Making semiconductors magnetic: new materials properties, devices, and future JAIRO SINOVA Texas A&M University Institute of Physics ASCR Hitachi Cambridge Jorg Wunderlich, A. Irvine, et al Institute of Physics ASCR Tomas Jungwirth, Vít Novák, et al Texas A&M L. Zarbo Ohio State University Oct 2 nd 2009 University of Nottingham Bryan Gallagher, Tom Foxon, Richard Campion, et al. NRI SWAN

OUTLINE Motivation Ferromagnetic semiconductor materials: –(Ga,Mn)As - general picture –Growth, physical limits on T c –Related FS materials (searching for room temperature) –Understanding critical behavior in transport Ferromagnetic semiconductors & spintronics –Tunneling anisotropic magnetoresistive device –Transistors (4 types)

Technologically motivated and scientifically fueled Incorporate magnetic properties with semiconductor tunability (MRAM, etc) Understanding complex phenomena: Spherical cow of ferromagnetic systems (still very complicated) Engineered control of collective phenomena Generates new physics: Tunneling AMR Coulomb blockade AMR Nanostructure magnetic anisotropy engineering ENGINEERING OF QUANTUM MATERIALS More knobs than usual in semiconductors: density, strain, chemistry/pressure, SO coupling engineering

1.Create a material that marriages the tunability of semiconductors and the collective behavior of ferromagnets; once created search for room temperature systems 2.Study new effects in this new material and utilize in metal-based spintronics 3.Develop a three-terminal gated spintronic device to progress from sensors & memories to transistors & logic Ferromagnetic semiconductor research : strategies

(Ga,Mn)As GENERAL PICTURE

Ferromagnetic semiconductors GaAs - standard III-V semiconductor Group-II Mn - dilute magnetic moments & holes (Ga,Mn)As - ferromagnetic semiconductor Need true FSs not FM inclusions in SCs Mn Ga As Mn +

Ga As What happens when a Mn is placed in Ga sites: Mn–hole spin-spin interaction hybridization Hybridization  like-spin level repulsion  J pd S Mn  s hole interaction Mn-d As-p In addition to the Kinetic-exchange coupling, for a single Mn ion, the coulomb interaction gives a trapped hole (polaron) which resides just above the valence band 5 d-electrons with L=0  S=5/2 local moment intermediate acceptor (110 meV)  hole

Mn Ga As Mn EFEF DOS Energy spin  spin  Transition to a ferromagnet when Mn concentration increases GaAs:Mn – extrinsic p-type semiconductor FM due to p-d hybridization (Zener local-itinerant kinetic-exchange) valence band As-p-like holes As-p-like holes localized on Mn acceptors << 1% Mn ~1% Mn >2% Mn onset of ferromagnetism near MIT Mn Ga As Mn Ga As Mn

Low-T MBE to avoid precipitation High enough T to maintain 2D growth  need to optimize T & stoichiometry for each Mn-doping Inevitable formation of interstitial Mn- double-donors compensating holes and moments  need to anneal out but without loosing Mn Ga high-T growth optimal-T growth (Ga,Mn)As GROWTH

Interstitial Mn out-diffusion limited by surface-oxide GaMnAs GaMnAs-oxide Polyscrystalline 20% shorter bonds Mn I ++ O Optimizing annealing-T another key factor Rushforth et al, ‘08 x-ray photoemission Olejnik et al, ‘08 10x shorther annealing with etch

(Ga,Mn)As GENERAL THEORY

HOW DOES ONE GO ABOUT UNDERSTANDING SUCH SYSTEMS 1.One could solve the full many body S.E.: not possible AND not fun 2.Combining phenomenological models (low degrees of freedom) and approximations and comparison to other computational technieques while checking against experiments “This is the art of condensed matter science, an intricate tango between theory and experiment whose conclusion can only be guessed at while the dance is in progress” A.H.M et al., in “Electronic Structure and Magnetism in Complex Materials” (2002).

Theoretical Approaches to DMSs First Principles LSDA PROS: No initial assumptions, effective Heisenberg model can be extracted, good for determining chemical trends CONS: Size limitation, difficulty dealing with long range interactions, lack of quantitative predictability, neglects SO coupling (usually) Microscopic TB models k.p  Local Moment PROS: “Unbiased” microscopic approach, correct capture of band structure and hybridization, treats disorder microscopically (combined with CPA), very good agreement with LDA+U calculations CONS: neglects (usually) coulomb interaction effects, difficult to capture non-tabulated chemical trends, hard to reach large system sizes PROS: simplicity of description, lots of computational ability, SO coupling can be incorporated, CONS: applicable only for metallic weakly hybridized systems (e.g. optimally doped GaMnAs), over simplicity (e.g. constant Jpd), no good for deep impurity levels (e.g. GaMnN) Jungwirth, Sinova, Masek, Kucera, MacDonald, Rev. of Mod. Phys. 78, 809 (2006)

Magnetism in systems with coupled dilute moments and delocalized band electrons (Ga,Mn)As coupling strength / Fermi energy band-electron density / local-moment density

Which theory is right? KP Eastwood Fast principles Jack Impurity bandit vs Valence Joe

How well do we understand (Ga,Mn)As? In the metallic optimally doped regime GaMnAs is well described by a disordered-valence band picture: both dc-data and ac-data are consistent with this scenario. The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V metallic DMSs very well in the optimally annealed regime: Ferromagnetic transition temperatures   Magneto-crystalline anisotropy and coercively   Domain structure   Anisotropic magneto-resistance   Anomalous Hall effect   MO in the visible range   Non-Drude peak in longitudinal ac-conductivity  Ferromagnetic resonance  Domain wall resistance  TAMR  Transport critical behaviour  Infrared MO effects  TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity formation energies, lattice constant variations upon doping

EXAMPLE: MAGNETO-OPTICAL EFFECTS IN THE INFRARED

T c LIMITS AND STRATEGIES

 Curie temperature limited to ~110K.  Only metallic for ~3% to 6% Mn  High degree of compensation  Unusual magnetization (temperature dep.)  Significant magnetization deficit But are these intrinsic properties of GaMnAs ?? “110K could be a fundamental limit on T C ” As Ga Mn Problems for GaMnAs (late 2002)

Can a dilute moment ferromagnet have a high Curie temperature ? The questions that we need to answer are: 1.Is there an intrinsic limit in the theory models (from the physics of the phase diagram) ? 2.Is there an extrinsic limit from the ability to create the material and its growth (prevents one to reach the optimal spot in the phase diagram)? EXAMPLE OF THE PHYSICS TANGO

COMBINATION OF THEORY APPROACHES PREDICTS: T c linear in Mn Ga local moment concentration; falls rapidly with decreasing hole density in more than 50% compensated samples; nearly independent of hole density for compensation < 50%. Jungwirth, Wang, et al. Phys. Rev. B 72, (2005) Intrinsic properties of (Ga,Mn)As

Extrinsic effects: Interstitial Mn - a magnetism killer Yu et al., PRB ’02: ~10-20% of total Mn concentration is incorporated as interstitials Increased T C on annealing corresponds to removal of these defects. Mn As Interstitial Mn is detrimental to magnetic order:  compensating double-donor – reduces carrier density  couples antiferromagnetically to substitutional Mn even in low compensation samples Blinowski PRB ‘03, Mašek, Máca PRB '03

Mn Ga and Mn I partial concentrations Microscopic defect formation energy calculations: No signs of saturation in the dependence of Mn Ga concentration on total Mn doping Jungwirth, Wang, et al. Phys. Rev. B 72, (2005) As grown Materials calculation

Annealing can vary significantly increases hole densities. Low Compensation Obtain Mn sub assuming change in hole density due to Mn out diffusion Open symbols & half closed as grown. Closed symbols annealed High compensation Jungwirth, Wang, et al. Phys. Rev. B 72, (2005) Experimental hole densities: measured by ordinary Hall effect

Theoretical linear dependence of Mn sub on total Mn confirmed experimentally Mn sub Mn Int Obtain Mn sub & Mn Int assuming change in hole density due to Mn out diffusion Jungwirth, Wang, et al. Phys. Rev. B 72, (2005) SIMS: measures total Mn concentration. Interstitials only compensation assumed Experimental partial concentrations of Mn Ga and Mn I in as grown samples

Can we have high Tc in Diluted Magnetic Semicondcutors? T c linear in Mn Ga local (uncompensated) moment concentration; falls rapidly with decreasing hole density in heavily compensated samples. Define Mn eff = Mn sub -Mn Int NO INTRINSIC LIMIT NO EXTRINSIC LIMIT There is no observable limit to the amount of substitutional Mn we can put in

8% Mn Open symbols as grown. Closed symbols annealed High compensation Linear increase of Tc with Mn eff = Mn sub -Mn Int Tc as grown and annealed samples ● Concentration of uncompensated Mn Ga moments has to reach ~10%. Only 6.2% in the current record Tc=173K sample ● Charge compensation not so important unless > 40% ● No indication from theory or experiment that the problem is other than technological - better control of growth-T, stoichiometry

“... Ohno’s ‘98 T c =110 K is the fundamental upper limit..” Yu et al. ‘03 “…T c = K independent of x Mn >10% contradicting Zener kinetic exchange...” Mack et al. ‘08 “Combinatorial” approach to growth with fixed growth and annealing T’s Tc limit in (Ga,Mn)As remains open ` 2008 Olejnik et al 188K!!

- Effective concentration of uncompensated Mn Ga moments has to increase beyond 6% of the current record T c =173K sample. A factor of 2 needed  12% Mn would still be a DMS - Low solubility of group-II Mn in III-V-host GaAs makes growth difficult Low-temperature MBE Strategy A: stick to (Ga,Mn)As - alternative growth modes (i.e. with proper substrate/interface material) allowing for larger and still uniform incorporation of Mn in zincblende GaAs More Mn - problem with solubility Getting to higher Tc: Strategy A

Find DMS system as closely related to (Ga,Mn)As as possible with larger hole-Mn spin-spin interaction lower tendency to self-compensation by interstitial Mn larger Mn solubility independent control of local-moment and carrier doping (p- & n-type) Getting to higher Tc: Strategy B

Weak hybrid. Delocalized holes long-range coupl. Strong hybrid. Impurity-band holes short-range coupl. InSb GaP d5d5 (Al,Ga,In)(As,P) good candidates, GaAs seems close to the optimal III-V host Other (III,Mn)V’s DMSs Mean-field but low T c MF Large T c MF but low stiffness Kudrnovsky et al. PRB 07

Using DEEP mathematics to find a new material 3=1+2 Steps so far in strategy B: larger hole-Mn spin-spin interaction : DONE BUT DANGER IN PHASE DIAGRAM lower tendency to self-compensation by interstitial Mn: DONE larger Mn solubility ? independent control of local-moment and carrier doping (p- & n-type)?

III = I + II  Ga = Li + Zn GaAs and LiZnAs are twin SC Masek, et al. PRB (2006) LDA+U says that Mn-doped are also twin DMSs L As p-orb. Ga s-orb. As p-orb. EFEF It can be n and p doped!!! No solubility limit for group-II Mn substituting for group-II Zn !!!!

UNDERSTANDING CRITICAL BEHAVIOUR IN TRANSPORT

Towards spintronics in (Ga,Mn)As: FM & transport Dense-moment MS F << d  -  Eu  - chalcogenides Dilute-moment MS F ~ d  -  Critical contribution to resistivity at T c ~ magnetic susceptibility Broad peak near T c disappeares with annealing (higher uniformity)??? 

TcTc EuCdSe When density of carriers is smaller than density of local moments what matters is the long range behavior of Γ (which goes as susceptibility) When density of carriers is similar to density of local moments what matters is the short range behavior of Γ (which goes as the energy) Ni TcTc

Optimized materials with x=4-12.5% and Tc=80-185K Remarkably universal both below and above Tc Annealing sequence d  /dT singularity at T c – consistent with k F ~d  -  V. Novak, et al “Singularity in temperature derivative of resistivity in (Ga,Mn)As at the Curie point”, Phys. Rev. Lett. 101, (2008).

OUTLINE Motivation Ferromagnetic semiconductor materials: –(Ga,Mn)As - general picture –Growth, physical limits on T c –Related FS materials (searching for room temperature) –Understanding critical behavior in transport Ferromagnetic semiconductors & spintronics –Tunneling anisotropic magnetoresistive device –Transistors (4 types)

AMR ~ 1% MR effect TMR ~ 100% MR effect TAMR Exchange split & SO-coupled bands: Exchange split bands: Au discovered in (Ga,Mn)As Gold et al. PRL’04

ab intio theory Shick, et al, PRB '06, Park, et al, PRL '08 TAMR in metal structures experiment Park, et al, PRL '08 Also studied by Parkin et al., Weiss et al., etc.

DMS DEVICES

Gating of highly doped (Ga,Mn)As: p-n junction FET p-n junction depletion estimates Olejnik et al., ‘08 ~25% depletion feasible at low voltages (Ga,Mn)As/AlOx FET with large gate voltages, Chiba et al. ‘06

AMR Increasing  and decreasing AMR and T c with depletion Tc

Persistent variations of magnetic properties with ferroelectric gates Stolichnov et al., Nat. Mat.‘08

Electro-mechanical gating with piezo-stressors Rushforth et al., ‘08 Strain & SO  Electrically controlled magnetic anisotropies via strain

Single-electron transistor Two "gates": electric and magnetic (Ga,Mn)As spintronic single-electron transistor Huge, gatable, and hysteretic MR Wunderlich et al. PRL ‘06

& electric & magnetic control of Coulomb blockade oscillations Q0Q0 Q0Q0 e 2 /2C  [ 010 ]  M [ 110 ] [ 100 ] [ 110 ] [ 010 ] SO-coupling  (M) SourceDrain Gate VGVG VDVD Q Single-electron charging energy controlled by V g and M Theory confirms chemical potential anisotropies in (Ga,Mn)As & predicts CBAMR in SO-coupled room-T c metal FMs

Variant p- or n-type FET-like transistor in one single nano-sized CBAMR device 0 ON OFF 1 0 ON OFF 1 V DD V A V B V A V B Vout OFF ON OFF ON OFF AB Vout ON OFF ON OFF ON 1 1 OFF 1 “OR” Nonvolatile programmable logic

V DD V A V B V A V B Vout Variant p- or n-type FET-like transistor in one single nano-sized CBAMR device 0 ON OFF 1 0 ON OFF 1 AB Vout “OR” Nonvolatile programmable logic

Physics of SO & exchange SET Resistor Tunneling device Chemical potential  CBAMR Tunneling DOS  TAMR Group velocity & lifetime  AMR Device designMaterials metal FMs FSs FSs and metal FS with strong SO

Conclusion No intrinsic or extrinsic limit to Tc so far: it is a materials growth issue In the metallic optimally doped regime GaMnAs is well described by a disordered-valence band picture: both dc-data and ac-data are consistent with this scenario. The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V metallic DMSs very well in the optimally annealed regime: BUT it is only a peace of the theoretical mosaic with many remaining challenges!! TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity formation energies, lattice constant variations upon doping Ferromagnetic transition temperatures   Magneto-crystalline anisotropy and coercively   Domain structure   Anisotropic magneto-resistance   Anomalous Hall effect   MO in the visible range   Non-Drude peak in longitudinal ac-conductivity  Ferromagnetic resonance  Domain wall resistance  TAMR  Transport critical behaviour  Infrared MO effects 

Allan MacDonald U of Texas Tomas Jungwirth Inst. of Phys. ASCR U. of Nottingham Joerg Wunderlich Cambridge-Hitachi Bryan Gallagher U. Of Nottingham Tomesz Dietl Institute of Physics, Polish Academy of Sciences Other collaborators: John Cerne, Jan Masek, Karel Vyborny, Bernd Kästner, Carten Timm, Charles Gould, Tom Fox, Richard Campion, Laurence Eaves, Eric Yang, Andy Rushforth, Viet Novak Hideo Ohno Tohoku Univ. Laurens Molenkamp Wuerzburg Ewelina Hankiewicz Fordham Univesrsity

· Model Anderson Hamiltonian: (s - orbitals: conduction band; p - orbitals: valence band) + (Mn d - orbitals: strong on-site Hubbard int.  local moment) + (s,p - d hybridization) · Semi-phenomenological Kohn-Luttinger model for heavy, light, and spin-orbit split-off band holes · Local exchange coupling: Mn: S=5/2; valence-band hole: s=1/2; J pd > 0 k.p  Local Moment - Hamiltonian ELECTRONS Mn ELECTRONS-Mn Large S: treat classically

T c LIMITS AND STRATEGIES

Can we have high Tc in Diluted Magnetic Semicondcutors? Define Mn eff = Mn sub -Mn Int (lines – theory, Masek et al 05) NO EXTRINSIC LIMIT Relative Mn concentrations obtained through hole density measurements and saturation moment densities measurements. T c linear in Mn Ga local (uncompensated) moment concentration; falls rapidly with decreasing hole density in heavily compensated samples. NO IDENTIFICATION OF AN INTRINSIC LIMIT Qualitative consistent picture within LDA, TB, and k.p

8% Mn Open symbols as grown. Closed symbols annealed High compensation Linear increase of Tc with Mn eff = Mn sub -Mn Int Tc as grown and annealed samples ● Concentration of uncompensated Mn Ga moments has to reach ~10%. Only 6.2% in the current record Tc=173K sample ● Charge compensation not so important unless > 40% ● No indication from theory or experiment that the problem is other than technological - better control of growth-T, stoichiometry

III = I + II  Ga = Li + Zn GaAs and LiZnAs are twin SC Masek, et al. PRB (2006) LDA+U says that Mn-doped are also twin DMSs n and p type doping through Li/Zn stoichiometry No solubility limit for group-II Mn substituting for group-II Zn !!!!

Indiana & California (‘03): “.. Ohno’s ‘98 T c =110 K is the fundamental upper limit..” Yu et al. ‘03 California (‘08): “…T c = K independent of x Mn >10% contradicting Zener kinetic exchange...” Nottingham & Prague (’08): T c up to 185K so far “Combinatorial” approach to growth with fixed growth and annealing T’s ? Mack et al. ‘08 Tc limit in (Ga,Mn)As remains open