Spin-orbit Effects in Semiconductor Spintronics. Laurens Molenkamp Physikalisches Institut (EP3) University of Würzburg

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1 Spin-orbit Effects in Semiconductor Spintronics Laurens Molenkamp Physikalisches Institut (EP3) University of Würzburg

2 Collaborators Hartmut Buhmann, Charlie Becker, Volker Daumer, Yongshen Gui Matthias König, Jian Liu, Markus Schäfer Volkmar Hock Alina Novik, Tomas Jungwirth, Jairo Sinova, Ewelina Hankiewicz DFG (SFB 41) ONR

3 Overview - Introduction: HgTe Quantum Wells - Interplay Rashba/Zeeman Splitting - Odd and Even Hall plateaus - Nanostructured Hall bars - Gated H-bars - Aharonov Casher effect

4 HgTe Fabrication: MBE 6. Bandgap vs. lattice constant (at room temperature in zinc blende structure) Bandgap energy (ev) lattice constant a [Å] CT-CREW 1999

5 HgTe: Semimetal or Semiconductor bandstructure zero gap: 1 E (mev) k (.1 ).5 1. fundamental gap D.J. Chadi et al. PRB, 358 (197) E Γ 6 E Γ8 3 mev

6 HgTe Quantum-Well 1 HgTe Hg.3 Cd.68 Te E (mev) VBO 8-5 E (mev) k (.1 ) k (.1 ) well barrier -15 VBO = 57 mev

7 Inverted Bandstructure Γ6 HgCdTe HgTe HgCdTe Γ8 type-iii QW

8 Band Structure of HgTe QWs 4 nm nm QW QW nm nm QW QW normal..15 semiconductor.1 E E..15 inverted semiconductor.1 Energy E(k) (ev) k =(k k =(k x,k x,k y ) y ) k (1,) k (1,) k (1,1) k (1,1) E1 H1 H1 H H H3 L k (.1-1 ) 1 L1 H4 H5 H d HgTe (1 ) k (.1 )

9 High Electron Mobility µ > 3 x 1 5 cm /Vsec 18, q1867 n Hall = 1,79*1 1 cm - n SdH = 1,74*1 1 cm -, 1 µ= 31 cm /Vs R xx (Ω) 1 8 1,5 1, Rxy (kω) 6 4, B (T),

10 Rashba Splitting (Bychkov-Rashba) subband splitting due to macroscopic asymmetric potential spin orbit coupling in an asymetric potential Rashba hamiltonian r h r r = + i E m H * r α ( ) σ Rashba term α: effective mass parameter σ: vector of Pauli spin matrices E: confining electric field energy dispersion ± h k E = Ei + ± αk * m 3... ± βk in case of a hole system E k y k x

11 Rashba Effect in HgTe ( ) (mev) =. V, Sym. Case =. V, Asym. Case (nm -1 ) A. Novik et al., PRB 7, 3531 (5). Y.S. Gui et al., PRB 7, (4). 8 x 8 k p band structure model 1 (mev) =. V (nm -1 ) Rashba splitting energy R, max = 3 mev 1

12 Magnetic QW: Hg 1-x Mn x Te V g Gate Mn concentration Metal Al O Insulator, nm 3 x = Source HgCdTe, x=.68, nm HgCdTe:I, 9nm HgCdTe, 5.5 nm Drain In contact % 7 % HgMnTe well, 11 nm HgCdTe, 5.5 nm HgCdTe: I, 9 nm HgCdTe x=.68 CdTe Buffer 1 % 15 % % CdZnTe(1) Substrate symmetically or asymmetrically doped

13 Interplay of Rashba and Zeeman Effect in Mn-doped Well H = H + H Z + H R H = h m * + V ( z), H Z = g * r r µ σ B, B H R = r r r α ( i E) σ Zeeman splitting subband splitting E g 1 ( + ) δ = hω ± n, ± c n * = adding Mn g* > 1 c [( * hω g B) δ hω µ enhanced g-factor due to sp-d exchange interaction c B + R 1 ] Zeeman Das, Datta, Reifenberger, PRB 41, 878 (199) Rashba

14 Landau Level Crossing two occupied subbands (n 1 n ) result in a beating of SdH SdH amplitude: A cos(πν ) ν = sublevel splitting δ h ω c E F hω c δ Landau level crossing nodes in the SdH oscillations

15 Zeeman or Rashba Effect? temperature dependence 1 Q1697; Symmetrically doped QW =. V 4. K node shift due to to strong sp-d exchange interaction.9 K ( ) K g* = g ( E) µ B B max B 5/ 5gMnµ BB kbt ( T + T ) 6.39 K (T) ν = even odd g Mn : g factor for Mn B 5/ : Brillouin function for S=5/ ( E) max : saturation spin splitting energy T : scaling temperature (accounts for spin spin interaction)

16 Zeeman Effect fitting of E Zeeman with g* = g ( E) µ B B max B 5/ 5gMnµ BB k T ( T + T B ) yielding ( E) max = 4.3 ±.5 mev T =.6 ±. 5 K

17 Rashba Effect gate voltage dependent node position 14 Q1697; Symmetrically doped QW T=.38K FFT analysis V.8 1 (1 1 cm - ) ( ) V. V. V 4. V (T) ν = even odd 1/ ( 1( 1 =)) Hall (1 1 cm - ) Hg.98 Mn. Te/Hg.3 Cd.7 Te =1. nm; =.38 K calculation 1 5 (mev) Hall (1 1 cm - ) FFT data QW

18 Total Subband Splitting c R [( * hω g B) δ hω µ c, and (mev) (mev) B Hg.98 Mn. Te/Hg.3 Cd.7 Te R 1 ] (T) QW (V) (mev) R > E S even in the presence of a strong sp-d exchange interaction Y.S. Gui, et al., Europhys. Lett. 65, 393 (4).

19 R (k ) R (k ) R (k ) R (k ) QHE in Magnetic QWs R (k ) xx Ω Q n = 4 x 1 cm 3 µ = 9 x 1 cm /Vs xy Ω R ( ) xx Ω 4 3 Q n = 14 x 1 cm 3 µ = 56 x 1 cm /Vs xy Ω R ( ) xx Ω B (T) 5 Q n = 9 x 1 cm µ = 5 x 1 cm /Vs B (T) xy Ω R ( ) xx Ω Q1714 B (T) n = 43 x 1 cm 3 µ = 43 x 1 cm /Vs B (T) xy Ω

20 Strong Subband Splitting and QHE ν = 3 5 δ = ν = odd even E F E F E F δ hω c δ hω c δ hω c only odd QHE plateaus node in SdH only even QHE plateaus

21 Strong Subband Splitting and QHE Q167 (% Mn) calculated Landau-level fan chart R xx (kω) Q167 d W = 11 nm n s = m - T = 1.3 K Γ =1.5 mev ν=7 ν=5 ν= R xy (kω) 15 finite LL broadening and LL crossingleads to a vanishing of even filling factor QH plateaus above above5 T: T: ν = 3 => => 3 filled filledll LL calculated DOS B (T) E (mev) 5 Q167 H. Buhmann et al., APL 86, 14 (5) A. Novik et al., PRB 7, 3531 (5).. above above8 T: T: ν = => => filled filledll LL B (T) E.G. Novik, HB et al., cond-mat/4h.

22 Strong Subband Splitting and QHE Temperature Effect K 3 K 1 1 calculated LL fan chart R xx (kω) R xy (kω) B (T) DOS 4 E (mev) 1 5 Q167 ν = 4 plateau is recovered! B (T) LL crossing is lifted HB et al., submitted to APL

23 How can this be explained? R xx / kω mk 15 R xy / kω B / T

24 HgTe Nanostructures ballistic transport in HgTe Hall probes sensor for magnetization processes in the Mn system searchforshe gated H-bars HgTe ring structures Aharonov-Casher Phase due to the strong Rashba effect Problem: how to do nano-technology with low thermal budget

25 HgTe-Nanostructures ballistic cross shape structure µ 1 1 m /(Vs) /(Vs) 4 nm 8 nm 4 nm V. Daumer et al., Appl. Phys. Lett. 83, 1376 (3)

26 y/wmax Ballistic Hall Crosses Non-local resistance: (Landauer-Büttiker) 1. Hall: V I 4 13 = h ( tl tr ) ( t + t ) T ( T + + t + t ) e r l r l. four-terminal: V I 3 14 = h T r l ( T + t + t ) ( t + t ) T + ( t + t ) e r l r l r l t t 3. three-terminal: V I = h e ( t + t )( T + t + t ) r l T r l Monte-Carlo simulations L / W W min t l T r min t r collimation rebound x/wmax L / W

27 Measurements four-terminal resistance: bend-resistance

28 H-bar for detection of Spin-Hall-Effect (electrical detection through inverse SHE) E.M. Hankiewicz et al., PRB 7, R4131 (4)

29 Actual gated H-bar sample HgTe-QW R = 5-15 mev 5 µm Gate- Contact ohmic Contacts

30 First Data Asymmetric HgTe-QW R = 5-15 mev

31 First Data HgTe-QW R = 5-15 mev Signal due to depletion...

32 Other Wafer Symmetric HgTe-QW R = -5 mev -5.E-8-1.E-7 I: 1->4 U:7-1 Signal less than 1-4 U_7-1 [V] -1.5E-7 -.E-7 -.5E-7-3.E V_gate14 [V]

33 Summary - HgTe Quantumwells offer controlable and very large Rashba splitting; moreover Mn-doping possible - Technology cumbersome because of low thermal budget - First nanostructures available: - quasi-ballistic transport; strong QI in small magnetic systems - H-bar: no SHE - AC phase in rings

34 Monte-Carlo Simulation of the diffusive ballistic Transition modelling of the scattering time τ trajectories in a cross-shaped structure 1. Initial parameters:.5 τ=3 W MAX = 7 nm y / W MAX. -.5 τ=.5 * * * τ=1.5 W MIN W MAX W MIN = 35 nm =.5 W MAX n DEG = cm - v F m/s τ = W MAX / v F s R = (h/e ) π / (k F W MAX ) 3 Ω B = m * v F / (e W MAX ).3 T x / W MAX

35 Three- and Four-terminal Resistance N R 3 / (h/e ) N R 4 / (h/e ) Calculation for different τ B/B τ/τ =1. τ/τ =1.4 τ/τ =1.6 N el = 7 τ = W MAX / v F m/s B = m * v F / (e W MAX ).3 T R 4, Ohm comparision with the experiment T = 1.5K -1, -,5,,5 1, B, T Experiment (sample 1819) Calculation: τ/τ =1.3 (B =.35 T, R =18 Ω ) τ/τ =1.35 (B =.38 T, R = Ω) τ = s < τ = trans s