Theory of ferromagnetic semiconductor (Ga,Mn)As

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 Mašek, František Máca, Josef Kudrnovský, Alexandr Shick,Karel Výborný, Jan Zemen, Vít Novák,Kamil Olejník, et al. Texas A&M Jairo Sinova, et al. Charles University, Prague Petr Němec, Petra Horodyská, Naďa Tesařová, Eva Rozkotová, et al. University of Texas Allan MaDonald, et al. Hitachi Cambridge, Univ. Cambridge Jorg Wunderlich, Andrew Irvine,Elisa de Ranieri, Byonguk Park, etal. H. Ohno,T. Dietl, M. Sawicki, C. Gould, L. Molenkamp, et al.

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

7% 2.5% >1% Mn ~ 1% x=0.07% FM (Ga,Mn)As: conventional valence-band picture of a doped semiconductor Ohno, Dietl et al. Science ’98,’00; Jungwirth et al. PRB ’99 Jungwirth et al. PRB ’07 <<0.1% Mn

7% 2.5% >1% Mn ~ 1% x=0.07% 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 Jungwirth et al. PRB ’07 <<0.1% Mn Conventional semiconductor picture of MIT reminiscent of p-GaAs:Zn

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

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

3%Mn 8% (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

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 long-range Coulomb ~30 meV Ga As Mn p ~1.5 eV Ga p MnGa-acceptor

Mn p Ga p 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 Mn d  As p  As Linnarsson PRB’97 Mn d  MnGa-acceptor

long-range Coulomb Ga As Mn p Ga p 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 Mn d  As p  broad resonance in V.B. Mn d 

>1% Mn ~ long-range Coulomb Ga As  h+ Mn p  h+ Ga p MnGa-acceptor Microscopics of the conventional semiconductor valence-band picture <<0.1% Mn short-range p-d hybridization short-range central cell Mn d  As p  Mn d 

As Ga Mn 6% Consistent valence-band pictures from full-potential density-functional in LDA+U and spd tight-binding approximation (tabulated atomic levels and overlaps) Harrison ‘80 Disorder-averaged band-structures

LDA+U x= DOS  Energy (eV) k . p: N0 1.2 eV 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) • Consistent with experiment where: • Mn d-level at ~4 eV  N0 = /Sx ~ 1- 3 eV (S=5/2)

LDA+U x= DOS  Energy (eV) 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) • 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

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

long-range Coulomb Ga As Mn p Ga p MnGa-acceptor 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 Mn d  As p 

Mn p Ga p 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 > 10’s eV see also Tang, Flatté et al. PRL’04

Microscopic realization of IB picture #2 0.1eV Mn-d short-range p-d hybridization As Mn Mn d  As p 

0.1eV Mn-d Shifted by 1.5eV TBAd: no detached narrow (<0.1eV) IB at >0.2% Mn

TBAd 3 eV LDA 0.1eV Mn-d 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)

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

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 (<0.1eV) IB at >0.2% Mn Exchange splitting N0 > then experimental limits (1-3 eV) Tang, Flatté et al. PRL’04,’05

long-range Coulomb Ga As Mn p Ga p MnGa-acceptor 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) short-range p-d hybridization short-range central cell Mn d  As p 

Critical behavior of resistivity near Tc Ordered magnetic semiconductors Disordered DMSs as-grown 6 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

singular singular Carrier scattering off correlated spin-fluctuations Fisher&Langer, PRL‘68 Strongest scattering (resonance) for correlated fluctuations of length-scale comparable to Fermi wavelength Eu0.95Gd0.05S Nickel

singular singular Carrier scattering off correlated spin-fluctuations Fisher&Langer, PRL‘68 Eu0.95Gd0.05S Nickel

singular singular Carrier scattering off correlated spin-fluctuations Fisher&Langer, PRL‘68 Eu0.95Gd0.05S GaMnAs Nickel 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)

 h+  h+ 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

Theory of ferromagnetic semiconductor (Ga,Mn)As