Current Issues & Understandings for Magnetic Semiconductors

1. Current Issues & Understandings for Magnetic Semiconductors Kwang Joo Kim Department of Physics, Konkuk University, Seoul, Korea

2. History of Ferromagnetism in Semiconductors • 1960’s : recognition of spin-related phenomena due to existence of • ferromagnetism (강자성) in semiconductors (at low temp.) • (2) 1980’s : research on magneto-resistance, magneto-optics etc. on • ferromagnetic semiconductors (FM) with low Curie temperature (TC) • (3) 2000’s : discovery of FMs with high TC > 100 K (e.g., Ga1-xMnxAs) stimulated • research on materials & devices that can manipulate both charge & • spin – spintronics • * Device requirement to overcome existing MOSFET technology • - 4 Gbit DRAM (54 nm gate length & access time < 0.1 ns) using Si technology • - Spintronics device may operate by supplying smaller amount of • current (which should be spin-polarized) than existing ones • - Possible to achieve higher speed, lower power consumption, • higher integration density by using concept of spintronics (?)

3. Field-Effect Transistor • * Possible candidates of electrodes (source & drain) for spintronics • - Ferromagnetic metals (e.g., NiFe) • good: abundant carriersweak: shottky-barrier formation, spin relaxation • - Conventional semiconductors (e.g., Si, GaAs with ferromagnetism) • good: developed technology weak: low Curie temperature (TC 200 K) • - Oxide compounds (e.g., Fe3O4 (ferrimagnetic), ZnO ) • good: chemical stability weak: underdeveloped technology

4. * Magnetic semiconductors (ordered compounds) – EuSe, EuO (NaCl); CdCr2S4, CdCr2Se4 (spinel) with TC 100 K – (La,Sr)MnO3 (perovskite) with TC 350 K – Fe3O4with TC  800 K (called half-metal, but behave like semiconductor) : difficult to be compatible with conventional semiconductors (IV, III- V, II-VI) for electronic device applications

5. * Diluted magnetic semiconductors – IV, III-V, II-VI semiconductors doped by magnetic elements, e.g., 3d transition metal (TM) : Ga1-xMnxAs, Cd1-xMnxTe, Si1-xMnx with rather low TC  200 K for device applications (narrow band gap) – Oxide semiconductors doped by magnetic elements, e.g., TM-doped ZnO, SnO2, TiO2, In2O3 with TC above room temperature (wide band gap) – Ga1-xMnxN, Si1-xFexC, : TC above room temp. (wide band gap)

6. Nonmagnetic Compound Semiconductor Ferromagnetic Semiconductor Diluted Magnetic Semiconductor Magnetic Hysteresis

7. Methods for checking ferromagnetism M-H (at 300K by VSM) M-T (by SQUID) SiC:Fe (3C, Eg = 2.4 eV) TC ~ 300K

8. In DMS, TM ions substitute cationic sites and so created charge carriers mediate ferromagnetic alignment of magnetic TM ions. * Can the ferromagnetism be properly explained theoretically (based on electronic structure)? * Any distinct properties of carriers in ferromagnetic regime (e.g., mobile or localized (magnetic polaron))? * Can DMSs properly supply spin-polarized current in wide temperature range?

9. Energy Energy Down spin Up spin Down spin Up spin EF EF H Solid-soluted magnetic ion E Cationic site Electron path Electron Conceptual electronic structure Extrinsic origin Intrinsic origin Spin-polarized Conduction band Magnetic cluster

10. Theoretical background for diluted ferromagnetism * RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction (a) indirect exchange coupling of local magnetic moments via carriers (conduction electron or hole) (b) hybridization (such as s-d & p-d) bet. carrier and local ion is important * Effective Hamiltonian kF, J0: Fermi wavevector & overlap integral (related to electronic structure)    

11. Theoretical predictions by Dietl et al., Science 287, 1019 (2000) (1) Strong dependence of Curie temperature on magnetic impurity density & hole density (2) For same hole density, smaller spin-orbit splitting (of valence bands) leads to higher TC – leads to preference of light elements (also with stronger p-d hybridization) (3) Formation of magnetic polaron helps maintain ferromagnetism * Calculated for 5% Mn and hole density p = 3.5 X 1020 cm-3 * Predicted TC > 300 K for GaAs with Mn density of 10% : never achieved (TC ~ 170 K) * Predictions for GaN & ZnO are good (but no p-type ZnO tested) * For Si, TC ~ 130 K predicted but for some exp. TC > 300 K  defect control is important

12. Expected spin-polarized electronic structure of Zn1-xTMxO * Formation of spin-split donor band * Under molecular-field approx. TC [S(S+1)x]1/2Jsd for x < 0.17 S: ionic spin Jsd: exchange int. bet. IB & 3d stronger for more hybridization Room-temp. measurements by Venkatesan et al, PRL 93, 177206 (2004) Ti3+(d1) Mn2+(d5) Co2+(d7) * No clear explanation on relation between magnetism & conductivity (carrier transport) * DMS properties have been observed for some later reports on ZnMnO  important to understand defect-related properties

13. Isolated polaron Trapped electron vacancy Antiferromagnetic pair Magnetic impurity ion Magnetic impurity ion Isolated ion F-center Overlapping polarons Magnetic polaron model [Coey et al., Nat. Mater. 4, 173 (2005)] * Polaron formation is known to be efficient in TiO2. -Rutile: small polaron (larger ) s ~ 100, m* ~ 20me, aH = 0.26 nm -Anatase: large polaron (smaller ) s ~ 31, m* ~ me, aH = 1.6 nm

14. Hole Magnetic impurity ion Magnetic impurity ion O2- • Saturation magnetization (m) decreases as • O2 partial pressure during film deposition • process increases. • IB (or carrier) density decreases with • increasing O2 partial pressure • O vacancies significantly contribute to • IB (or CB) High IB density Low IB density As x increases, superexchange coupling of magnetic ions via O2- ion leads to antiferromagnetic alignment  Decrease of m at high TM doping

15. Ferromagnetism in wide-band-gap TiO2 • (1) Three distinct crystalline phases rutile: tetragonal, a=4.593Å, c=2.959Å anatase: tetragonal, a=3.785Å, c=9.514Å brookite: orthorhombic, a=5.436Å, b=9.166Å, c=5.135Å (2) Thermodynamic stability • rutile – stable • anatase, brookite – metastable (easily converted into rutile at high temp.) • (3) Band structure • rutile – direct band gap (~3.3 eV) • anatase – indirect band gap (~3.8 eV) • * wide band gap rutile type TiO2 anatase type TiO2

16. XRD TiO2-:Ni Ionic radius (Å) (octahedral site) Ti4+(3d0) : 0.745 Ni2+(3d8): 0.830 Ni3+(3d7, low): 0.700 Ni3+(3d7, high): 0.740 Ni4+(3d6): 0.620 • For Ni-doped rutile TiO2-δ films, • →lattice constants increase linearly • →Unit-cell volume increase for x = 5 at.% • from that of undopedTiO2-δ is about 0.6% Above 6 at.%, Ni clusters are observed as marked by *

17. X-rayPhotoelectronspectroscopy(TiO2-:Ni) • Both 2p3/2 and 2p1/2 lines are split into two peaks • Binding energy difference between the two peaks of ~ 3.5 eV lead to an interpretation that they are due to Ni2+and Ni3+ions Mater. Chem.. Phys. 77, 384 (2002). • Finite density of Ni2+ions in TiO2-δ:Ni is likely • to induce an increase of lattice constants. • Through Doniach-Sunjic line-shape fitting Ni 4 at.% Ni 9 at.% (with Ni clusters) Ni2+:Ni 3+ = 3.5:6.5 Ni2+:Ni 3+ = 5.3:4.7 • For Ni (9 at.%) → Ni clusters was detected by XRD → Inversion of XPS intensity ratio is attributable to Ni clusters (Ni0) → The 2p binding energies of electrons in Ni0are known to be close to those in Ni2+ within 1 eV Handbook of X-ray Photoelectron Spectroscopy, Perkin-Elmer Co., 1992. →Ni clusters tend to exist at the surface region and are likely to interact with oxygen ions, thus, having effective ionic valences 4 at.% 9 at.% Ni cluster

18. Hall Effect Measurements (TiO2-:Ni) • Up to 5 at.%:p-type conductivity • (p ~ 1019 cm-3) attributable to • Ni2+ & Ni3+ substitution of Ti4+ sites • At higher Ni doping: n-type conductivity • attributable to creation of Ni clusters

19. Ni (4 at.%) doped TiO2-δ • XPS Ni2+:Ni 3+ = 3.5:6.5 • spin moment Ni2+(t2g6eg2) Mspin = 2 μB • Ni3+(t2g5eg2) Mspin = 3 μB • Cal. MS≈ 2.7 μB/Ni • Exp. MS≈ 3 μB/Ni • The observed magnetic moment is • attributable to the alignment of Ni • impurity spins. Vibrating Sample Magnetometry (TiO2-:Ni) • Ferromagnetic strength is likely to be • related to mobile carrier (hole) density • Decrease in net magnetization with • increase of Ni content : increase in antiferromagnetic superexchange coupling strength between neighboring Ni ions via a nearby O2- ion (as in NiO) is possible

20. TiO2-:Co • * Intrinsic ferromagnetism persists at high • Co doping (for Ni, Fe, Mn,  6 at.%). • * Large saturation magnetization (Ms) as in • Ni doping. • * Co ions have valences +2 & +3 (by XPS). • * Ferromagnetic strength decreases with • increasing Co content (probably due to • antiferromagnetic Co2+-O2--Co2+).

21. TiO2-:Fe * No thickness dependence: rare possibility for surface segregation of Fe * Neither Fe cluster nor Fe3O4 was detected * Ferromagnetism is due to magnetic polaron rather than moble carrier x = 1.3 at.%: p-type 1018 cm-3 x = 2.4 at.%: p-type 1017 cm-3 x = 5.8 at.%: insulating

22. TiO2-:Mn * p-type samples exhibited ferromagnetism. * Ferromagnetic strength is not related to hole density. * Mn3+(d4) & Mn4+(d3) ions are dominant.

23. SQUID polaronic model A. Kaminski et al., PRL 88, 247202 (2002). TC > 400 K for all samples

24. TiO2:TM (Ni, Co, Fe, Mn) * Saturation magnetization per dopant ion differs significantly (large for Co & small for Mn)  in agreement with ZnO case (IB picture) *Ferromagnetic strength persists at high Co doping (12 at.%) compared to others ( 6 at.%) * Conduction type change from n to p by TM doping (no p-type in ZnO)

25. Pure TiO2- & TiO2-:Sb * Ferromagnetism is observed for pure TiO2- films (stronger for rutile than anatase) * Sb doping leads to an increase of saturation magnetization

26. Spin-polarized energy band structure FLAPW calculation for rutile TiO2- (with O vacancy)(Hong & Kim, J. Phys:C 21,195405 (2009) * DOS indicates net spin-polarization of Ti d-bands (due to lattice distortion) and resultant net magnetic moment of 0.22 B/Ti for rutile TiO2- (no such result obtained for anataseTiO2-).

27. Transport properties of spin-polarized carriers (1) Magnetoresistance ZnMnO MR = [(H) - (0)]/(0) * Increase in resistivity at low temp. (positive MR) is attributable to s-d exchange coupling. * Decrease in resistivity at high temp. (negative MR) is attributable to magnetic polaron (formed near O vacancy), which is unstable at low temp. Z. Yang et al., JAP 105, 053708 (2009)

28. VxFe3-xO4 Negative MR due to carrier hopping

29. (2) Anomalous Hall effect RHall = (HR0 + 4MRs)/d = ROHE + RAHE = VH/Ix d: sample thickness R0: ordinary Hall coeff. (= -1/ne) due to classical Lorenz force Rs: anomalous Hall coeff. due to asymmetric scattering from spin-orbit interaction under magnetization indicating carrier-mediated ferromagnetism (s-d exchange)

30. Electrical Resistivity Linear behavior can be understood in terms of polaronic hopping of spin-polarized carriers.

31. Stand on a new world and look beyond it for another one • Room-temperature ferromagnetism is observable for 3d TM-doped wide-band-gap III-V (e.g., GaN), II-VI (e.g., ZnO), VI-VI (e.g., SiC), & other oxide (e.g., TiO2) DMSs. * Some results are still controversial. • Both carriers in valence or conduction bands (via p-d or s-d exchange coupling) and impurity bands (via magnetic polaron) contribute to ferromagnetism. * need to independently control density of carriers and density of TM ions to better understand ferromagnetism. * high carrier density, low TM density (low defects)  exchange coupling (high carrier mobility, low M)  often appears for non-oxide DMSs * low carrier density, high TM density (high defects)  magnetic polaron (low carrier mobility, high M)  frequently appears for oxide DMSs

32. ћω ћω Ti 3d Ti 3d eg k t2g eg k Spin down Spin up t2g Spin up Spin down O 2p O 2p Optical properties * Spin-exchange interaction is likely for low Mn and Fe doping. p-d exchange (bandgap shrink) p-d hybridization (bandgap expansion)

33. a Mn Te c MnTe films (MBE grown) NiAs (hexagonal) “Semiconducting” & p-type (p ~ 1019 cm-3)

34. MnSb films (MBE grown) “High Curie Temp.” ~ 600 K “Metallic behavior” & p-type (p ~ 1021 cm-3)

35. TiO2-:Fe Ionic radius (Å) (octahedral site) Ti4+(3d0) : 0.745 Fe2+(3d6, low): 0.750 Fe2+(3d6, high): 0.920 Fe3+(3d5, low): 0.690 Fe3+(3d5, high): 0.785 Fe4+(3d4): 0.725 * Anatase samples show larger variation of lattice constants than rutile ones.

36. TiO2-:Fe Mossbauer Spectroscopy For x = 5.8 at.%, only Fe3+ ions are detected, excluding possibility of Fe3O4 contribution to ferromagnetism. Spinel Fe3O4: (Fe3+)[Fe2+,Fe3+]O2-4

37. Rop Eop Eos Ros N0 N1 Spectroscopic Ellipsometry (SE) Ellipsometry can measure Snell’s law Fresnel’s equations dielectric function D = E optical conductivity  = (-i/4)( - 1) J = E :Contains information on optical transition in solids  knowledge of electronic structure

38. Lineary polarized light Modulated phase by analyzer Elliptically polarized light Light Detector Polarizer Analyzer SE Measurement process Jones matrix Intensity of photon I = k0 + k1 cos2(A-As) + k2 sin2(A-As) Fourier transformation ki = ki (Im) cos  = cos  (k0, k1, k2) tan  = tan  (k0, k1, k2) (0 = tan ) Get  & 

39. 1 2  ħ Dipole selection rule EG k Interband transition (absorption) Electric–dipole approximation e.g., s  p, p  d Transition rate

40. Band-gap Distribution of Semiconductors ZnTe CdTe ZnSe TiO2 SnO2 InAs GaAs AlAs ZnO ZnS Ge CuAlO2 InP InN GaP Si GaN 1 2 3 4 eV