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

2. 2 (1)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 (T C ) (3) 2000’s : discovery of FMs with high T C > 100 K (e.g., Ga 1-x Mn x As) 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 (?) History of Ferromagnetism in Semiconductors

3. * Possible candidates of electrodes (source & drain) for spintronics - Ferromagnetic metals (e.g., NiFe) good: abundant carriers weak: shottky-barrier formation, spin relaxation - Conventional semiconductors (e.g., Si, GaAs with ferromagnetism) good: developed technology weak: low Curie temperature (T C  200 K) - Oxide compounds (e.g., Fe 3 O 4 (ferrimagnetic), ZnO ) good: chemical stability weak: underdeveloped technology Field-Effect Transistor

4. * Magnetic semiconductors (ordered compounds) – EuSe, EuO (NaCl); CdCr 2 S 4, CdCr 2 Se 4 (spinel) with T C  100 K – (La,Sr)MnO 3 (perovskite) with T C  350 K – Fe 3 O 4 with T C  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 4

5. * Diluted magnetic semiconductors – IV, III-V, II-VI semiconductors doped by magnetic elements, e.g., 3d transition metal (TM) : Ga 1-x Mn x As, Cd 1-x Mn x Te, Si 1-x Mn x with rather low T C  200 K for device applications (narrow band gap) – Oxide semiconductors doped by magnetic elements, e.g., TM-doped ZnO, SnO 2, TiO 2, In 2 O 3 with T C above room temperature (wide band gap) – Ga 1-x Mn x N, Si 1-x Fe x C, : T C above room temp. (wide band gap) 5

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

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

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? 8

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

10. 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 k F, J 0 : Fermi wavevector & overlap integral (related to electronic structure)     

11. Theoretical predictions by Dietl et al., Science 287, 1019 (2000) 11 (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 T C – 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 10 20 cm -3 * Predicted T C > 300 K for GaAs with Mn density of 10% : never achieved (T C ~ 170 K) * Predictions for GaN & ZnO are good (but no p-type ZnO tested) * For Si, T C ~ 130 K predicted but for some exp. T C > 300 K  defect control is important

12. Expected spin-polarized electronic structure of Zn 1-x TM x O 12 Ti 3+ (d 1 ) Mn 2+ (d 5 )Co 2+ (d 7 ) * Formation of spin-split donor band * Under molecular-field approx. T C  [S(S+1)x] 1/2 J sd for x < 0.17 S: ionic spin J sd : exchange int. bet. IB & 3d stronger for more hybridization Room-temp. measurements by Venkatesan et al, PRL 93, 177206 (2004) * 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. 13 Magnetic polaron model [Coey et al., Nat. Mater. 4, 173 (2005)] * Polaron formation is known to be efficient in TiO 2. -Rutile: small polaron (larger  )  s ~ 100, m* ~ 20m e, a H = 0.26 nm -Anatase: large polaron (smaller  )  s ~ 31, m* ~ m e, a H = 1.6 nm vacancy Magnetic impurity ion F-center Trapped electron Magnetic impurity ion

14. 14 High IB density Low IB density As x increases, superexchange coupling of magnetic ions via O 2- ion leads to antiferromagnetic alignment  Decrease of m at high TM doping As x increases, superexchange coupling of magnetic ions via O 2- ion leads to antiferromagnetic alignment  Decrease of m at high TM doping O 2- Hole Magnetic impurity ion Magnetic impurity ion Saturation magnetization (m) decreases as O 2 partial pressure during film deposition process increases.  IB (or carrier) density decreases with increasing O 2 partial pressure  O vacancies significantly contribute to IB (or CB) Saturation magnetization (m) decreases as O 2 partial pressure during film deposition process increases.  IB (or carrier) density decreases with increasing O 2 partial pressure  O vacancies significantly contribute to IB (or CB)

15. 15 (1) Three distinct crystalline phases rutile: tetragonal, a=4.593 Å, c=2.959 Å anatase: tetragonal, a=3.785 Å, c=9.514 Å brookite: orthorhombic, a=5.436 Å, b=9.166 Å, c=5.135 Å (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 Ferromagnetism in wide-band-gap TiO 2 rutile type TiO 2 anatase type TiO 2

16. 16 TiO 2-  :Ni  For Ni-doped rutile TiO 2-δ films, → lattice constants increase linearly → Unit-cell volume increase for x = 5 at.% from that of undoped TiO 2-δ is about 0.6%  For Ni-doped rutile TiO 2-δ films, → lattice constants increase linearly → Unit-cell volume increase for x = 5 at.% from that of undoped TiO 2-δ is about 0.6% Ionic radius ( Å ) (octahedral site) Ti 4+ (3d 0 ) : 0.745 Ni 2+ (3d 8 ): 0.830 Ni 3+ (3d 7, low): 0.700 Ni 3+ (3d 7, high): 0.740 Ni 4+ (3d 6 ): 0.620 Above 6 at.%, Ni clusters are observed as marked by * Above 6 at.%, Ni clusters are observed as marked by * XRD

17. 17 X-ray Photoelectron spectroscopy (TiO 2-  :Ni)  Both 2p 3/2 and 2p 1/2 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 Ni 2+ and Ni 3+ ions Mater. Chem.. Phys. 77, 384 (2002).  Finite density of Ni 2+ ions in TiO 2-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) Ni 2+ :Ni 3+ = 3.5:6.5 Ni 2+ :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 (Ni 0 ) → The 2p binding energies of electrons in Ni 0 are known to be close to those in Ni 2+ 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  Both 2p 3/2 and 2p 1/2 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 Ni 2+ and Ni 3+ ions Mater. Chem.. Phys. 77, 384 (2002).  Finite density of Ni 2+ ions in TiO 2-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) Ni 2+ :Ni 3+ = 3.5:6.5 Ni 2+ :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 (Ni 0 ) → The 2p binding energies of electrons in Ni 0 are known to be close to those in Ni 2+ 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 9 at.% Ni cluster 4 at.%

18. 18 Hall Effect Measurements (TiO 2-  :Ni)  Up to 5 at.%: p-type conductivity (p ~ 10 19 cm -3 ) attributable to Ni 2+ & Ni 3+ substitution of Ti 4+ sites  At higher Ni doping: n-type conductivity attributable to creation of Ni clusters  Up to 5 at.%: p-type conductivity (p ~ 10 19 cm -3 ) attributable to Ni 2+ & Ni 3+ substitution of Ti 4+ sites  At higher Ni doping: n-type conductivity attributable to creation of Ni clusters

19. 19 Vibrating Sample Magnetometry (TiO 2-  :Ni)  Ni (4 at.%) doped TiO 2-δ XPS Ni 2+ :Ni 3+ = 3.5:6.5 spin moment Ni 2+ (t 2g 6 e g 2 ) M spin = 2 μ B Ni 3+ (t 2g 5 e g 2 ) M spin = 3 μ B Cal. M S ≈ 2.7 μ B /Ni Exp. M S ≈ 3 μ B /Ni  The observed magnetic moment is attributable to the alignment of Ni impurity spins.  Ni (4 at.%) doped TiO 2-δ XPS Ni 2+ :Ni 3+ = 3.5:6.5 spin moment Ni 2+ (t 2g 6 e g 2 ) M spin = 2 μ B Ni 3+ (t 2g 5 e g 2 ) M spin = 3 μ B Cal. M S ≈ 2.7 μ B /Ni Exp. M S ≈ 3 μ B /Ni  The observed magnetic moment is attributable to the alignment of Ni impurity spins.  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 O 2- ion (as in NiO) is possible  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 O 2- ion (as in NiO) is possible

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

21. 21 TiO 2-  :Fe * No thickness dependence: rare possibility for surface segregation of Fe * Neither Fe cluster nor Fe 3 O 4 was detected * Ferromagnetism is due to magnetic polaron rather than moble carrier x = 1.3 at.%: p-type 10 18 cm -3 x = 2.4 at.%: p-type 10 17 cm -3 x = 5.8 at.%: insulating

22. 22 TiO 2-  :Mn * p-type samples exhibited ferromagnetism. * Ferromagnetic strength is not related to hole density. * Mn 3+ (d 4 ) & Mn 4+ (d 3 ) ions are dominant.

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

24. 24 * 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) TiO 2 :TM (Ni, Co, Fe, Mn)

25. 25 Pure TiO 2-  & TiO 2-  :Sb * Ferromagnetism is observed for pure TiO 2-  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 TiO 2-  (with O vacancy) (Hong & Kim, J. Phys:C 21,195405 (2009) 26 * 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 TiO 2-  (no such result obtained for anatase TiO 2-  ).

27. Transport properties of spin-polarized carriers 27 (1) Magnetoresistance 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. ZnMnO Z. Yang et al., JAP 105, 053708 (2009)

28. 28 V x Fe 3-x O 4 Negative MR due to carrier hopping

29. 29 (2) Anomalous Hall effect R Hall = (HR 0 + 4  MR s )/d = R OHE + R AHE = V H /I x d: sample thickness R 0 : ordinary Hall coeff. (= -1/ne) due to classical Lorenz force R s : anomalous Hall coeff. due to asymmetric scattering from spin-orbit interaction under magnetization indicating carrier-mediated ferromagnetism (s-d exchange)

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

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

33. MnTe films (MBE grown) 33 a c Mn Te NiAs (hexagonal) “Semiconducting” & p-type (p ~ 10 19 cm -3 )

34. 34 MnSb films (MBE grown) “Metallic behavior” & p-type (p ~ 10 21 cm -3 ) “High Curie Temp.” ~ 600 K

35. 35 TiO 2-  :Fe Ionic radius ( Å ) (octahedral site) Ti 4+ (3d 0 ) : 0.745 Fe 2+ (3d 6, low): 0.750 Fe 2+ (3d 6, high): 0.920 Fe 3+ (3d 5, low): 0.690 Fe 3+ (3d 5, high): 0.785 Fe 4+ (3d 4 ): 0.725 * Anatase samples show larger variation of lattice constants than rutile ones.

36. 36 TiO 2-  :Fe Mossbauer Spectroscopy Isomer shift (mm/s) ferro para X = 2.4 at.% 0.49 0.97 (Fe 3+ ) (Fe 2+ ) X = 5.8 at.% 0.28 0.27 (Fe 3+ ) (Fe 3+ ) For x = 5.8 at.%, only Fe 3+ ions are detected, excluding possibility of Fe 3 O 4 contribution to ferromagnetism. Spinel Fe 3 O 4 : (Fe 3+ )[Fe 2+,Fe 3+ ]O 2- 4

37. 37 Snell ’ s law Fresnel ’ s equations R os R op E op E os N1N1 N0N0 Spectroscopic Ellipsometry (SE) Ellipsometry can measure dielectric function D =  E optical conductivity  = (-i  /4  )(  - 1) J =  E : Contains information on optical transition in solids  knowledge of electronic structure

38. 38 Lineary polarized lightModulated phase by analyzer Light Polarizer Detector Analyzer Elliptically polarized light Jones matrix Intensity of photon I = k 0 + k 1 cos2(A-A s ) + k 2 sin2(A-A s ) k i = k i (I m ) cos  = cos  (k 0, k 1, k 2 ) tan  = tan  (k 0, k 1, k 2 ) Fourier transformation Get  &  SE Measurement process (  0 = tan  )

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

40. 40 InAs InP 1 234 eV GaAs InN AlAs GaP GaN ZnTe ZnO Band-gap Distribution of Semiconductors Ge Si CuAlO 2 ZnSeCdTe SnO 2 TiO 2 ZnS