Magnetic properties of Ferromagnetic Semiconductor (Ga,Mn)As

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1 Magnetic properties of Ferromagnetic Semiconductor (Ga,Mn)As M. Sawicki Institute of Physics, Polish Academy of Sciences, Warsaw, Poland. In collaboration with: T. Dietl, et al., Warsaw B. Gallagher, et al., Nottingham L.W. Molenkamp, et al., Wuerzburg H. Ohno, et al., Sendai Support by: Japanese ERATO, EU FENIKS, Polish MNiI School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 1

2 Outlook Introduction - motivation/history T C and M S Uniaxial magnetic anisotropy due to confinement and/or biaxial (epitaxial) strain - reorientation transition Biaxial (cubic, 4-fold) in-plane anisotropy Uniaxial in-plane anisotropy - reorientation transition - single domain behaviour Hole driven ferro-dms, mostly (Ga,Mn)As School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 2

3 Spintronics Making spins to: store and reveal information in a faster way transmit information (supplementing charge and light) process information (supplementing charge) Spin valve (or MTJ) Anti Ferro Ferro Conductor/Oxide Ferro Substrate Main applications: magnetic field sensors read heads galvanic isolators Magnetoresistive RAMs Why semiconductor spintronics? School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 3

4 Semiconductor Spin-electronics (Spintronics) Spin-related phenomena in semiconductors an additional degree of freedom (spin + charge spintronics) spin including magnetism spintronics electronics optics School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 4

5 Ferromagnetic semiconductors May offer a possibility to replace of All metal Spin-Based Electronic Devices they posses both spins and mechanism that effectively couples spins with carriers. technological compliance with semiconductor industry. School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 5

6 Towards ferromagnetic semiconductors magnetic semiconductors magnetic semiconductors and insulators: short-range antiferromagnetic superexchange EuTe,..., NiO,... short-range ferromagnetic super- or double exchange EuS, ZnCr 2 Se 4, La 1-x Sr x MnO 3,... EuS/KCl,... diluted magnetic semiconductors Standard semiconductor + magnetic ion II-VI: Cd 1-x Mn x Te,..., Hg 1-x Mn x Se,... IV-VI: Sn 1-x Mn x Te,..., Pb 1-x Eu x S III-V: In 1-x Mn x Sb,..., Ga 1-x Er x N IV: Ge 1-x Mn x,..., Si 1-x Ce x School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 6

7 History of DMS School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 7

8 Most of DMS: random antiferromagnet short range antiferromagnetic superexchange B School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 8

9 Evidences for antiferromagnetic interactions: magnetic susceptibility Curie-Weiss law χ = C/(T Θ) C = gµ B S(S+1)xN o /3k B Θ < 0 antiferro A. Lewicki et al. School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/2005 9

10 Magnetisation of localized spins 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 no spontaneous magnetisation Y. Shapira et al. School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

11 Determination of sp-d exchange integrals: - giant splitting of exciton states E ~ M ~ B S (H) ENERGY c.b. v.b. σ+ σ+ σ- σ- g eff > s-d: I sd αn o 0.2 ev no s-d hybridization => potential s-d exchange J. Gaj et al., R. Planel,.. A. Twardowski et al. G. Bastard, -- p-d: I pd βn o -1.0 ev large p-d hybridization and large intra-site Hubbard U => kinetic p-d exchange School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

12 Effect of acceptor doping on magnetic susceptibility in 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 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

13 Ferromagnetic temperature in p-(zn,mn)te Ferromagnetic Temp. T F / x eff (K) Hole concentration (cm -3 ) x (Zn,Mn)Te:N (Zn,Mn)Te:P Insulating Metallic ferromagnetism disappears in the absence of holes ferromagnetism on both sides of metal-insulator transition Ferrand et al. (Grenoble, Warsaw) PRB 01 Sawicki et al. (Warsaw) pss 02 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

14 Ferromagnetism in DMS the origin -- carriers localized by impurities (BMP): inoperative Bhatt et al., Dugaev et al., Inoue et al., Das Sarma et al., Dagotto et al., delocalized carriers (Zener/RKKY model) Ryabchenko, et al., Dietl et al., MacDonald et al., Boselli et al., Petukhov, Sham et al., hole world E F k Mn Mn k Mn world + Mn Mn Mn Mn Mn Mn T T C School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/ E F Exchange spin splitting redistributes the carriers between spin subbands thus lowering their energy

15 Ferromagnetism in DMS the origin -- carriers localized by impurities (BMP): inoperative Bhatt et al., Dugaev et al., Inoue et al., Das Sarma et al., Dagotto et al., delocalized carriers (Zener/RKKY model) Ryabchenko, et al., Dietl et al., MacDonald et al., Boselli et al., Petukhov, Sham et al., T C =x eff N 0 S(S+1)J 2 A F ρ(ε F )/12k F holes!!! = valence band Mn Mn k -- s-d: I sd αn o 0.2 ev no s-d hybridization -- p-d: I pd βn o -1.0 ev large p-d hybridization Mn T T C E F Exchange spin splitting redistributes the carriers between spin subbands thus lowering their energy Mn School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

16 Why DMS, why (Ga,Mn)As? Carrier mediated ferromagnetism in semiconductors: GaSb InAs InP InSb ZnSe ZnTe CdTe x = 0.05, p = cm -3 Ge AlAs GaP GaAs AlP GaN ZnO Curie temperature (K) T. Dietl, et al., Science 2000 Si C More than 20 compounds showed ferro- coupling so far Operational criteria: Scaling of T C and M with x and p Interplay between semiconducting and ferromagnetic properties School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

17 (Ga,Mn)As: single phase ferro-dms M [110] (T) / M Sat (5K) [ r.u. ] M REM (M Spontaneous ) [ a.u. ] Remnant Magnetisation % (Ga,Mn)As Temperature [ K ] 8% (Ga,Mn)As T C = 173 K T = 172 K T = 175 K 25 nm thick Magnetic Field [ Oe ] K-Y. Wang, et al., JAP 04 & ICPS 27 χ -1 [ a.u. ] T F = x eff N 0 S(S+1)J 2 A F ρ(ε F )/12k F T C ~ xp 1/ Total x Mn ( % ) School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/ T C ( K ) T. Dietl, H. Ohno, F. Matsukura, PRB 01 T C = 173 K = -100 o C

18 Operational criteria for carrier-controlled ferromagnetic semiconductors Spin-LED Ferro-FET Also: Y. Ohno et al., Nature 99 H. Ohno et al., Nature 00 Current induced domain wall switching J C ~10 5 A/cm 2 Electrically assisted magnetisation reversal M. Yamanouchi, et al., Nature 04 D. Chiba, et al., Science 03 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

19 Why DMS, why (Ga,Mn)As? Carrier mediated ferromagnetism in semiconductors: GaSb InAs InP InSb ZnSe ZnTe CdTe x = 0.05, p = cm -3 Ge AlAs GaP GaAs AlP GaN ZnO Curie temperature (K) T. Dietl, et al., Science 2000 Si C More than 20 compounds showed ferro- coupling so far Operational criteria: Scaling of T C and M with x and p Interplay between semiconducting and ferromagnetic properties School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

20 T C in (Ga,Mn)As: prospects Record T C (K) LT annealing Increase Mn incorporation High index surfaces? 173 K Date School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

21 Mn in GaAs Mn(...3d 5 4s 2 ) + GaAs = 3d 4 (A 0 ) + e+e+e v.b. 3d e e e e e e e h e 3d e 3d 5 +h = 3d 4 A 0 J = 1 h v.b. 3d e e e e e 3d 4+1 = 3d 5 A - S = 5/2, L = 0 Mn = spin 5/2 + hole School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

22 Growth of (Ga,Mn)As Mn source Mn total hole + S=5/2 SUBSTRATE p [ cm -3 ] (Ga,Mn)As zero compensation limit Something went wrong! x tot [ % ] K. Yu, et al. School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

23 Mn interstitials c-rbs and c-pixe reveal: in low-temperature MBE grown ferromagnetic (Ga,Mn)As Mn atoms occupy three distinct positions in the lattice substitutional Mn Ga, interstitial Mn I, and random (MnAs) in proportions depending on annealing. Mn Mn ++ As Ga K. Yu, et al., PRB 02 interstitial Mn I : Double donor Does not play ferro AF bonds to Mn Ga Blinowski, Kacman, PRB 03 Low temperature annealing!! Potashnik et al., 02 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

24 Growth of (Ga,Mn)As Mn source Mn source Mn total hole + S=5/2 K. Yu, et al. Mn Ga hole + S=5/2 Mn I 2e+? SUBSTRATE SUBSTRATE p [ cm -3 ] (Ga,Mn)As x tot [ % ] zero compensation limit p [ cm -3 ] (Ga,Mn)As x tot [ % ] zero compensation limit p = x Annealing Wang, et al., 2004 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

25 (apparent) Magnetisation deficit µ tot = M S / x tot M S =N 0 x eff X + p (-1) Mn I paramagnetic: x eff = x Sub Mn I AF to Mn Ga : x eff = x Sub - x I µ tot [ µ B /Mn ] X [ µ B /Mn sub ] X [ µ B /Mn sub ] 6 4 As-Grown Annealed x total [ % ] School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

26 ... summary (Ga,Mn)As emerges as the best understood model ferromagnet with a number of attractive functionalities Control of magnetism and magnetization direction is possible by external means Beginning of the road for high temperature ferromagnetic semiconducting system School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

The magnetic anisotropy - Testing/verification for models - Device engineering magnetoresistive AMR ~ cos 2 ( ) j, M ) spin injection/detection Injector Ferromagnetic polarizer

27 The magnetic anisotropy - Testing/verification for models - Device engineering magnetoresistive AMR ~ cos 2 ( ) j, M ) spin injection/detection Injector Ferromagnetic polarizer Electrical gate Electric field Detector Ferromagnetic analyser Datta & Das (1990) utilisation of the magnetic anisotropy School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

28 Magnetocrystalline vs. shape anisotropy Despite the expected for the layered material in-plane arrangement of M (H A = M S ), relatively strong perpendicular (uniaxial) magnetic anisotropy has been observed since the very beginning of the studies: (In,Mn)As/GaAs Munekata 93 some (Ga,Mn)As/InGaAs Ohno, Shono QW (Cd,Mn)Te Haury 97 (Ga,Al,Mn)As/GaAs Takamura 02 (Ga,Mn)As/GaAs Sawicki 02 H A >> M S magnetocrystalline anisotropy dominates over the shape effects School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/ H M M S in 5% (Ga,Mn)As 600 Oe Oe for Fe

29 Magnetic anisotropy in cubic materials T d symmetry of the host lattice magnetic anisotropy is expected on <100> and <111> directions School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

30 MA of p-dms: the epitaxial origin H M Tensile strain Perpendicular Magnetic Anisotropy Marginal role of the shape anisotropy!! K s = M 2 (D a D c )/2 H M Compressive strain In plane Magnetic Anisotropy Shen et al (Sendai) + lots of confusing information? [100], [110]? about in plain easy axis School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

31 Excellent micromagnetic properties Large values of K a (= M S H a / 2) and A hinder domain formation Dilute systems: low M S Domain wall energy E = (K a A) 1/2 (Ga,Mn)As 1 mm Welp et al., PRL 03 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

32 Magnetic anisotropy the origin EPR studies shows that Mn single ion anisotropy is negligible p-d Zener Model - Mn - Mn interaction is mediated by holes, characterised by a non-zero orbital momentum Fedorych et al., 2002 Dietl, Ohno, Matsukura, PRB 2001 (cf. Abolfath, Jungwirth, Brum, MacDonald, PRB 2001 ) It is the anisotropy of the carrier-mediated exchange interaction stemming from spin-orbit coupling of hole gas. School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

33 Valence band structure (Zinc-blende Γ 7 and Γ 8 ) Schrödinger equation: ( + H + H ) Ψ = EΨ basis function: H kp pd bs 1 1 u u2 = i [( X + iy ) 2Z ] u3 = [( X iy ) + 2Z ] 1 1 = ( X + iy ) 2, 1 4 = i ( X iy ) 2, u 6 = i ( X iy ) + Z 3 1 u u 5 = [( X + iy ) + Z ] [ ] 0,1 GaAs 3,, Fermi Surface at E F = 100 mev,. 0,0 2 (x10 7 ) E (ev) -0,1-0,2 k z (cm -1 ) 1-0,3-0, L Γ X [111] (x10 7 [100] ) k (cm -1 ) 0 (x10 7 ) 1 k x (cm -1 ) k y (cm -1 ) (x10 7 ) School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

34 Dispersion of strained (Ga,Mn)As GaAs GaAs ε xx = E (ev) E (ev) L Γ X [111] (x10 7 [100] ) k (cm -1 ) L Γ X [111] (x10 7 ) [100] k (cm -1 ) Fermi Surface at E F = 100 mev 2 (x10 7 ) 2 (x10 7 ) k z (cm -1 ) 1 k z (cm -1 ) 1 0 (x10 7 ) 1 k x (cm -1 ) k y (cm -1 ) (x10 7 ) 0 (x10 7 ) 1 k x (cm -1 ) 0 1 k y (cm -1 ) 2 (x10 7 ) School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

35 Uniaxial MA epitaxial origin Pseudomorphic low temperature MBE growth: growth axis (001) (GaMn)As T d Compressive Biaxial strain (GaMn)As D 2d GaAs T d GaAs T d School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

36 Uniaxial MA epitaxial origin 1. strain, confinement or both split the hh from lh Energy lh hh, lh hh j z = ± 3/2 hh lh j z = ± 1/2 Tensile 0 Compressive strain confinement School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

37 Ferromagnetism in DMS the origin Mn Mn k Uniaxial MA epitaxial origin 1. strain, confinement or both split the hh from lh 2. if M 0 the lower energy state: for hh (l=±1) when k M Compressive case, low hole density Mn T T C j z = ± 3/2 E F Mn hh hh Energy MIS M: M. S awicki on (Ga,Mn)As - Moscow 29/06/ j z = ± 1/2 lh Energy lh ~ Js S M z M in plane hh. subband occupied easy [001] (K U > 0; strong) School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

38 Uniaxial MA epitaxial origin 1. strain, confinement or both split the hh from lh 2. if M 0 the lower energy state: for lh (l=0) when k M Ferromagnetism in DMS the origin Mn Mn k Tensile case, low hole density Mn T T C E F Mn j z = ± 3/2 lh lh Energy MIS M: M. S awicki on (Ga,Mn)As - Moscow 29/06/ j z = ± 1/2 hh Energy ~ Js S hh hh M z M in plane hh. subband occupied easy (001) (K U < 0; weak) School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

39 Magnetic anisotropy epitaxial origin Epitaxial (biaxial) strain Splitting of the hole states Ferromagnetism in DMS the origin Mn Mn k Compressive case: Mn T T C E F Mn hh hh j z = ± 3/2 Energy lh MIS M: M. S awicki on (Ga,Mn)As - Moscow 29/06/ j z = ± 1/2 Energy lh ~ Js S M z uniaxial anisotropy M in plane hh. subband occupied perpendicular anisotropy (strong) lh. subband occupied in-plane anisotropy (weak) School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

40 Valence band engineering (Cd,Mn)Te QW Compensation of confinement induced hh/lh splitting by epitaxial tensile strain compressive ε xx = % tensile ε xx = 0.11% tensile ε xx = 0.13% QW 10 nm x = 5.3% QW 10nm x = 4.9% QW 15nm x = 5.6% Cd 1-z Zn z Te 12% Zn CdTe CdTe e e e hh lh hh lh lh hh S. Tatarenko J. Cibert (Grenoble) School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

41 The measurements Faraday configuration σ ENERGY σ+ σ- σ+ σ- χ = δ(e -E + )/δh at H 0 E ~ M σ + (Warsaw, Grenoble) School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

42 Tailoring the magnetic anisotropy Perp. anisotropy Ising case no splitting for B Z χ -1 P. Kossacki et al., Physica E 04 By strain (Cd,Mn)Te QW e hh lh In-plane like anisotropy e lh hh School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

43 hh/lh influence on uniaxial anisotropy T 2d D 2d symmetry lowering, growth direction is the quantisation axis, hh/lh population plays decisive role K u = f ( k p 6 6 H + H p-d, H Strain ) E F For biaxial compression e hh lh Typically, easy axis in plane Hole density [ cm -3 ] H M [001] <110> Easy z-axis <100> x = 5.3% ε xx = -0.27% T / T C Easy plane Calculations: Dietl, Ohno, Matsukura, PRB 2001 M H T C =33K School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

44 hh/lh influence on anisotropy Hole density [ cm -3 ] M [001] <110> Easy z-axis <100> x = 5.3% ε xx = -0.27% Easy plane M T / T C Two important features emerge: 1) Both types of anisotropy possible 2) 2nd order phase transition in-between School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

45 Perpendicular magnetic anisotropy 1) For low enough p perpendicular magnetic anisotropy in compressively strained (Ga,Mn)As/GaAs is observed (in-plane for tensile case) M / M Sat (5K) [ a.u. ] T = 5 K H M H M x Mn =0.023 M H M H A H Magnetic Field [ Oe ] School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

46 hh/lh influence on anisotropy 2) The reorientation: easy axis easy plane Hole density [ cm -3 ] [001] <110> Easy z-axis <100> x = 5.3% ε xx = -0.27% Easy plane H M M H T / T C Calculations: Dietl, Ohno, Matsukura, PRB 2001 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

47 The reorientation transition: temperature Temperature influence on hh/lh population ratio: hω s ~ M = f(t) Hole density [ cm -3 ] [001] x = 5.3% ε xx = -0.27% Easy (001) plane Easy z-axis 0,1 0,0 0,2 0,4 0,6 0,8 1,0 T / T C M / M Sat (5K) [ rel. u. ] 1,0 0,5 0,0-0,5-1,0 Perpendicular 5 K H M H M x Mn = ,4 0,2 0,0-0,2-0,4 22 K In-plane Magnetic Field [ Oe ] M. Sawicki, et al., PRB 04 H M H M School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

48 Tailoring the magnetic anisotropy Perp. anisotropy Ising case no splitting for B Z χ -1 P. Kossacki et al., Physica E 04 By strain (Cd,Mn)Te QW T = 5 K In-plane like anisotropy Magnetic Field [ Oe ] 22 K Compressed (Ga,Mn)As By temperature (and hole density) School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

49 The reorientation transition: hole density Hole density [ cm -3 ] M [001] <110> Easy z-axis <100> x = 5.3% ε xx = -0.27% Easy plane M E F E F e hh lh e hh lh T / T C Calculations: Dietl, Ohno, Matsukura, PRB 2001 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

50 The reorientation transition: hole density Gate Light InMnAs InMnAs/GaSb heterojunction H. Ohno et al., Nature 00 Magnetization (emu/cm 3 ) H M M z <M H=10oe normal to plane H M M z =M Temperature (K) ρ Hall (B) [Ωcm] M. S awicki on magnetic anisotropy - S endai 28/07/ w/ illumination w/o illumination Magnetic Field [T] T=10K Koshihara et al., 97; X. Liu et al., 04 Compensation Hydrogenation Lemaitre et al., 27 ICPS 04 Brandt et al., 04 ρ Hall ~ M LT annealing Penn State 02, Nottingham 03, & everywhere else p b < p c < p d < p e Thevenard, et al., 05 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

51 Hole density change: LT annealing Post growth LT annealing increases hole density Annealing influence on magnetic anisotropy/ REM(T) needed reorientation transition M / M Sat (5K) [ rel. u. ] 1,0 0,5 0,0-0,5-1,0 Perpendicular 5 K H M H M x Mn = ,4 0,2 0,0-0,2-0,4 22 K Magnetic Field [ Oe ] In-plane H M H M School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

52 Hole density change: LT annealing Hole density [ cm -3 ] Post growth LT annealing increases hole density 20 Annealing influence on magnetic anisotropy/ 15 reorientation transition Easy z-axis x = 5.3% ε xx = -0.27% 0,1 0,0 0,2 0,4 0,6 0,8 1,0 T / T C Easy plane School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/ Perpendicular component of REM [ a.u. ] In-plane component of REM [ a.u. ] M. Sawicki, et al., PRB annealing annealing Temperature [ K ] Temperature [ K ] As grown 28 h ann. 57 h ann. T Tr

53 Control of the magnetism in nano scale Controlling quantum magnetic dots Patterning magnetic nanostructures Patterning magnetic nanostructures Ferromagnetic Quantum Wires Ferromagnetic Quantum Dot Array School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

54 ...summary Confinement and Strain induced magnetocrystalline anisotropy observed. - character - magnitude - reorientation transition consistent with p-d Zener model School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

55 The in-plane magnetic anisotropy The epitaxially induced D 2d symmetry suggests 4-fold (biaxial) magnetic inplane anisotropy School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

56 4-fold in-plane magnetic anisotropy Hole density [ cm -3 ] 10 1 <110> [001] <100> <110> x = 5.3% Easy plane: cubic anisotropy 4-fold symmetry Easy z-axis 180 [010] [-110] 135 H = 0 [100] 90 M [110] 0 0,1 0,0 0,2 0,4 0,6 0,8 1,0 T / T C Calculations: Dietl, Ohno, Matsukura, PRB 2001 Can we observe this? School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

57 Field induced coherent rotation [110] 135 M [100] 90 H - [110] = 0 H - [110] > [110] [110] 135 [100] 90 M 45 H - [110] [010] [010] m = M /M S 1 [110] 2K C /M S / 2 T << T C H <100> School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

58 Field induced coherent rotation: low T 1/ 2 m = M /M S 1 [110] 2K C /M S H H [110] H [100] 45 H - [110] Sample Moment [ a.u. ] % [100] = [010] <100> [-110] T = 5 K Magnetic Field [ Oe ] [010] A proof of: Formation of macroscopically large domains 4-fold magnetic symmetry 0 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

59 Temperature dependence of in-plane magnetic anisotropy 40 [100] 40 71% Sample Moment [ a.u. ] [-110] [110] T = 5 K Magnetic Field [ Oe ] REM Moment [ a.u. ] A [100] B [-110] C [100] D [110] Ga 1-x Mn x As x = 6.5% H = Temperature [ K ] biaxial anisotropy 4-fold symmetry winning at low T uniaxial anisotropy 2-fold symmetry winning at high T cf. Katsumoto et al., Hrabovsky et al., Tang et al., Welp et al., Ferre et al., Liu et al.,..., & EVERYONE ELSE. The new reorientation transition when system crosses from biaxial to uniaxial anisotropy dominating temperature range School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

60 Temperature dependence of in-plane magnetic anisotropy 40 [100] 40 71% Sample Moment [ a.u. ] [-110] [110] T = 5 K Magnetic Field [ Oe ] REM Moment [ a.u. ] A [100] B [-110] C [100] D [110] Ga 1-x Mn x As x = 6.5% H = Temperature [ K ] As grown samples: Uni_easy [-110] Cubic_easy <100> Uni_hard [110] School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

61 In-plane uniaxial magnetic anisotropy Strong uniaxial behaviour with either [-110] or [110] the easy axis, seen on all studied samples, usually dominating close to T C Magnetisation [ a.u. ] T / T C = 0.65 T / T C = _ [110] [110] Ga 1-x Mn x As x = 3 % Magnetic Field [ Oe ] T = 15 K School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/ Magnetisation [ a.u. ] (near perfect single domain behaviour!!) 2 [110] _ [110] Magnetic Field [ Oe ] T=135K (Ga,Mn)As x = 6.7 % M. Sawicki, et al.,, PRB 05

62 In-plane uniaxial magnetic anisotropy Precluded by symmetry considerations. Not expected in D 2d. Thickness independent: seen from 7 µm down to 5 nm Not sensitive to etching Sample Moment [ a.u. ] % (Ga,Mn)As 50 nm Annealed [110] [-110] T = 0.92 T C Magnetic Field [ Oe ] Welp et al., 04 Nottingham, 04 Not sensitive to the state of the surface; surface/interface anisotropy not important School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/ x0.81 x0.50 Before: 50nm 2x etch 4x etch: 25nm

63 In-plane uniaxial magnetic anisotropy D 2d C 2v symmetry lowering: (In C 2v [110] and [-110] are not equivalent) - Mn concentration gradient along growth axis - preferential incorporation of Mn during growth Sadowski et al., 2004 Welp et al., 2004 More information required... School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

64 In-plane uniaxial magnetic anisotropy There are samples with the easy axis switching from [-110] to [110] on increasing T M REM ( emu/cm 3 ) T R [-110] easy [110] easy _ [110] (Ga,Mn)As x = 8.4% Annealed [110] Temperature ( K ) M. Sawicki, et al., PRB 05 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

65 In-plane uniaxial magnetic anisotropy There are samples with the uniaxial easy axis switching from [-110] to [110] on increasing T; It switches also upon annealing if p > ~ cm p ( cm -3 ) (Ga,Mn)As _ [110] - easy x ( % ) [110] - easy M. Sawicki, et al., PRB 05 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

66 M(T) in presence of two competing in-plane anisotropies: single domain case E m = K C /4 sin 4 (2θ) + K U sin 2 θ MHcos(ϕ θ) K C ~ M 4 S K U ~ M 2 S Temperature dependence of in-plane magnetic anisotropy expected [100] REM Moment [ a.u. ] A [100] B [-110] C [100] D [110] Ga 1-x Mn x As x = 6.5% H = Temperature [ K ] Sample Moment [ a.u. ] % [110] [-110] T = 5 K Magnetic Field [ Oe ] Two competing terms Magnetic easy axis reorientation transition when K C = K U K. Wang, et al., cond-mat 05 M. S awicki on magnetic anisotropy - S endai 28/07/ School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

67 Phenomenological description of magnetic anisotropy in single domain (Ga,Mn)As E m = K C /4 sin 4 (2θ) + K U sin 2 θ MHcos(ϕ θ) K C ~ M 4 expected S K U ~ M 2 S M [-110]2 + M [110]2 = M 2 S M (emu/cm 3 ) T = 5 K M (emu/cm 3 ) (2K C + (2K 2K ) / M U S C - 2K ) / M U S H (Oe) H (Oe) T = 50 K K U, K C (10 3 erg/cm 3 ) K C = K U , T (K) M S ( emu/cm 3 ) K U = b M S (2.1±0.1) K C = a M S (3.8±0.2) K. Wang, et al., cond-mat 05 School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

68 Conclusions Magnetic anisotropy in hole-controlled ferro-dms: magnetic anisotropy effect of s-o interaction in the valence band z-axis (perpendicular)/in plane anisotropies controlled by confinement and epitaxial strain in-plane anisotropy: competition of biaxial(cubic) and uniaxial anisotropy origin not yet understood three Spin Reorientation Transitions observed: perpendicular in plane <100> [-110] [-110] [110] possibility of easier magnetisation manipulation phenomenological self-consistent description possible in single domain model School of Magnetism: M. Sawicki on (Ga,Mn)As - Constanta 9/09/

Making Semiconductors Ferromagnetic: Opportunities and Challenges

Making Semiconductors Ferromagnetic: Opportunities and Challenges J.K. Furdyna University of Notre Dame Collaborators: X. Liu and M. Dobrowolska, University of Notre Dame T. Wojtowicz, Institute of Physics,