Mn in GaAs: from a single impurity to ferromagnetic layers Paul Koenraad Department of Applied Physics Eindhoven University of Technology Materials D e v i c e s S y s t e m s COBRA Inter-University Research Institute on Communication Technology KITP, 17 April 006 1
Mn in GaAs: from a single impurity to ferromagnetic layers D e v i c e s Materials S y s t e m s COBRA Inter-University Research Institute on Communication Technology Outline Introduction Single impurities Symmetry breaking Coupled impurities Delta doping layers Albuquerque, 16 July 005
Mn-Doping Atoms 3
Electronic Structure magnetic doping: a part of the atoms in the crystal is replaced by magnetic transition metal impurities 4sp 4sp 4sp 4sp Ga-atom GaAs 3d 3d 3d 3d 3d Mn on Ga-site in GaAs (3d 5 +h) 4sp 4sp 4sp Mn-atom GaAs h 3d 5 3d 3d 3d 3d 3d Mn p-d interaction results in anti-ferromagnetic alignment 4
Electronic Structure Mn-atom in GaAs 3d 3d 3d 3d 3d d-states split by cubic crystal symmetry Anti-bonding (bound acceptor state) Impurity band resonant with the valence band States with Γ 15 symmetry split due to SO interaction 4sp Valence band states GaAs 4sp 4sp 4sp 113 mev ground state populated at T=0 when in neutral condition triplet T doublet Γ 15 Γ 1 E The p-d coupling to is strongest for d-states with Γ 15 symmetry Tang en Flatté PRL 9, 04701 (004) 5
Assessment at the Atomic Scale by Cross-Sectional STM 15 nm * 30 nm STM tip 9 nm * 8 nm InAs self-assembled quantum dot in GaAs Two Si impurities in GaAs 110-surface cleaved III/V sample UHV (10-11 torr) 6
Impurity Imaging Iso-electronic impurities Charged impurities InGaAs-wetting layer 30 nm * 30 nm Counting demonstrated up to 40 % Si:InP 100 nm * 100 nm sharp (surface Si-atoms) diffuse (sub-surface Si-ions) 7
Scanning Tunneling Microscopy on Semiconductors z I E c E F E v E gap E F E F ev ev E v E F E C V sample sample tip 8
Scanning Tunneling Microscopy on Semiconductors Positive sample voltage (empty states) Negative sample voltage (filled states) z E F z E c E F E v E gap ev E c E F E v E gap E F ev sample tip sample tip Depletion, accumulation, inversion 9
A and A o Charge States of Mn Ionized Mn A (V=-1.1 V) Neutral Mn A o :(ion + hole) (V=+1.1 V) [110] [001] 70 nm * 70 nm 3*10 18 /cm -3 70 nm * 70 nm Grown by J. De Boeck et al., IMEC, Belgium Same position is imaged at both voltages Contrast depends on depth of Mn-atom below cleaved surface 10
Manipulation of the Charge State by STM tip Ionized Mn acceptor Neutral Mn acceptor E c Negative sample voltage E c Positive sample voltage A 0 I TUNNEL E v E F p-type sample A I TUNNEL tip E v E F p-type sample tip 11
A and A o Charge States of Mn Ionized Mn A (V=-0.9 V) Neutral Mn A o :(ion + hole) (V=+0.7 V) 14 nm * 14 nm Contrast is due to Coulomb field [110] [001] Tunneling to the bound hole (Mn in ~ 3 rd sublayer) 5.6 nm * 5.6 nm 1
Spectroscopic Signature of Mn Current map at +1. V away from Mn on the Mn 0,04 Current (na) 0,0 0,00 00x00 points p-type E v E F Mn 00 * 00 I(V)-curves taken around impurity -0,0 ~100 mev Binding energy Mn 113 mev E c E c E F Mn 0-0,8-0,4 0,0 0,4 0,8 1, 1,6 Bias (V) E v p-type sample tip 13
Contrast Mechanism Ionized acceptor Screened acceptor Negative sample voltage z Positive sample voltage z E F E c E c E gap ev E F E v E gap - E F ev E F E v p-type sample tip p-type sample tip Around charged acceptor bands bend upwards this increases current (height STM tip) Bright feature Around screened acceptor weak band bending. Due to impurity LDOS increase of current (height STM tip) Bright feature 14
Modeling of Impurity States in Semiconductors 15
16 Effective Mass Donor l=0 l=1 l= m=0 m=1 m=0 m=0 m=1 m= n=1 n= n=3 ε e ε hh ε lh J=1/ J=3/ m l n m l n m l n r o m l n e r z y x m k,,,,,,,, * 1 ψ ε ψ ε ε ψ = + + + Pure s-like ground state ), ( ) ( ) 1 ( 0 0, 0 / 1 ϕ θ ψ Y r S = R ( ) * z y x e k k k m + + = ε http://www.orbitals.com/orb/index.html
J=1/ ε e Luttinger Hamiltonian J=3/ ε hh (m J =3/) ε lh (m J =1/) H Lut ( k x, k y, k z ) ψ + V ( r) ψ = ε ψ i i i i Luttinger Hamiltonian H Lut ( k x, k y, k z ) = m o H + c b 0 hh + c H b 0 lh + b 0 H c lh + H 0 b c hh ψ i ϕ1 ϕ = ϕ 3 ϕ4 3/, + 3/ 3/, + 1/ 3/, 1/ 3/, 3/ 4-vector representation based on spin-projection H H hh lh = = b = c = ( kx + k y )( γ 1 + γ ) + kz ( γ 1 γ ) ( k + k )( γ γ ) + k ( γ + γ ) x 3γ ( k 3 3 x y [ γ ( k k ) iγ k k ] x 1 ik y y ) k z 3 z x 1 y γ 1, γ and γ 3 Luttinger parameters Spin-orbit coupling mixes the light and heavy hole bands in confined states γ = γ 3 isotropic dispersion 17
Effective Mass Acceptor Ground state components ψ 1 + ψ = ε ψ H Lut n, l, m n, l, m n, l, m n, l, m ε oε rr Isotropic dispersion ψ Y0,0 Y,0 0 Y = R + β R 0 Y, 0 0 3/,1 3/ 0 ψ 0 Y Y Y = R + β R 0 0 0 Y, 1 3/ 0,0,0 1/ 0, Y l,m spherical harmonics R l radial distribution 3/ 3/ ψ 3/ ψ 1/ and their Kramers conjugates and Bir, Pikus in Symmetry and straininduced effects in semiconductors the ground state has a mixed s + d character l=0 l= m=0 m=0 m=1 m= + β 18
Effective Mass Acceptor ψ 1 + ψ = ε ψ H Lut n, l, m n, l, m n, l, m n, l, m ε oε rr Y0,0 0 Y,0 3/ 0 T Y,1 0 ψ E 3/ = R 0 + β R + β R 0 Y, Y, Y, + Y, 0 0 0 [010] [100] [001] Cubic symmetry of crystal selects d-components l=0 l= m=1 l= m= m=0 m= T E + + β Ε β Τ 19
Effect of Crystal Anisotropy η=1 corresponds with isotropic dispersion Cut at 6 monolayer's trough impurity state along a 110 plane Effective mass model η=0 corresponds with a pure T symmetry [001] [010] η = βe β T 8 nm * 8 nm 110 plane [100] 0
Electronic Structure Tight Binding of Mn-acceptor Experiment J.-M. Tang M. Flatté, Iowa, US 6 nm * 6 nm [001] [110] Grown by J. De Boeck et al., IMEC, Belgium Effective mass model Yakunin et al. PRL 9, 16806 (004) 1
Real Space Fourier Space Experiment Mn in ~ 4 th sublayer Effective mass model = E T η β / β = 0 Tight-binding model (M. Flatté, University of Iowa) = E T η β / β 0 1 nm *1 nm 0.8 nm -1 * 0.8 nm -1 Yakunin et al. PRL 9, 16806 (004)
Improved Effective Mass Model Experiment Effective mass model Inclusion of anisotropy (γ γ 3 ) in the dispersion A. Monakhov & N. Averkiev, Ioffe Institute 3
Symmetry Breaking by crystal symmetry 4
Broken Symmetry Mn:GaAs Bulk or surface symmetry?? Zn:GaAs 6 nm * 6 nm [001] [110] 110-surface 1-10-surface Yakunin et al. PRL 9, 16806 (004) Mathieu et al. PRL 94, 06407 (005) 5
Inversion Asymmetry Figure: S. Loth, Goettingen Ga As impurity 110-surface 1-10-surface Mathieu et al. PRL 94, 06407 (005) 6
Inversion Asymmetry Ga As impurity 110-surface 1-10-surface Figure: S. Loth, Goettingen 7
Symmetry Breaking by strain 8
Stacked Quantum Dots 9 55 nm * 55 nm Grown by M. Hopkinson, Sheffield (UK) current image Bruls et al. APL 8, 3758 (003)
Lattice Constant Profile Growth direction 0,65 InAs/GaAs dot Lattice constant [nm] 0,60 0,55 0,50 0 5 30 35 40 45 Distance [nm] Grown by K. Pierz, PTB-Braunschweig, Germany nm * nm 30
Strained Mn impurity GaAs host QD (InAs) [001] [1-10] Fourier filtered experimental image Effective mass 31 nm * 33 nm Mn 1 Mn adsorbent Grown by J. De Boeck et al., IMEC, Belgium TBM 31
Strained Unstrained (a) Mn1 m m m1 m 1 1.3 nm 60 nm * 60 nm Mn impurity [001] [1-10] 60 nm * 60 nm (b) Strained m m m1 m 1 Mn Mn 1 0,3 m 1 Mn 1 Mn Mn Measured height, nm 0, 0,1 m GaAs host Mn 1 QD (InAs) 0,0-4 - 0 4 Distance along [1-10] direction, nm Mn 3
Strained Mn impurity Unstrained Strained EMA [1-11] TBM [001] [110] 33
Symmetry Breaking Shallow Impurities 34
Broken Symmetry Shallow Impurities Be A 0 Co-doped GaAs:Be,Mn Mn A 0 30 nm * 30 nm [001] [110] 35
Shallow & Deep Acceptor states C:GaAs Be:GaAs Zn:GaAs Cd:GaAs Shallow E B = 6 mev E B = 8 mev E B = 31 mev E B = 35 mev Reusch et al. Univ. Of Gottingen C 6 mev Be 8 mev Zn Mahieu et al. PRL 94, 06407 (005) Cd 35 mev 30 mev Mn 113 mev Co 150 mev Zheng et al. APL 64, 1836 (1994) van der Wielen et al. PRB 63, 15336 (001) Mn:GaAs Deep Valence band E B = 113 mev Yakunin et al. PRL 9, 16806 (004) 36
Interaction with Surface Broken symmetry III V Broken symmetry III V X X Shallow Deep Zn:GaAs Effective localization radius of a neutral acceptor Mn:GaAs a 0 = m * E b 37
Spin-orbit Interaction 38
Spin-orbit Interaction 0.9 Acceptor with E b = 113 mev at 6 monolayers below surface 0.8 Split-off Energy (ev) 0.7 0.6 0.5 0.4 0.3 0. 0.1 0.0-0.1 1 3 4 N 7 Cd Al 13 Ga 31 In 49 Zn Mn P 15 As 33 Sb 51 [001] [110] 8 nm * 8 nm 39
Spatial Structure of Zn in GaP(110) Bulk GaP intentionally doped with Zn (~x10 18 cm -3 ) [001] [1-10] 11 nm * 8 nm 40
Anisotropy & Spin-orbit Interaction η=1 corresponds with isotropic dispersion Acceptor with E b = 113 mev at 6 monolayers below surface η=0 corresponds with a pure T symmetry Crystal anisotropy dominates see also Yakunin et al. PRL 9, 16806 (004) [001] [110] 8 nm * 8 nm 41
Missing link Topography image Fourier filtered image Zn in GaAs E b (Zn) = 30meV a 0 = 1.8nm Zn in GaP E b (Zn) = 70meV a 0 =~ 0.6nm! 10.5 nm * 7.5 nm 11 nm * 8 nm 6 nm * 4 nm 9 nm * 5 nm Mn in GaAs E b (Mn) = 110meV a 0 = 1nm 1 * 8 nm 9 nm * 6 nm 4
Symmetry of Impurities Mn in GaAs Zn in GaP Zn in GaAs O 8 T d A A T E T E A [001] [001] T E [100] [010] Effective mass Tight binding Ab-initio modelling [100] [010] [1-10] [001] [100] [010] Yakunin et al. PRL 9, 16806 (004) Figure: S. Loth [100] [110] S. Loth et al. PRL 96, 066403 (005) 43 Mathieu et al. PRL 94, 06407 (005)
Pairs of magnetic impurities 44
Mn-delta Doped Layers Intentional Mn concentration N=3 10 13 cm - Growth direction [001] 53 nm * 40 nm Grown by J. De Boeck et al., IMEC, Belgium 45
Interacting Impurities 5 th sub-surface layer surface atom sub-surface atom 6 nm * 6 nm Mn 0 Mn 1 Mn [1-10] [001] Separation 0.8 nm A. Yakunin et al. PRL 95, 5640 (005) Ga As Grown by J. De Boeck et al., IMEC, Belgium 1 nm * 10 nm 1 nm * 10 nm Separation 1.38 nm 46
Experimental TBM Simulation 0.8 nm 1.4 nm h h 3d 5 Mn Mn J.-M. Tang M. Flatté Iowa, US A. Yakunin PRL 95, 5640 (005) 6 nm * 6 nm 6 nm * 6 nm anti-parallel spin 3d 5 [1-10] parallel spin [001] 1 nm * 10 nm 1 nm * 10 nm 47
Delta layers 48
Impurity-Impurity Interaction Mn-Mn pair (70 nm) Mn-Mn pair (1.4 nm) Mn-As Ga pair 49 140 nm * 140 nm 1 nm * 10 nm 60 nm * 80 nm
Directional Dependence Mn-overlap 10 0 d-character dominates far from impurity Calculated overlap 10-1 3% [010] [100] [001] 34% 10 - EMA [001] EMA [011] EMA [111] 0 1 3 4 5 Mn-Mn separation r (nm) 50
Directional Dependence Mn-overlap 10 0 d-character dominates far from impurity Calculated overlap 10-1 TBM [001] TBM [011] TBM [111] 43% [010] [100] [001] 10-56% 0 1 3 4 5 Mn-Mn separation r (nm) 51
Directional Dependence Mn-overlap 10 0 d-character dominates far from impurity Calculated overlap 10-1 TBM [001] TBM [011] TBM [111] 43% 3% [010] [100] [001] 34% 10 - EMA [001] EMA [011] EMA [111] 56% 0 1 3 4 5 Mn-Mn separation r (nm) 5
Directional Dependence Mn-overlap A separation (nm) 0.5 1 B Bohr radius 0.9 nm B A 3 d-character dominates far from impurity [010] [100] [001] 4 5 53
Directional Dependence Mn-overlap A [111] [011] [001] separation (nm) 0.5 B 1 Bohr radius 0.9 nm B A 3 d-character dominates far from impurity [010] [100] [001] 4 5 54
Overlap Expectation on [i,j,k] Plane 4*10 14 cm - (100%) 4*10 1 cm - (1%) Highest T curie on the [111] doping plane? [001] doping plane [011] doping plane [111] doping plane [001] [001] [001] [010] [100] [010] [100] [010] [100] 55
High Concentration Mn Delta Layers Local bonds surface Mn -3 V Mn in ionized state Local Coulomb potential 35 nm * 35 nm Grown at PDI, Berlin, Germany - V Ga 0.8 Mn 0. As delta layers (1*10 14 cm - ) -1. V 56
Acknowledgements A. Yakunin, C. Celebi, A. Silov, J.H. Wolter (TU/e) W. Van Roy, J. De Boeck (IMEC-Leuven, Belgium) X. Guo, K. Ploog (PDI-Berlin, Germany) J.M. Tang, M. Flatté (University of Iowa, USA) A. Monakhov, N. Averkiev (Ioffe-institute, Russia) 57