Making semiconductors magnetic: new materials properties, devices, and future

Transcription

1 Making semiconductors magnetic: new materials properties, devices, and future JAIRO SINOVA Texas A&M University Institute of Physics ASCR Texas A&M L. Zarbo Institute of Physics ASCR Tomas Jungwirth, Vít Novák, et al Hitachi Cambridge Jorg Wunderlich, A. Irvine, et al University of Utah November 9 th 2010 University of Nottingham Bryan Gallagher, Tom Foxon, Richard Campion, et al. NRI SWAN

2 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)

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

4 Ferromagnetic semiconductor research : strategies 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

5 (Ga,Mn)As GENERAL PICTURE

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

7 Ga As What happens when a Mn is placed in Ga sites: Mn hole spin-spin interaction Mn Mn-d As-p hybridization 5 d-electrons with L=0 S=5/2 local moment intermediate acceptor (110 mev) hole Hybridization like-spin level repulsion J pd S Mn s hole interaction 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

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

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

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

11 (Ga,Mn)As GENERAL THEORY

12 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).

13 Theoretical Approaches to DMSs First Principles LSDA Jungwirth, Sinova, Masek, Kucera, MacDonald, Rev. of Mod. Phys. 78, 809 (2006) 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 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 k.p Local Moment 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)

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

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

16 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

17 EXAMPLE: MAGNETO-OPTICAL EFFECTS IN THE INFRARED

18 EXAMPLE: INFRARED ABSORPTIN not so red shifted after all PRL 2010

19 T c LIMITS AND STRATEGIES

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

21 Can a dilute moment ferromagnet have a high Curie temperature? EXAMPLE OF THE PHYSICS TANGO 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)?

22 Intrinsic properties of (Ga,Mn)As 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)

23 Extrinsic effects: Interstitial Mn - a magnetism killer" Interstitial Mn is detrimental to magnetic order:! hcompensating double-donor reduces carrier density! hcouples antiferromagnetically to substitutional Mn even in! low compensation samples Blinowski PRB 03, Mašek, Máca PRB '03 Mn As 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.!

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

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

26 Experimental partial concentrations of Mn Ga and Mn I in as grown samples Theoretical linear dependence of Mn sub on total Mn confirmed experimentally! 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 "

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

28 Tc as grown and annealed samples Linear increase of Tc with Mn eff = Mn sub -Mn Int Open symbols as grown. Closed symbols annealed 8% Mn 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

29 Tc limit in (Ga,Mn)As remains open... Ohno s 98 T c =110 K is the fundamental upper limit.. Yu et al K!! 2008 Olejnik et al 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

30 Getting to higher Tc: Strategy A - 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

31 Getting to higher Tc: Strategy B 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) "

32 Other (III,Mn)V s DMSs Kudrnovsky et al. PRB 07 Weak hybrid. Delocalized holes long-range coupl. Mean-field but low T c MF InSb d 5 Strong hybrid. Impurity-band holes short-range coupl. Large T c MF but low stiffness GaP (Al,Ga,In)(As,P) good candidates, GaAs seems close to the optimal III-V host

33 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)? " Using DEEP mathematics to find a new material 3=1+2

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

35 UNDERSTANDING CRITICAL BEHAVIOUR IN TRANSPORT

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

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

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

39 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)

40 Exchange split & SO-coupled bands: Au Exchange split bands: discovered in (Ga,Mn)As Gold et al. PRLʼ04!

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

42 DMS DEVICES

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

44 Increasing ρ and decreasing AMR and T c with depletion Tc Tc AMR

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

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

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

48 Single-electron charging energy controlled by V g and M Source Q V D Drain Q 0 Q0 Gate V G e 2 /2C Σ [110] [100] [010] Φ M control of Coulomb blockade oscillations [110] [010] SO-coupling µ(m) Theory confirms chemical potential anisotropies in (Ga,Mn)As & predicts CBAMR in SO-coupled room-t c metal FMs

49 Nonvolatile programmable logic Variant p- or n-type FET-like transistor in one single nano-sized CBAMR device 0 1 V DD OFF ON V A OFF ON V B V A OFF ON OFF ON V B OFF ON 1 01 Vout OR ON OFF A B Vout

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

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

52 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 Transport critical behaviour Infrared MO effects 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

53 Tomas Jungwirth Inst. of Phys. ASCR U. of Nottingham Hideo Ohno Tohoku Univ. Allan MacDonald U of Texas Laurens Molenkamp Wuerzburg Tomesz Dietl Institute of Physics, Polish Academy of Sciences Joerg Wunderlich Cambridge-Hitachi Ewelina Hankiewicz Fordham Univesrsity Bryan Gallagher U. Of Nottingham 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

54

55 k.p Local Moment - Hamiltonian Model Anderson Hamiltonian: (s - orbitals: conduction band; p - orbitals: valence band) ELECTRONS + (Mn d - orbitals: strong on-site Hubbard int. local moment) Mn + (s,p - d hybridization) ELECTRONS-Mn 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 Large S: treat classically

56 T c LIMITS AND STRATEGIES

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

58 Tc as grown and annealed samples Linear increase of Tc with Mn eff = Mn sub -Mn Int Open symbols as grown. Closed symbols annealed 8% Mn 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

59 III = I + II Ga = Li + Zn GaAs and LiZnAs are twin SC! 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!!!! Masek, et al. PRB (2006)!

60 Tc limit in (Ga,Mn)As remains open 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... Mack et al. 08 Nottingham & Prague ( 08): T c up to 185K so far? Combinatorial approach to growth with fixed growth and annealing T s