Jairo Sinova (TAMU) Challenges and chemical trends in achieving a room temperature dilute magnetic semiconductor: a spintronics tango between theory and.

Jairo Sinova (TAMU) Challenges and chemical trends in achieving a room temperature dilute magnetic semiconductor: a spintronics tango between theory and experiment NERC SWAN Rice University April 28 th 2008

OUTLINE DMS: intro to the phenomenology –General picture –Theoretical approaches to DMSs Are we stuck with low Tc? –Intrinsic limits –Extrinsic limits –Strategies to increase Tc Impurity band and valence band in doped semicondcutors Low doped insulating GaAs:Mn –Activation energy: dc-transport and doping trends –Ac-conductivity and doping trends Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn –Dc-transport: lack of activation energy –Ac-conductivity –Red-shift of ac-conductivity mid-infrared peak in GaMnAs Other successful descriptions of system properties within the disordered- valence band treatment of metallic GaMnAs –Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect Conclusions

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 QUANUTM MATERIALS More knobs than usual in semiconductors: density, strain, chemistry/pressure, SO coupling engineering

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

Ga As Mn 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

(Ga,Mn)As synthesis 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 high-T growth optimal-T 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

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 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)

· 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 THE SIMPLE MODEL ELECTRONS Mn ELECTRONS-Mn Large S: treat classically

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

 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, 165204 (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, 165204 (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, 165204 (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, 165204 (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

Indiana & California (‘03): “.. Ohno’s ‘98 T c =110 K is the fundamental upper limit..” Yu et al. ‘03 California (‘08): “…T c =150-165 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

- 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 !!!!

OUTLINE DMS: intro to the phenomenology –General picture –Theoretical approaches to DMSs Are we stuck with low Tc? –Intrinsic limits –Extrinsic limits –Strategies to increase Tc Impurity band and valence band in doped semiconductors Low doped insulating GaAs:Mn –Activation energy: dc-transport and doping trends –Ac-conductivity and doping trends Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn –Dc-transport: lack of activation energy –Ac-conductivity –Red-shift of ac-conductivity mid-infrared peak in GaMnAs Other successful descriptions of system properties within the disordered- valence band treatment of metallic GaMnAs –Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect Conclusions

Example: Si:P --- shallow impurity where most of the binding energy is hydrogenic-like. MI transition occurs when impurity bound states begin to overlap For GaAs shallow impurities (C,Be,Zn,..) this occurs at 10 18 cm -3 For intermediate impurities (E a ~110 meV) this occurs at higher impurity concentration N Mn ~10 20 cm -3 In Ga 1-x Mn x As x=1% corresponds to a substitutional doping concentration of N Mn ~2.2 x 10 20 cm -3 General picture of MI transition in doped semiconductors

General picture of MI transition in doped semiconductors: cross over from IB to VB

OUTLINE DMS: intro to the phenomenology –General picture –Theoretical approaches to DMSs Are we stuck with low Tc? –Intrinsic limits –Extrinsic limits –Strategies to increase Tc Impurity band and valence band in doped semiconductors Low doped insulating GaAs:Mn –Activation energy: dc-transport and doping trends –Ac-conductivity and doping trends Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn –Dc-transport: lack of activation energy –Ac-conductivity –Red-shift of ac-conductivity mid-infrared peak in GaMnAs Other successful descriptions of system properties within the disordered- valence band treatment of metallic GaMnAs –Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect Conclusions

Low doped insulating GaAs:Mn Activation energy from dc-transport J. S. Blakemore, W. J. Brown, M. L. Stass, and D. A. Woodbury, J. Appl. Phys. 44, 3352 (1973).

Low doped insulating GaAs:Mn Activation energy from dc-transport Sample Mn(4D) has Mn density 1.6 x10 17 cm −3(, M5: 1.1 x10 18 cm−3, M10:1.9 x10 19 cm −3, Mn5A: 9.3 x10 19 cm −3. J. S. Blakemore, W. J. Brown, M. L. Stass, and D. A. Woodbury, J. Appl. Phys. 44, 3352 (1973). M. Poggio, R. C. Myers, N. P. Stern, A. C. Gossard, and D. D. Awschalom, Phys. Rev. B 72, 235313 (2005). MBE grown samples.

Low doped insulating GaAs:Mn Activation energy from dc-transport Infrared photoabsorption crossection measurements in bulk GaAs:Mn. Mn(4): 1.7 x10 17 cm −3, Mn(5): 9.3 x10 18 cm−3. W. J. Brown and J. S. Blakemore, J. Appl. Phys. 43, 2242 (1972). Expected absorption cross section for a non-shallow impurity (peak at 2E a ) Consistent with the E a obtained from the dc-transport, a peak at ~ 200 meV is observed in the weakly doped Mn(4) GaAs:Mn samples. At higher doped sample Mn(5) the peak is slightly red shifted (~ 180 meV) and broadened

Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: dc-transport Jungwirth, Sinova, MacDonald, Gallagher, Novak, Edmonds, Rushforth, Campion, Foxon, Eaves, Olejnik, Masek, Yang, Wunderlich, Gould, Molenkamp, Dietl, Ohno, PRB 07 For Mn doping around 1%, the conductivity curves can no longer be separated into an impurity-band dominated contribution at low temperatures and an activated valence-band dominated contribution at higher temperatures Above 2%, no activation energy is observed even as high as 500 K where activation across the gap takes over

Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: dc-transport Jungwirth, Sinova, MacDonald, Gallagher, Novak, Edmonds, Rushforth, Campion, Foxon, Eaves, Olejnik, Masek, Yang, Wunderlich, Gould, Molenkamp, Dietl, Ohno, PRB 07 same growth conditions but <1% insulating Comparable mobilities of shallow and intermediate acceptor systems

K. S. Burch, et al, Phys. Rev. Lett. 97, 087208 (2006), E. J. Singley, et al, Phys. Rev. Lett. 89, 097203 (2002). E. J. Singley, et al, Phys. Rev. B 68, 165204 (2003). T=292 K T=7 K Associating peak to an IB is implausible because of: (i) the absence of the activated dc-transport counterpart in the high-doped metallic samples, (ii) the blue-shift of this mid-infrared feature with respect to the impurity band transition peak in the NMn 10 19 cm −3 sample, (iii) the appearance of the peak at frequency above 2Ea, (iv) the absence of a marked broadening of the peak with increased doping. Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: ac-absorption experiments

W. Songprakob, R. Zallen, D. V. Tsu, and W. K. Liu, J. Appl. Phys. 91, 171 (2002). J. Sinova, et al. Phys. Rev. B 66, 041202 (2002). GaAs x=5% C-doped (shallow acceptor) experiments at a doping well within the metal side Virtual crystal approximation (no localization effects). hole density: p=0.2, 0.3,....., 0.8 nm -3 Hirakawa, et al Phys. Rev. B 65, 193312 (2002)

Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: red-shift of the IR peak in GaMnAs At low doping near the MI transition Non-momentum conserved transitions to localized states at the valence edge take away spectral weight from the low frequency As metallicity/doping increases the localized states near the band edge narrow and the peak red-shifts as the inter-band part adds weight to the low-frequency part

FINITE SIZE EXACT DIAGONALIZATION STUDIES S.-R. E. Yang, J. Sinova, T. Jungwirth, Y.P. Shim, and A.H. MacDonald, PRB 67, 045205 (03) No-localization approximation Exact diagonalization results in reasonable agreement with as-grown samples x=4.0%, compensation from anti-sites x=4.5%, Lower compensation x 2

FINITE SIZE EXACT DIAGONALIZATION STUDIES S.-R. E. Yang, J. Sinova, T. Jungwirth, Y.P. Shim, and A.H. MacDonald, PRB 67, 045205 (03) 6-band K-L model p=0.33 nm -3, x=4.5%, compensation from anti-sites p=0.2 nm -3, x=4.0%, compensation from anti-sites 6-band K-L model GaAs

MAGNETIC ANISOTROPY M. Abolfath, T. Jungwirth, J. Brum, A.H. MacDonald, Phys. Rev. B 63, 035305 (2001) Condensation energy depends on magnetization orientation compressive strain   tensile strain experiment:

 theory experiment Ferromagnetic resonance: Gilbert damping A a,k (  )

Anisotropic Magnetoresistance exp. T. Jungwirth, M. Abolfath, J. Sinova, J. Kucera, A.H. MacDonald, Appl. Phys. Lett. 2002

ANOMALOUS HALL EFFECT T. Jungwirth, Q. Niu, A.H. MacDonald, Phys. Rev. Lett. 88, 207208 (2002) anomalous velocity: M0M0 M=0 J pd N pd (meV) Berry curvature: AHE without disorder Experiments Clean limit theory Minimal disorder theory

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)??? 

Ni (Ga,Mn)As (Prague Nottingham) Fe Critical contribution at Tc to d  /dT like TM FMs d  /dT ~ c v F ~ d  -  Fisher & Langer ’68 Novak et al., ‘08

TcTc d  /dT Scattering off short range correlated spin-fluctuation Fisher&Langer ‘68

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: 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  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

BEFORE 2000 CONCLUSION: directors cut BUT it takes MANY to do the physics tango!! Texas A&M U., U. Texas, Nottingham, U. Wuerzburg, Cambirdge Hitachi, …. It IS true that it takes two to tango 2000-2004 2006 NEW DMSs, More heterostructures NEXT

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: 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 Jairo Sinova Texas A&M Univ. Ewelina Hankiewicz Fordham Univesrsity

Jairo Sinova (TAMU) Challenges and chemical trends in achieving a room temperature dilute magnetic semiconductor: a spintronics tango between theory and.

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Jairo Sinova (TAMU) Challenges and chemical trends in achieving a room temperature dilute magnetic semiconductor: a spintronics tango between theory and.

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Presentation on theme: "Jairo Sinova (TAMU) Challenges and chemical trends in achieving a room temperature dilute magnetic semiconductor: a spintronics tango between theory and."— Presentation transcript:

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