1. Jairo Sinova Texas A &M University References: Jungwirth, Sinova et al, arXive:0707.0665, and Jungwirth et al, Theory of ferromagnetic (III,Mn)V semiconductors, to appear in Rev. of Mod. Phys. (2006). Character of states near the Fermi level in (Ga,Mn)As: Impurity to valence band crossover Los Alamos National Laboratory, July 11 th 2007 NERC SWAN

2. 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.

3. OUTLINE DMS: intro to the phenomenology –General picture –Theoretical approaches to DMSs 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

4. 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

5. 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

6. (Ga,Mn)As material 5 d-electrons with L=0  S=5/2 local moment intermediate acceptor (110 meV)  hole - Mn local moments too dilute (near-neghbors cople AF) - Holes do not polarize in pure GaAs - Hole mediated Mn-Mn FM coupling Mn Ga As Mn

7. H eff = J pd || -x Mn As Ga h eff = J pd || x Hole Fermi surfaces Ferromagnetic Mn-Mn coupling mediated by holes

8. 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

9. 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)

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

11. OUTLINE DMS: intro to the phenomenology –General picture –Theoretical approaches to DMSs 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

12. 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

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

14. 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)

15. OUTLINE DMS: intro to the phenomenology –General picture –Theoretical approaches to DMSs 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

16. 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).

17. 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.

18. 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

19. OUTLINE DMS: intro to the phenomenology –General picture –Theoretical approaches to DMSs 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

20. 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

21. 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

22. 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).

23. 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

24. 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)

25. 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

26. 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

27. 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

28. OUTLINE DMS: intro to the phenomenology –General picture –Theoretical approaches to DMSs 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

29. As Ga Mn Intrinsic properties of (Ga,Mn)As Intrinsic properties of (Ga,Mn)As: 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)

30. 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

31. 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

32. Annealing can very 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

33. 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 MnGa and MnI in as grown samples

34. Tc=173K 8% Mn Open symbols as grown. Closed symbols annealed Tc as grown and annealed samples

35. 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

36. 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

37. 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:

38. Lopez-Sanchez and Bery 2003 Hwang and Das Sarma 2005 Resistivity temperature dependence of metallic GaMnAs

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

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

41. 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]

42. 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

43. ANOMALOUS HALL EFFECT IN GaMnAs Experiments Clean limit theory Minimal disorder theory

44. OUTLINE DMS: intro to the phenomenology –General picture –Theoretical approaches to DMSs 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

45. Conclusion 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

46. EXTRA BELOW

47. Unconventional metallic state in ferromagnetic Ga 1-x Mn x As Massive holes Burch et al. PRL 97, 87208 (2006)   -1 cm -1 Ga 1-x Mn x As 5.2% T C =120 K annealed cm -1 STM Yakunin et al. PRL 95, 256402 (05) Penn State, UCSB, Nottingham Jungwirth et al. PRB72, 165204 (05) EFEF Mn Impurity band conduction x, % m*=10-50 m e ????? Hot electron PL Sapega et al. PRL 94, 137401 (05) ARPES Fujimori prb64, 125304 (2001) Resonant tunneling Thomas APL90, 82106 (2007) Magneto-transport Rokhinson, Furdyna, et al. (APS March Meeting 2007)

49. ● 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 ● New growth or chemical composition strategies to incorporate more MnGa local moments or enhance p-d coupling ● Window in this difficult phase space is narrow and obtaining the optimal strength of the coupling and technical difficulties for GaMnAs may make it impossible to reach room Tc ● May want to look into materials close to this material but higher coupling strength to find the optimal system Prospects of high Tc in DMSs