Diluted Magnetic Semiconductors - An Introduction -

Transcription

1 International Conference and School on Spintronics and Quantum Information Technology (Spintech VI) School Lecture 2 Diluted Magnetic Semiconductors Matsue, Japan, August 1, 2011 Diluted Magnetic Semiconductors - An Introduction - Hideo Ohno 1,2 1 Center for Spintronics Integrated Systems, Tohoku University, Sendai, Japan 2 Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Sendai, Japan 1. What you need to know about nonmagnetic semiconductors Band structure 2. How you make a semiconductor magnetic Doping and sp-d exchange 3. The consequences of exchange interaction Spin-split bands and ferromagnetism 4. Making use of ferromagnetism in semiconductors Electrical control of ferromagnetism Current induced domain wall motion Tunneling with magnetism I am indebted to lecturers of earlier Spintechs, many collaborators, particularly Tomasz Dietl and Fumihiro Matsukura, for a number of materials used here.

2 1. What you need to know about nonmagnetic semiconductors Band structure

3 Electronic band structure From Wikipedia, the free encyclopedia

4 ε p (Ga) ε p (As) ε s (Ga) ε s (As) taken from Walter A. Harrison Electronic Structure and the Properties of Solids The Physics of Chemical Bond, 1980 J. R. Chelikowsky and M. L. Cohen, Phys. Rev. B14, 556 (1976) Bottom of the conduction band: Ga 4s Top of the valence band: As 4p

5 Density of states up spin states down spin states conduction band E C E V valence band

6 2. How you make a semiconductor magnetic Doping and sp-d exchange

7 Making semiconductor magnetic EuS CuCr 2 Se 4 diluted magnetic semiconductors Si III-V II-VI

8 Magnetic ion: Mn Hund rule: Distributing n electrons over 2(2l+1) degenerate atomic orbitals, the lowest energy state is the state that maximize the total spin angular momentum S Mn: l=2, n=5 -> S=5/2

9 Magnetic ion: Mn 3d - intra site correlation energy U = E n+1 E n for n = 5, U 15 ev - intra-site exchange interaction: ferromagnetic Hund s rule: S the highest possible for n = 5, E S=3/2 E S=5/2 2 ev 4s - transition metal atoms, 3d n 4s 1, e.g., Mn: ferromagnetic E S=2 E S=3 1.2 ev J s-d 0.4 ev

10 II-VI Diluted Magnetic Semiconducotors + =

11 Density of states with transition metal impurity majority spin states minority spin states s-d exchange interaction (potential exchange) p-d exchange interaction (hybridization; kinetic exchange) H sd E = H pd E = = xn αs S xn α S = xn βs S xn 0 β S d states x : Mn composition N 0 : Density of cation site N α, N β : Exchange energy 0 0

12 Virtual crystal approximation molecular-field approximation mean-field approximation ( 1 ) ( ) ( ) ( ) H = x U r R + xu r R xj r R s S n 0 n n n n x S V n n xn 0 ( ) M r gµ B ( ) S r ; M ; M = M r gµ B M r ( ) = xn gµ S( r) ( ) 0 B

13 III-V Diluted Magnetic Semiconductors h + = h h not to scale (Ga,Mn)As, (In,Mn)As, (Ga,Mn)Sb

14 Mn in GaAs Mn on Ga site: 113 mev acceptor d 5 +hole (weak coupling) d 4 d 5 +hole (strong coupling) from spectroscopy 2 2 e r H = T V0 exp xn0βs S ε r r 0 N 0 β = -0.9 ev kinetic, Coulomb, central cell correction, p-d exchange interaction theory: Bhattacharjee & C. Benoit a la Guillaume, Solid State Commun. 113, 17 (2000) exp: M. Linnarsson et al. Phys. Rev. B 55, 6938 (1997)

15 3. The consequences of exchange interaction Spin-split bands and ferromagnetism

16 Magnetization of localized spins no holes M(T,H) = gµ B Sx eff N o B S [gµ B H/k B (T + T AF )] antiferromagnetic interactions x eff < x T AF > 0 Modified Brillouin function Y. Shapira et al. no spontaneous magnetization

17 Density of states with transition metal impurity majority spin states minority spin states s-d exchange interaction E = xn α S 0 p-d exchange interaction E = xn0 β S d states

18 J. Gaj, Spintech III

19 Faraday effect o

20 Splitting of the bands E C xn 0 α<s> E V xn 0 β<s> xn 0 β<s> /3

21 Measurements of the band splitting σ E +1/2 1/2 σ + σ σ + 3/2 +3/2 k E=2g eff µ B HS, S=1/2 g eff ~400 > 0 Follows M not H SPINTECH II Joel Cibert magnetoreflectance: Aggarwal et al. Phys. Rev. B34, 5894 (1986)

22 sp-d exchange material (Cd,Mn)Te N 0 α (ev) 0.22 N 0 β (ev) (Cd,Mn)Se (Cd,Mn)S (Zn,Mn)Te (Zn,Mn)Se (Cd,Fe)Se N 0 β (ev) 2 1 ZnO ZnS CdS CdSe ZnTe CdTe ZnSe (Zn,Fe)Se (Cd,Co)Se a (nm) circles: photoemission squares: optical spectroscopy

23 3. The consequences of exchange interaction Spin-split bands and ferromagnetism GaAs (or InAs) + Mn

24 Material Science

25 Molecular beam epitaxy of (Ga,Mn)As - MBE system o C (Ga,Mn)As (1x2) Single crystal (Ga,Mn)As Intensity (arb. unit) shutter opening time (sec) (Ga,Mn)As T S = 250 o C

26 Molecular beam epitaxy of (Ga,Mn)As 250 o C Zinc-blende [-110] azimuth HT-GaAs c(4x4) LT-GaAs (1x1) 170 o C Polycrystalline (Ga,Mn)As spotty ZB-(Ga,Mn)As can be grown by selecting appropriate growth temperature 320 o C MnAs segregation Highest Mn composition without segregation is about 10%. (Ga,Mn)As (1x2) (Ga,Mn)As spotty A. Shen et al., J. Cryst. Growth 175/176, 1069 (1997).

27 Extended X-ray-Absorption Fine Structure (EXAFS) Sample Incident X-ray X-ray Target atom Transmitted X-ray Adjacent atoms Absorption coefficient Absorption edge Incident X-ray energy X-ray is absorbed by target atom creation of photoelectron Photoelectron is scattered by adjacent atoms Interference of photoelectron and reflected photoelectron Oscillating structure in absorption spectra includes the information of local structure around target atom

28 Local Structures - Extended X-ray-Absorption Fine Structure (EXAFS) (Ga,Mn)As 4As 12Ga 12As x = FT(kχ) (arb. units) 4As 6As 6As 4As 2Mn 6Mn 2Mn 6Mn 12Ga 12Mn 6As 6As 12Ga 12As 6As 12Mn 6As 12As x = MnAs MnAs (cal.) Mn in GaAs (cal.) R (nm) R. Shioda et al., Phys. Rev. B 58, 1100 (1998). Most of Mn substitute III-cation site (Mn 2+ acceptor)

29 Atom Probe Microscopy of (Ga,Mn)As Surface direction Ga Analysis direction ~ 45 nm ~ 90 nm ~ 10 nm Mn ~ 42 nm As (Ga,Mn)As M. Kodzuka, T. Ohkubo, K. Hono (NIMS) F. Matsukura, and H. Ohno (Tohoku), Ultramicroscopy 2009

30 Magnetism, transport, and more materials science

31 Magnetization of (Ga,Mn)As (Ga,Mn)As & (In,Mn)As: Mn acts as a source of spin and hole Ferromagnetism in (In,Mn)As: H. Ohno et al., Phys Rev. Lett and in (Ga,Mn)As: H. Ohno et al., Appl. Phys. Lett x eff = 0.09, t = 5 nm D. Chiba et al., APL 90, (2007)

32 Magnetization and transport of (Ga,Mn)As R Hall = (R 0 /d)b + (R S /d)m 0.00 M (T) x = T = 5 K 0.03 M r (T) B // plane B plane B plane (from transport) T (K) B (T) R Hall = V Hall /I R sheet V sheet /I H. Ohno et al. Appl. Phys. Lett H. Ohno Science 1998

33 Hall Effects Ordinary Hall effect Anomalous Hall effect Spin Hall effect

34 Low-temperature & high-field measurements Ga Mn As 30 [ Mn] = cm 21 3 R Hall (Ω) R Hall (Ω) experimental linear fit p = 3.5 x cm -3 (30% of Mn) ρ/ρ (a) (b) 10K K 100K B (T) B (T) x Mn = mK ρ = ( R B + R M ) Hall 0 R 0 B 1 = B qpd T. Omiya et al. Physica E, 2000 S

35 Low-temperature annealing ρ (Ωcm) (Ga,Mn)As x = 0.05 annealed for 15 min T S = 210 o C as-grown T a = 310 o C T a = 220 o C As 4 /Ga ~ 3 a (nm) T C (K) (x10 19 ) 7 6 p (cm -3 ) 10-2 T a = 260 o C T (K) T. Hayashi et al., Appl. Phys. Lett. 78, 1691 (2001) T a ( o C) Low-temperature annealing o C Decreases lattice constant Increases electrical conductivity Increases hole concentration Increases ferromagnetic transition temperature Mn i Correlation between T C and p See also K. W. Edmonds et al., Appl. Phys. Lett. 81, 4991 (2002).

36 Ferromagnetism

37 Like other thermodynamic quantities, Fc[M] is expected to be weakly perturbed by static disorder We suggest that the holes in the extended or weakly localized states mediate the long-range interactions between the localized spins on both sides of the MIT in the III- V and II-VI magnetic semiconductors.

38

39 p-d Zener model of ferromagnetism Ferromagnetic (Ga,Mn)As Mn acts as a source of spin and hole H. Ohno et al. Appl. Phys. Lett H. Ohno Science 1998 Carrier spins M 0 Mn spins β H pd exchange = xn β < S 0 > s T c = xn ( S + 1) A ρ ( E ) 2 0S F F β 12 k B T. Dietl, et al. Science 287, 1019 (2000) and PRB 63, (2001) also Koenig et al. Phys. Rev. Lett. 2000

40 T C by the p-d Zener model Carrier spins M 0 Mn spins β exchange χ Mn = g 2 2 µ BxN0S 3k T B F = F + F ( S + 1) total Mn c 2 M χc = H 2χ 2 Mn 2 χ = µ ρ ( E ) 2 c B F

41 ( ) ( ) c total Mn F B B B M F H E M g g xn S S k T χ χ ρ β µ µ == = B B E H M g µ β µ = = B B B E H E xn S M xn g S M E g µ β µ β µ = = = = ( ) ( ) 8 F F c B A E F M M g ρ β µ ( ) ( ) F c B xn S S E T k ρ β + = T C by the p-d Zener model

42 Valence band structure (Γ 7, Γ 8 ) H kp Ψ = EΨ Basis functions k p matrix = Q 2( k x + k y 2k z ) P γ 1 k 2 2 = γ L = 2 3γ 3 ( k x ik y ) k z M = 3[ γ 2( kx ky ) 2iγ 3kxky ],,, γ 1 = 6.85, γ 2 = 2.1, γ 3 = 2.58, = 0.34 ev for GaAs T. Dietl, H. Ohno and F. Matsukura, Phys. Rev. B63, (2001)

43 Valence band structure with p-d exchange (Γ 7, Γ 8 ) ( H + H ) Ψ EΨ kp pd = p-d exchange interaction matrix B 1 6 β = xn 0 S z, βx bxβ =, β = b β z z wz = Sz S w± = ( Sx ± i Sy ) S, x 2 S = S + S + y 2 S z T. Dietl, H. Ohno and F. Matsukura, Phys. Rev. B63, (2001)

44 Exchange energy: N 0 β Core level photoemission and modeling: N 0 β = -1.2 ± 0.2 ev Okabayashi et al., Phys. Rev. B58, 1998.

45 Comparison of exp. and calculated T C 150 (Ga,Mn)As, x = T C (K) , exp., cal. (In,Mn)As, x = 0.03 Fermi surface of (Ga,Mn)As (x10 20 ) Hole concentration, p (cm -3 )

46 Strain induced-anisotropy: Theory vs. Experiment T C (K) Theory tensile strain 0.7 % x=0.05 N 0 β=-1.2 ev A F =1.2 M // [100] : in-plane M // [110] : in-plane M // [001] : plane compressive strain 0.3 % R Hall (KΩ) Experiment 200-nm (Ga Mn )As/(In 0.16 Ga 0.84 )As T=10 K ^ 0 o 15 o 30 o 60 o 1.5-µm (Ga Mn )As/LT-GaAs T=2.3 K tensile strain θ B easy axis compressive strain (x10 20 ) p (cm -3 ) B (T) θ B easy Hole bands are responsible for the anisotropy axis

47 Acceptor doping and susceptibility of Zn 1-x Mn x Te:P 5 4 p -Zn 1-x Mn x Te x = p cm -3 p χ -1 vs. T χ -1 [ a.u. ] 3 2 p cm T CW Temperature [ K ] Sawicki et al. (Warsaw) pss 02 Kępa et al. (Warsaw, Oregon) PRL 03

48 Comparison of Experimental and Calculated T C 100 exp, cal, (Ga,Mn)As, x = T C (K) 10, (In,Mn)As, x = 0.03, 1 (Zn,Mn)Te, x eff = p (cm -3 ) exp.:(ga,mn)as:t. Omiya et al., Physica E 7, 976 (2000). (In,Mn)As: D. Chiba et al., J. Supercond. and Novel Mag.16, 179 (2003). (Zn,Mn)Te: D. Ferrand et al., Phys. Rev. B 63, (2001).

49 p-d exchange energy N 0 β comparison

50 4. Making use of ferromagnetism in semiconductors Electrical control of ferromagnetism Current induced domain wall motion Tunneling with magnetism

51 4. Making use of ferromagnetism in semiconductors Electrical control of ferromagnetism Current induced domain wall motion Tunneling with magnetism

52 Electric-field control of ferromagnetism 800 nm 5 nm 10 nm 400 nm 100 nm Au/Cr polyimide (In 0.97 Mn 0.03 )As InAs (Al 0.6 Ga 0.4 )Sb AlSb GaAs sub. (In,Mn)As 95/5 nm R Hall = (R 0 /d)b + (R S /d)m R Hall (Ω) K (In,Mn)As 0 V +1.5 MV/cm -1.5 MV/cm 0 V B (mt) H. Ohno et al., Nature 408, 944 (2000).

53 Electric-field control: the case of (Ga,Mn)As 100/5 nm 50 nm 7 nm 30 nm 500 nm 100 nm R S Hall (kω) Au/Cr Al 2 O 3 (Ga Mn )A (Al 0.80 Ga s 0.20 )As (In 0.13 Ga 0.87 )As GaAs (001) GaAs sub (In,Mn)As, H. Ohno et al., Nature 408, 944 (2000) MV/cm MV/cm p (cm -3 ) -5 MV/cm T (K) T C (K) (x10 20 ) D. Chiba et al. Appl. Phys. Lett See also Y. Nishitani et al., Phys. Rev. B 81, (2010) and M. Sawicki, et al., Nature Physics, 6, 22 (2010)

54 Field-effect structures of (Ga,Mn)As backgate structure ferroelectric-gate structure (Ga,Mn)As piezoelectric hybrid structure I. Stokichnov et al., Nature Mater. 7, 464 (2008). PZT electric double layer M. Endo et al., Appl. Phys. Lett. 96, (2010). K. Olejník et al., Phys. Rev. B 78, (2008); M. S. H. Owen et al., New J. Phys. 11, (2009). M. Overby et al., Appl. Phys. Lett 92, (2008); A. W. Rushforth et al., Phys. Rev. B 78, (2008); S. T. B. Goennenwein et al., phys. stat. sol. (RRL) 2, 96 (2008); C. Bihler et al., Phys. Rev. B 78, (2008).

55 Electric-field control of magnetization direction 10 Ga 0.9 Mn 0.1 As 5 2K M Angle ϕ (deg.) 0-5 [100] axis -10 H = Gate electric Field E (MV/cm) D. Chiba et al. Nature (2008).

56 Electric-field effects on metals FePt, FePd: M. Weisheit et al., Science (2007). Au/ ultrathin Fe: T. Maruyama et al., Nature Nanotechnology (2009). CoFeB: M. Endo, S. Kanai, S. Ikeda, F. Matsukura, and H, Ohno, Appl. Phys. Lett. Multiferroics: T. Arima et al., PASPS (2009/1/27). All at room temperature O-23 Kanai et al.

57 4. Making use of ferromagnetism in semiconductors Electrical control of ferromagnetism Current induced domain wall motion Tunneling with magnetism

58 Well defined domains: (Ga,Mn)As 5 µm 1 mm Welp et al., PRL 2003 compressive strain in-plane easy axis 90o domains Shono et al., APL 2000 tensile strain perpendicular easy axis stripe domains

59 Current induced domain wall motion Sample structure channel layer buffer layer easy axis Ga Mn As 30 nm In 0.22 Al 0.78 As 75 nm In 0.18 Al 0.82 As 75 nm In 0.13 Al 0.87 As 75 nm In Al As 75 nm GaAs 100 nm S. I. GaAs (001) sub. perpendicular easy axis [-110] [110] (I) (II) Au/Cr electrode 60 µm 20 µm 20 nm 30 nm T c ~ 112 K T c ~ 115 K 5 µm etching H c H c Patterning of coercive force H c etching of (Ga,Mn)As by Preparation of domain wall

60 Current induced domain wall motion v eff (m/s) K 107 K 106 K K 104 K 103 K 102 K 101 K 100 K 100 K x10 5 j (A/cm 2 ) M. Yamanouchi et al., Phys. Rev. Lett. 96, (2006)

61 Mechanism Adiabatic spin transfer (conservation of angular momentum) current electron j Mn E F d state

62 Domain wall motion: Theory (Spin transfer) Square root dependence G. Tatara and H. Kohno, Phys. Rev. Lett. 92, (2004). v = A 2 2 1/ 2 ( j jc ) P g µ B A = 2e M j C 2e K δ w = π ħ P P : spin polarization g : g factor of Mn spin µ B : Bohr magneton e : charge of electron M : magnetization K : transverse anisotropy δ w : DW width

63 Current induced domain wall motion v eff (m/s) K 107 K 106 K K 104 K 103 K 102 K 101 K 100 K 100 K x10 5 j (A/cm 2 )

64 Transfer factor and threshold current density 2.5 x x10 5 A (m 3 /C) exp. (linear) exp. (square root) theory j C (A/cm 2 ) exp. (square root) theory exp. (linear) temperature (K) temperature (K) A = P g µ B 2e M j C = 2e K δ w π ħ P M. Yamanouchi et al., Phys. Rev. Lett. 96, (2006)

65 j C = 2e K δ w π ħ P (Ga,Mn)As (T/T c ~ 0.9) Metal (in plane) Metal (perpendicular) K (hard axis anisotropy, J/m 3 ) δ w (domain wall width, nm) P (spin polarization, %) 60 4x j C (A/m 2 ) 6x10 9 7x x10 12

66

67 4. Making use of ferromagnetism in semiconductors Electrical control of ferromagnetism Current induced domain wall motion Tunneling with magnetism

68 Tunnel Magnetoresistance (TMR) 20 nm (Ga Mn )As nm GaAs nm (Ga Mn )As nm GaAs:Be 560 p + - GaAs (001) sub 300 TMR = 2P 1 2 P %, P = 77 % MR (%) K +0.5 mv Sample A B [100] (T) R (kω ) MR (%) B[100](mT) D. Chiba et al. Physica E 2004

69 Resonant Tunneling Diode with a Ferromagnetic Emitter

70 Resonant Tunnel Diode with a Ferromagnetic Emitter Sample structures (Ga Mn )As GaAs AlAs GaAs AlAs GaAs GaAs:Be (5x10 17 cm -3 ) GaAs:Be (5x10 18 cm -3 ) p + GaAs sub. 200 nm 15 nm 5 nm d W nm 5 nm 5 nm 150 nm 150 nm H. Ohno et al. Appl. Phys. Lett., 1998

71 Ultra-high doping of Mn in III-V compounds T. Jungwirth et al., Phys. Rev. B76, (2007)

72 Spintech VI, O-10

73 arxiv v2 (Spintech VI poster FP-42) (Formation of 2D holes in GaAs:Be explains the resonant tunnel-like feature and the thickness dependence)

74 Diluted Magnetic Semiconductors 1. What you need to know about nonmagnetic semiconductors Band structure 2. How you make a semiconductor magnetic Doping and sp-d exchange 3. The consequences of exchange interaction Spin-split bands and ferromagnetism 4. Making use of ferromagnetism in semiconductors Electrical control of ferromagnetism Current induced domain wall motion Tunneling with magnetism