Ga
Mn d  As p 
As
Mn p
Ga p
Mn d 
MnGa- acceptor
Consistent valence-band pictures from full-potential density-functional in LDA+U
and spd tight-binding approximation (tabulated atomic levels and overlaps)
Harrison ‘80
Ga
As
Mn
6%
Disorder-averaged band-structures
Consistent valence-band pictures from LDA+U, 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)
DOS
LDA+U
x=

Energy (eV)
k . p: N0  1.2 eV
Consistent with experiment where:
 Mn d-level at ~4 eV
 N0 = /Sx ~ 1- 3 eV (S=5/2)
Consistent valence-band pictures from LDA+U, 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)
DOS
LDA+U
x=

 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,..
Energy (eV)
 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
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
3)
Revisiting experimental characteristics of
(Ga,Mn)As epilayers with Tc up to ~190K and high
uniformity
 h+
 h+
Mn-p
Impurity band picture #1
Mn-d
Impurity band picture #2
As-p
Impurity band picture #3
microscopic realizations of
single MnGa bound state
<<0.1% Mn
microscopic band-structures
at dopings of FM (Ga,Mn)As
>1% Mn
~
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
long-range Coulomb
Ga
Mn d  As p 
As
Mn p
Ga p
MnGa- acceptor
0.1eV
Mn-p
Microscopic realization of IB picture #1
cannot use DFT (too much ab initio)
 TBA ideal tool
short-range central cell
Ga
Mn
Mn p
Ga p
TBAp : no bound-state even for Mn p-level shifts > 10’s eV
see also Tang, Flatté et al. PRL’04
0.1eV
Mn-d
Microscopic realization of IB picture #2
short-range p-d hybridization
As
Mn
Mn d  As p 
|  d | V | p |2
~
| Ed |
0.1eV
Mn-d
Shifted by 1.5eV
TBAd : no detached narrow (<0.1eV) IB at >0.2% Mn
0.1eV
Mn-d
TBAd
3 eV
LDA
Similarity between TBAd and LDA:
both shift Mn-d upwards and enhance p-d hybridization
d
0.1eV
Mn-d
TBAd : not dominant Mn d but still mixed
with As(Ga) p
Exchange splitting N0 > then experimental limits (1-3 eV)
0.1eV
As-p
Microscopic realization of IB picture #3
short-range p-d hybridization
As
As
Mn d 
Mn d  As p 
|  p | V | d  |2
~
| Ed |
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
Tang, Flatté et al. PRL’04,’05
no detached narrow (<0.1eV) IB at >0.2% Mn
Exchange splitting N0 > then experimental limits (1-3 eV)
Bound state without long-range Coulomb potential 
likely overestimated exchange splitting (distortion) of
one-electron DOS in FM (Ga,Mn)As
short-range p-d hybridization
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)
short-range central cell
long-range Coulomb
Ga
Mn d  As p 
As
Mn p
Ga p
MnGa- acceptor
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
3)
Revisiting experimental characteristics of
(Ga,Mn)As epilayers with Tc up to ~190K and high
uniformity
 h+
 h+
Critical behavior of resistivity near Tc
Disordered DMSs
as-grown
Eu
chalcogenides
Tc
4
annealed
Tc
0
Sharp critical behavior of resistivity at Tc
6
Tc
100
T (K)
2
 (103 cm)
Ordered magnetic semiconductors
300
Broad peak near Tc which disappeares
in annealed (presumably more uniform)
materials
Carrier scattering off correlated spin-fluctuations
 


 (T ) ~  Si  S0    Si    S0 
singular  (F
 d ) ~ 
Fisher&Langer, PRL‘68
Strongest scattering (resonance) for
correlated fluctuations of length-scale
comparable to Fermi wavelength
Eu0.95Gd0.05S
Nickel
 (F ~ d ) ~ U
singular
d / dT ~ dU / dT  cv
Carrier scattering off correlated spin-fluctuations
 


 (T ) ~  Si  S0    Si    S0 
singular  (F
 d ) ~ 
Fisher&Langer, PRL‘68
Eu0.95Gd0.05S
Nickel
 (F ~ d ) ~ U
singular
d / dT ~ dU / dT  cv
Carrier scattering off correlated spin-fluctuations
 


 (T ) ~  Si  S0    Si    S0 
singular  (F
 d ) ~ 
Eu0.95Gd0.05S
Fisher&Langer, PRL‘68
GaMnAs
Nickel
 (F ~ d ) ~ U
singular
d / dT ~ dU / dT  cv
Novak et al., PRL‘08
Materials prepared to minimize
unintentional impurities and
non-uniformity
Materials prepared to minimize
unintentional impurities and
non-uniformity
Annealing sequence of
one (Ga,Mn)As material
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)
Summary
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
 h+
 h+