JAIRO SINOVA Research fueled by: NERC Challenges and Chemical Trends in Achieving a Room Temperature Dilute Magnetic Semiconductor: A Spintronics Tango 2007: Frontiers in Chemical Physics Workshop February 22 th 2007, Knoxville TN

Allan MacDonald U of Texas Tomas Jungwirth Inst. of Phys. ASCR U. of Nottingham Joerg Wunderlich Cambridge-Hitachi Bryan Gallagher U. Of Nottingham Ewelina Hankiewicz U. of Missouri Texas A&M U. Mario Borunda Texas A&M U. Other collaborators: Jan Masek, Karel Vyborny, Bernd Kästner, Carten Timm, Laurens Molencam, Charles Gould, Tomas Dietl, Tom Fox, Richard Campton Xin Liu Texas A&M U. Alexey Kovalev Texas A&M U.

OUTLINE Intro: Spintronics and Semiconductor Spintronics Intro to Diluted Magnetic Semiconductors Can we have a high Tc DMS? What is the data telling us in GaMnAs: thumbs up or down? Strategies to achieve high Tc DMSs

ELECTRONICS UP TO NOW: electronics mostly based on the manipulation of the charge of the electron Mr. Electron Two parts to his personality ! CHARGE SPIN Spintronics = Controlling spin and spin flow with electric fields magnetic fields …

There is plenty of room at the bottom - Feynman, 1959 "... Up to now we have been content to dig in the ground to find minerals.... We should consider, whether - in the great future - we can arrange atoms the way we want, the very atoms, all the way down!... We can use not just circuits, but some system involving the quantized energy levels, or interactions of quantized spins." Courtesy of The Archives, California Institute of Technology

Why semiconductors are better Bloch Wilson allowed energy band in crystal allowed energy band in crystal isolated atomic levels Pauli 1931: “One shouldn’t work with semiconductors, that is a filthy mess; who knows whether they really exist”

New a la Feynman revolution in spintronics: diluted magnetic semiconductors Goal: use the storing capacity of ferromagnetism and the processing capacity of semiconductors Goal: use the storing capacity of ferromagnetism and the processing capacity of semiconductors Does nature give us the material already? No Does nature give us the material already? No Can we make it? Yes Can we make it? Yes Can we understand it? Getting there Can we understand it? Getting there Can we improve it: that is the tango Can we improve it: that is the tango + Spin: used for storage Charge: used for computation

Dilute Magnetic Semiconductors: the simple picture 5 d-electrons with L=0  S=5/2 local moment moderately shallow acceptor (110 meV)  hole Jungwirth, Sinova, Mašek, Kučera, MacDonald, Rev. Mod. Phys. (2006), - Mn local moments too dilute (near-neghbors cople AF) - Holes do not polarize in pure GaAs - Hole mediated Mn-Mn FM coupling FERROMAGNETISM MEDIATED BY THE CARRIERS!!!

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 BUT THINGS ARE NOT THAT SIMPLE

T c ~ 100 K, metallic hard magnets (III,V) DMS: man made ferromagnets a la Feynman ( ) anomalous Hall effect normal: R Hall ~ B anomalous: R Hall ~ M Ohno, et al PRL (1992) (InMnAs) 7.5 K Ohno, et al APL (1996) (GaMnAs) 55 K Ohno, Science (1998) 110 K

 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)

OUTLINE Intro: Spintronics and Semiconductor Spintronics DMS’s Introduction Can we have a high Tc DMS? What is the data telling us in GaMnAs: thumbs up or down? Strategies to achieve high Tc DMSs

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)?

Effective magnetic coupling Effective magnetic coupling: Coulomb correlation of d-electrons & hopping  AF kinetic-exchange coupling J pd = meV nm 3 Origin of coupling between localized moments and dilute carriers Microscopic Microscopic: atomic orbitals & Coulomb correlation of d-electrons & hopping J pd S Mn.s hole

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

Theoretical Approaches to DMSs First Principles Local Spin Density Approximation (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 Tight Binding models Phenomenological k.p  Local Moment PROS: “Unbiased” microscopic approach, correct capture of band structure and hybridization, treats disorder microscopically (combined with CPA), good agreement with LDA+U calculations CONS: neglects 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)

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

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, (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 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, (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

OUTLINE Intro: Spintronics and Semiconductor Spintronics DMS’s Introduction Can we have a high Tc DMS? What is the data telling us in GaMnAs: thumbs up or down? Strategies to achieve high Tc DMSs

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

OUTLINE Intro: Spintronics and Semiconductor Spintronics DMS’s Introduction Can we have a high Tc DMS? What is the data telling us in GaMnAs: thumbs up or down? Strategies to achieve high Tc DMSs

- 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

conc. of wide gap component 0 1 lattice constant (A) (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

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

No reduction of Mn I in (Al,Ga)As Mixing P in GaAs more favorable for suppressing Mn int formation higher in (Al,Ga)As and Ga(As,P) than in GaAs smaller interstitial space only in Ga(As,P) theory Mn i formation in mixed (Al,Ga)As and Ga(As,P)

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 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

Additional interstitial Li in Ga tetrahedral position - donors n-type Li(Zn,Mn)As No solubility limit for group-II Mn substituting for group-II Zn theory

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

SUMMARY No intrinsic limit to Tc: need to think in terms of effective Mn concentration No intrinsic limit to Tc: need to think in terms of effective Mn concentration Should use knowledge gained in (Ga,Mn)As to create new a la carte materials Should use knowledge gained in (Ga,Mn)As to create new a la carte materials Using multiple theoretical approaches and knowing what each is best and when IS the theory silver bullet Using multiple theoretical approaches and knowing what each is best and when IS the theory silver bullet Alloying P can help Tc Alloying P can help Tc 3=2+1 3=2+1

BEFORE 2000 CONCLUSION: directors cut BUT it takes MANY to do the spintronics tango!! Texas A&M U., U. Texas, U. Buffalo, Nottingham, U. Wuerzburg, U. Notre Dame, U. of Tennessee, U. of Maryland, UCSB, Penn State, …. It IS true that it takes two to tango NEW DMSs, Heterostructures NEXT

EXTRA

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

Potashnik et al 2001 Lopez-Sanchez and Bery 2003 Hwang and Das Sarma 2005 Resistivity temperature dependence of metallic GaMnAs

 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

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]

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

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

The valence band picture of IR absorption F =  d  Re[  (  )] =  e 2 p / 2m opt m opt independent of (within 10%): · density · disorder · magnetic state GaAs m op  0.24 m e infrared absorption  accurate density measurement hole density: p=0.2, 0.3,....., 0.8 nm -3 exp. J. Sinova, et al. Phys. Rev. B 66, (2002). x=5% Exps: Singley et al Phys. Rev. Lett. 89, (2002) Hirakawa, et al Phys. Rev. B 65, (2002)

FINITE SIZE EXACT DIAGONALIZATION STUDIES S.-R. E. Yang, J. Sinova, T. Jungwirth, Y.P. Shim, and A.H. MacDonald, PRB 67, (03) 6-band K-L model parabolic band 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 f-sum rule accurate within 10 %

● Energy dependence of Jpd ● Localization effects ● Contributions due to impurity states: Flatte’s approach of starting from isolated impurities ● Systematic p and x eff study (need more than 2 m eff data points) Possible issues regarding IR absorption

Keeping Score The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V shallow acceptor metallic DMSs very well in the regime that is valid: 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

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

OUTLINE Intro: Spintronics and Semiconductor Spintronics DMS’s Intro: III-V Semiconductors: the basic picture Perhaps Pauli was right: the messy reality Discovery and cool down of expectations Can we have a high Tc DMS? Origin of the coupling between local moments and delocalized carriers Basic phase diagram Theoretical approaches: no silver bullet but a good arsenal Is there an intrinsic limitation from theory Extrinsic limitations What is the data telling us in GaMnAs: thumbs up or down? Strategies to achieve high Tc DMSs Strategy A: focus on GaMnAs Strategy B: use what we have learned from DMSs to search for other materials Increasing coupling strength but still sallow levels Mathematical strategy: decompose 3

d4d4 d Weak hybrid. Delocalized holes long-range coupl. Strong hybrid. Impurity-band holes short-range coupl. d 5  d 4 no holes InSb, InAs, GaAs T c : 7  173 K (GaN ?) GaP T c : 65 K Similar hole localization tendencies in (Al,Ga)As and Ga(As,P) Scarpulla, et al. PRL (2005) d5d5 Limits to carrier-mediated ferromagnetism in (Mn,III)V