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

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.

Outline

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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

Outline

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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~

x=0.07%

1%

2.5%

7%

Conventional semiconductor picture of MIT reminiscent of p-GaAs:Zn

Jungwirth et al. PRB ’07


Ohno, Dietl et al. Science ’98,’00; Jungwirth et al. PRB ’99

<<0.1% Mn

~0.1% Mn

>1% Mn~

(Ga,Mn)As

(Ga,Mn)As

Novak et al. PRL ’08


>1% Mn~

(Ga,Mn)As

(Ga,Mn)As

Ni

d/d

T~c

v

T

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Ferromagnetically split itinerant bands reminiscent of conventional FMs Fe, Co, Ni,..



Tunable by doping

and by gating


Owen et al. NJP ’09 3%Mn8%

(Ga,Mn)As: combined FM and SC properties in one system

Microscopics of the conventional semiconductor valence-band picture

long-range Coulomb

MnGa- acceptor

~30 meV

Ga

As


short-range central cell

long-range Coulomb

MnGa- acceptor

Ga

AsMn p

Ga p

~30 meV

~1.5 eV



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



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.



As p

Mn d

long-range Coulomb

MnGa- acceptor

Ga

AsMn d

Mn p

Ga p

<<0.1% Mn

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>1% Mn~

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

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)

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

Outline

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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

Impurity-band picture: binding primarily due to short-range potentials (screening and IB broadening play minor role)


As p

0.1eV

long-range Coulomb

MnGa- acceptor

Ga

As


Mn d

Mn p

Ga p


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

0.1eV Mn-d Microscopic realization of IB picture #2


As p Mn d

Mn

As

||

||||~

2

dE

pVd

0.1eV Mn-d

TBAd : no detached narrow (<0.1eV) IB at >0.2% Mn

Shifted by 1.5eV

0.1eV Mn-d

Similarity between TBAd and LDA:both shift Mn-d upwards and enhance p-d hybridization

TBAd

LDA

3 eV

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)

0.1eV Microscopic realization of IB picture #3


As p Mn d

As-p

Mn d

As

As

||

||||~

2

dE

dVp

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


As p

long-range Coulomb

MnGa- acceptor

Ga

As


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)

Outline

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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

~)( 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

00~)( SSSST ii

Fisher&Langer, PRL‘68 ~)( dFsingular

Nickel

UdF ~)~(


Eu0.95Gd0.05S


00~)( SSSST ii

Fisher&Langer, PRL‘68 ~)( dFsingular

Nickel

UdF ~)~(


GaMnAsEu0.95Gd0.05S

Novak et al., PRL‘08


Materials prepared to minimize unintentional impurities and non-uniformity

Annealing sequence ofone (Ga,Mn)As material

Materials prepared to minimize unintentional impurities and non-uniformity

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

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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

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

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