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 ASCR Jan 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&M Jairo 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  h+ h+  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  Revisiting experimental characteristics of (Ga,Mn)As epilayers with Tc up to ~190K and high uniformity

Outline  h+ h+  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  Revisiting experimental characteristics of (Ga,Mn)As epilayers with Tc up to ~190K and high uniformity

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 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 ~

(Ga,Mn)As Novak et al. PRL ’08 FM (Ga,Mn)As: conventional valence-band picture of a doped semiconductor >1% Mn ~

(Ga,Mn)As Ni d  /dT~c v T  h+ h+  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

Tunable by doping and by gating Novak et al. PRL ’08 Owen et al. NJP ’09 3%Mn 8% (Ga,Mn)As: combined FM and SC properties in one system

Microscopics of the conventional semiconductor valence-band picture long-range Coulomb Mn Ga - acceptor ~30 meV Ga As

Microscopics of the conventional semiconductor valence-band picture short-range central cell long-range Coulomb Mn Ga - acceptor Ga As Mn p Ga p ~30 meV ~1.5 eV

Microscopics of the conventional semiconductor valence-band picture short-range central cell short-range p-d hybridization As p  Mn d   ~0.1eV Mn Ga acceptor state long-range Coulomb Mn Ga - acceptor Ga As Mn p Ga p ~30 meV Linnarsson PRB’97

Microscopics of the conventional semiconductor valence-band picture short-range p-d hybridization As p  Mn d  long-range Coulomb Mn Ga - acceptor Ga As Mn d  Mn p Ga p short-range central cell no bound-state above V.B. broad resonance in V.B.

Microscopics of the conventional semiconductor valence-band picture short-range p-d hybridization As p  Mn d  long-range Coulomb Mn Ga - acceptor Ga As Mn d  Mn p Ga p <<0.1% Mn  h+ h+ h+h+ short-range central cell >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  N 0  =  /Sx ~ 1- 3 eV (S=5/2) Energy (eV) DOS LDA+U  x= k. p: N 0   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) DOS 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  h+ h+  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  Revisiting experimental characteristics of (Ga,Mn)As epilayers with Tc up to ~190K and high uniformity

Mn-p Impurity band picture #1 Impurity band picture #2 Mn-d As-p Impurity band picture #3 <<0.1% Mn >1% Mn ~ microscopic realizations of single Mn Ga bound state microscopic band-structures at dopings of FM (Ga,Mn)As

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 Mn Ga - acceptor Ga As short-range central cell Mn d  Mn p Ga p

short-range central cell Mn p Ga p 0.1eV Mn-p Microscopic realization of IB picture #1 cannot use DFT (too much ab initio)  TBA ideal tool TBA p : 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 short-range p-d hybridization As p  Mn d  Mn As

0.1eV Mn-d TBA d : no detached narrow ( 0.2% Mn Shifted by 1.5eV

0.1eV Mn-d Similarity between TBA d and LDA: both shift Mn-d upwards and enhance p-d hybridization TBA d LDA 3 eV

0.1eV Mn-d d TBA d : not dominant Mn d but still mixed with As(Ga) p Exchange splitting N 0  > then experimental limits (1-3 eV)

0.1eV Microscopic realization of IB picture #3 short-range p-d hybridization As p  Mn d  As-p Mn d  As

0.1eV As-p Mn d  spd-TBA pd : 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 ( 0.2% Mn Exchange splitting N 0  > then experimental limits (1-3 eV) Enhanced ~2.5x Tang, Flatté et al. PRL’04,’05

short-range p-d hybridization As p  long-range Coulomb Mn Ga - 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 ( 0.2% Mn in any of the microscopic band-structure realizations (spd-TBA d, spd-TBA pd )

Outline  h+ h+  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  Revisiting experimental characteristics of (Ga,Mn)As epilayers with Tc up to ~190K and high uniformity

Ordered magnetic semiconductors Disordered DMSs Sharp critical behavior of resistivity at T c Broad peak near T c which disappeares in annealed (presumably more uniform) materials Eu  chalcogenides TcTc as-grown annealed TcTc  (10 3  cm) T (K) TcTc Critical behavior of resistivity near T c

singular Nickel Carrier scattering off correlated spin-fluctuations singular Eu 0.95 Gd 0.05 S Strongest scattering (resonance) for correlated fluctuations of length-scale comparable to Fermi wavelength Fisher&Langer, PRL‘68

singular Nickel singular Eu 0.95 Gd 0.05 S Carrier scattering off correlated spin-fluctuations

Fisher&Langer, PRL‘68 singular Nickel singular GaMnAs Eu 0.95 Gd 0.05 S Novak et al., PRL‘08 Carrier scattering off correlated spin-fluctuations

Materials prepared to minimize unintentional impurities and non-uniformity

Annealing sequence of one (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  h+ h+  h+ h+ 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