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Jairo Sinova (TAMU) Making semiconductors magnetic: A new approach to engineering quantum materials NERC SWAN
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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
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Mn Ga As Mn Ferromagnetic semiconductors GaAs - standard III-V semiconductor Group-II Mn - dilute magnetic moments & holes & holes (Ga,Mn)As - ferromagnetic semiconductor semiconductor More tricky than just hammering an iron nail in a silicon wafer
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Mn Ga As Mn Mn–hole spin-spin interaction hybridization Hybridization like-spin level repulsion J pd S Mn s hole interaction Mn-d As-p
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(Ga,Mn)As 5 d-electrons with L=0 S=5/2 local moment intermediate acceptor (110 meV) hole - Mn local moments too dilute (near-neighbours couple AF) - Holes do not polarize in pure GaAs - Hole mediated Mn-Mn FM coupling Mn Ga As Mn Ohno, Dietl et al. (1998,2000); Jungwirth, Sinova, Mašek, Kučera, MacDonald, Rev. Mod. Phys. (2006), http://unix12.fzu.cz/ms
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H eff = J pd || -x Mn As Ga h eff = J pd || x Hole Fermi surfaces Ferromagnetic Mn-Mn coupling mediated by holes
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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 Benchmark for our understanding of strongly correlated systems 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
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Dilute moment nature of ferromagnetic semiconductors Ga As Mn 10-100x smaller M s One Current induced switching replacing external field Tsoi et al. PRL 98, Mayers Sci 99 Key problems with increasing MRAM capacity (bit density): - Unintentional dipolar cross-links - External field addressing neighboring bits 10-100x weaker dipolar fields 10-100x smaller currents for switching Sinova et al., PRB 04, Yamanouchi et al. Nature 04
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GaMnAs Au AlOx Au Tunneling anisotropic magnetoresistance (TAMR) Bistable memory device with a single magnetic layer only Gould, Ruster, Jungwirth, et al., PRL '04 Giant magneto-resistance (Tanaka and Higo, PRL '01) [100] [010] [100] [010] [100] [010] Recently discovered in metals as well!
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One Dipolar-field-free current induced switching nanostructures Micromagnetics (magnetic anisotropy) without dipolar fields (shape anisotropy) ~100 nm Domain wall Strain controlled magnetocrystalline (SO-induced) anisotropy Can be moved by ~100x smaller currents than in metals Humpfner et al. 06, Wunderlich et al. 06
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Huge & tunable magnetoresistance in (Ga,Mn)As side-gated nano-constriction FET Wunderlich, Jungwirth, Kaestner, Shick, et al., preprint Single-electron transistor
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Coulomb blockade anisotropic magnetoresistance Band structure (group velocities, chemical potential scattering rates, chemical potential) depend on Spin-orbit coupling If lead and dot different (different carrier concentrations in our (Ga,Mn)As SET) & electric & magnetic control of Coulomb blockade oscillations
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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
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Magnetism in systems with coupled dilute moments and delocalized band electrons (Ga,Mn)As coupling strength / Fermi energy band-electron density / local-moment density
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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).
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· 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
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Two Approximations 2-Mean Field Approximation Field felt by band electrons Field felt by local moments 1-Virtual Crystal Approximation Bastard, J. de Physique, 39 p. 87 (1978) Gaj, Phys. Stat. Solidi 89 p.655 (1978)
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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)
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Which theory is right? KP Eastwood Fast principles Jack Impurity bandit vs Valence Joe
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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
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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)
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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
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As Ga Mn 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
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Ga As Mn Ferromagnetic: x=1-8% Ga 1-x Mn x As Low Temperature - MBE courtesy of D. Basov Inter- stitial Anti- site Substitutioanl Mn: acceptor +Local 5/2 moment As anti-site deffect: Q=+2e Interstitial Mn: double donor Extrinsic effects: Interstitial Mn - a magnetism killer
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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
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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
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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
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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
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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
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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
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- 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
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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
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conc. of wide gap component 0 1 lattice constant (A) 5.4 5.7 (Al,Ga)As Ga(As,P) (Al,Ga)As & Ga(As,P) hosts d5d5 d5d5 local moment - hole spin-spin coupling J pd S. s Mn d - As(P) p overlapMn d level - valence band splitting GaAs & (Al,Ga)As (Al,Ga)As & Ga(As,P)GaAs Ga(As,P) Mn As Ga
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Smaller lattice const. more important for enhancing p-d coupling than larger gap Mixing P in GaAs more favorable for increasing mean-field T c than Al Factor of ~1.5 T c enhancement p-d coupling and T c in mixed (Al,Ga)As and Ga(As,P) Mašek, et al. PRB (2006) Microscopic TBA/CPA or LDA+U/CPA (Al,Ga)As Ga(As,P) 10% Mn 5% Mn theory
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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)?
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III = I + II Ga = Li + Zn GaAs and LiZnAs are twin SC Wei, Zunger '86; Bacewicz, Ciszek '88; Kuriyama, et al. '87,'94; Wood, Strohmayer '05 Masek, et al. PRB (2006) LDA+U says that Mn-doped are also twin DMSs No solubility limit for group-II Mn substituting for group-II Zn !!!!
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Electron mediated Mn-Mn coupling n-type Li(Zn,Mn)As - similar to hole mediated coupling in p-type (Ga,Mn)As L As p-orb. Ga s-orb. As p-orb. EFEF Comparable T c 's at comparable Mn and carrier doping and Li(Mn,Zn)As lifts all the limitations of Mn solubility, correlated local-moment and carrier densities, and p-type only in (Ga,Mn)As Li(Mn,Zn)As just one candidate of the whole I(Mn,II)V family
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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
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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
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General picture of MI transition in doped semiconductors: cross over from IB to VB
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Mn-d-like local moments As-p-like holes Mn Ga As Mn EFEF DOS Energy spin spin with 5 d-electron local moment on the Mn impurity valence band As-p-like holes As-p-like holes localized on Mn acceptors << 1% Mn onset of ferromagnetism near MIT Jungwirth et al. RMP ‘06 ~1% Mn >2% Mn MI transition in GaMnAs: cross over from IB to VB (no sharp boundary)
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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
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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).
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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.
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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
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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
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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, arXiv:0707.0665 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
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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, arXiv:0707.0665 same growth conditions but <1% insulating Comparable mobilities of shallow and intermediate acceptor systems
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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
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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)
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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
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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
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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
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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
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Effective Moment density, Mn eff = Mn sub -Mn Int due to AF Mn sub -Mn Int pairs. Tc increases with Mn eff when compensation is less than ~40%. No saturation of Tc at high Mn concentrations Closed symbols are annealed samples High compensation Linear increase of Tc with effective Mn
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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:
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Lopez-Sanchez and Bery 2003 Hwang and Das Sarma 2005 Resistivity temperature dependence of metallic GaMnAs
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theory experiment Ferromagnetic resonance: Gilbert damping A a,k ( )
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Anisotropic Magnetoresistance exp. T. Jungwirth, M. Abolfath, J. Sinova, J. Kucera, A.H. MacDonald, Appl. Phys. Lett. 2002
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ANOMALOUS HALL EFFECT T. Jungwirth, Q. Niu, A.H. MacDonald, Phys. Rev. Lett. 88, 207208 (2002) anomalous velocity: M0M0 M=0 J pd N pd (meV) Berry curvature: AHE without disorder
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ANOMALOUS HALL EFFECT IN GaMnAs Experiments Clean limit theory Minimal disorder theory
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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
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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
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Mn-d-like local moments As-p-like holes Mn Ga As Mn EFEF DOS Energy spin spin GaAs:Mn – extrinsic p-type semiconductor with 5 d-electron local moment on the Mn impurity valence band As-p-like holes As-p-like holes localized on Mn acceptors << 1% Mn onset of ferromagnetism near MIT Jungwirth et al. RMP ‘06 ~1% Mn >2% Mn STILL LARGELY UNEXPLORED SYSTEMATICALLY: MIT
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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
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Integrated read-out, storage, and transistor Low current driven magnetization reversal Parkin, US Patent (2004) Magnetic race track memory Yamanouchi et al., Nature (2004) 2 orders of magnitude lower critical currents in dilute moment (Ga,Mn)As than in conventional metal FMs Sinova, Jungwirth et al., PRB (2004) Wunderlich, et al., PRL (2006) Ideal to study spintronics fundamentals Family of extraordinary MR effects, R(M), in ohmic, tunneling, Coulomb-blockade regimes
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Low M s (1-10% Mn moment doping): 100-10 x weaker mag. dipolar interactions can allow for 100-10 x denser integration without unintentional dipolar cross-links Strong SO-coupling: magnetocrystalline anisotropy ~ 10 mT & doping and strain dependent can replace demagnetizing shape anisotropy fields & local control of magnetic configurations... and more yet to be fully exploited
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Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: ac-absorption experiments Hot electron photoluminescence studies: comparison of Zn doped and Mn doped Left panel: HPL spectra of GaAs doped with ~ 1017 cm−3 of Zn and ~ 1019 cm−3 of Zn. (replotted in logarithmic scale). HPL spectra of GaAs doped with ~ 1017 cm−3 of Mn, and of ≈ 1% and ≈ 4% GaAs:Mn materials. Eex is the HPL excitation energy. Arrows indicate the spectral feature corresponding to impurity band transitions in the low-doped materials. A. Twardowski and C. Hermann, Phys. Rev. B 32, 8253 (1985). V. F. Sapega, M. Moreno, M. Ramsteiner, L. D¨aweritz, and K. H. Ploog, Phys. Rev. Lett. 94, 137401 (2005).
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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
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