Localization effects in magnetic two-dimensional hole system: from weak to strong localization Ursula Wurstbauer

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1 Localization effects in magnetic two-dimensional hole system: from weak to strong localization Ursula Wurstbauer Columbia University, New York, USA

2 Collaborators Prof. Dr. Werner Wegscheider University of Regensburg, now ETH Zurich Prof. Dr. Tomasz Dietl Polish Academy of Science and University of Warsaw Prof. Dr. Dieter Weiss University of Regensburg Dr. Cezary Śliwa Polish Academy of Science Prof. Dr. Wolfgang Hansen University of Hamburg Stefan Knott University of Hamburg financial support: DFG - SFB 689 spin phenomena in reduced dimension Free and Hanseatic City of Hamburg: cluster of excellence nanospintronics

3 Outline Motivation and introduction Basic properties of Mn doped metamorphic strained InAs QW structures Weak localization phenomena: Low-temperature magnetotransport on Mn modulation-doped 2DHGs without Mn in the channel Strong localization phenomena: Low-temperature magnetotransport on Mn modulation-doped 2DHGs with Mn in the channel Conclusion

4 Why magnetic two-dimensional hole systems? Doping III-Vs with Mn: ferromagnetic semiconducturs Modulation doping: high-μ two dimensional systems J. Fabian et al. acta physica slovacia 57(4), 565 Mn incoporated on the group III-site dual role: acceptor and S = 5/2 hole mediated ferromagnetism p-d exchange coupling model system for spintronic devices T = 3 mk 1/3 [] 3. [-1] / /5 1/2 1 3/ /2 2/ Modulation doped two-dimensional hole systems with ultra-high mobility clean material with mean free path of several microns.5. Rxy (h/e2 ) Combine the advantages of both concepts and prepare Mn modulation doped QW structures

5 Searching the host material AlGaAs/GaAs: Highest electron and hole mobilities Lattice-matched growth - Mn localized in the AlGaAs barrier no hole transfer to the GaAs QW (K. Takamura et al. APL 81(14), 259) active layer In.75Al.25As virtual substrate InAlAs graded buffer In content increases from to.75 superlattice GaAs substrate InAlAs/InGaAs/InAs: smaller energy gap for hole channel modulation doping with Mn - metamorphic MBE growth needed poorer quality of QW structure lower mobility

6 Basic properties of InAs QW structures Layer sequence of QW region: In.75 Al.25 As barrier, In.75 Ga.25 As QW with embedded InAs channel HR-TEM Crystal quality: Active structure grown on top of metamorphic buffer for strain relaxation good crystal quality! Morphology: cross-hatched morphology caused by spatially asymmetric In concentration local strain variation Transport anisotropy between [1] and [-1] M. Soda, J. Zweck AFM Compressive strain ε = Δa/a : active region: ε = 1.9x -3 InAs channel ε ~ -2 counts QW region XRD GaAs (4) θ (deg)

7 Different QW structures normal single sided doped QW InAlAs cap inverted single sided doped QW InAlAs cap InAlAs buffer (75% In) InAlAs:Mn InAlAs spacer InGaAs InAs InGaAs growth direction InAlAs buffer (75% In) InGaAs InAs InGaAs InAlAs spacer InAlAs:Mn segregation of Mn during MBE-growth (confirmed by SIMS measurements) normal doped QW: QW region free of manganese, pure 2DHG inverted doped QW: significant amount of Mn ions in the QW region ( < 18 cm -3 ) UW et al. J. Cryst. Growth 311, 216

8 Magnetotransport normal single sided doped QW without Mn in the channel inverted single sided doped QW with Mn in the channel 5 4 T = 1.7K T = 1.7 K Rxy Rxy D magnetotransport (normal Halleffect, QHE, SdH-oscillations, ) positive Hall-coefficient -> 2D hole system (2DHG) Transport is done in macroscopic Hall-bar devices (1 mm x 2 μm) UW et al. J. Cryst. Growth 311, 216

9 Influence of p on localization mechanism T = 4.2K T = 4.2K sample A cooling # 3 carrier density gate-dependence T = 4.2 K variation of p via field effect variation of p via Mn doping variation of strain p ( 11 cm -2 ) T = 4.2 K carrier density p Mn concentration 837 C 833 C 828 C 82 C 8 C 79 C Increasing p via field effect for fixed amount of Mn decreases localization effect ( ()) Increasing Mn doping concentration increases p and localization effect Localization given by ratio of itinerant holes p an localized Mn ions in the InAs channel (magnetic disorder) UW et al. APL 96, 223.

10 Magnetotransport normal single sided doped QW without Mn in the channel inverted single sided doped QW with Mn in the channel 5 4 T = 1.7K T = 1.7 K Rxy Rxy D magnetotransport (normal Halleffect, QHE, SdH-oscillations, ) positive Hall-coefficient -> 2D hole system (2DHG)

11 6 5 4 Normal doped magnetic 2DHG T = 5mK ν = 1 [1] [-1] ν = 4 ν = 5 ν = 3 ν = Rxy (h/e2 ) Parameter determined from transport: p = cm UW et al. Phys. Rev. B 79,

12 Normal doped QW: Low-field region 1.42 Longitudinal resistance.4 Transverse resistance, [1] sweep direction 5mK mK 4mK 6mK mK 7mK 1.5K K T 6 mk: weak antilocalization (WAL) T 6 mk: superpostion of WAL and hysteretic like anisotropic magnetoresistance R xy.2. 2mK 4mK -.2 6mK 6mK 7mK 1.6K 4.2K Coexistence of ferromagnetism and weak antilocalization T > ~2 K: normal Hall effect (HE) T 6 mk: superposition of normal and anomalous HE T 6 mk: superposition of normal-, anomalous- and planar HE UW et al. Phys. Rev. B 79, (29)

13 Magnetotransport normal single sided doped QW without Mn in the channel inverted single sided doped QW with Mn in the channel 5 4 T = 1.7K T = 1.7 K Rxy Rxy D magnetotransport (normal Halleffect, QHE, SdH-oscillations, ) positive Hall-coefficient -> 2D hole system (2DHG)

14 Transport at millikelvin-temperatures (B perp. 2DHG) High-field regime Low-field regime ν = sample A cooling # 6 T = 3mK U =.5V 8 6 B c ν = 3 ν = 2 1 K 15 Rxy (Ω) mk sweep direction sweep direction Quantized transport phenomena in longitudinal and transverse resistance Abrupt resistance changes over more than 6 orders of magnitude Hysteretic behaviour 2-terminal geometry (apply constant voltage U, measure the current I)

15 Insulating metastable phase: R (B, U) 1. B.8 T = 4mK.6 U bias (V) R U-I (Ω) E6 2.5E6 5.E6 1.5E7 5.E7 1.5E8 5.E8 1.5E9 5.E9 1.5E 5.E 1.5E11 5.E11 1.5E12

16 U bias - driven MIT: Dependence of B 1E-6 1E-7 1 T B I (A) 1E-8 1E-9 T 1E- 1E-11 sample A T = 4mK cooling # 2 T U (V) U bias - driven metal to insulator transition, additional spikes at low B

17 Insulating metastable phase: R (B, U) 1. B.8 T = 4mK.6 U bias (V) R U-I (Ω) E6 2.5E6 5.E6 1.5E7 5.E7 1.5E8 5.E8 1.5E9 5.E9 1.5E 5.E 1.5E11 5.E11 1.5E12

18 B-driven MIT: Temperature dependence U bias U bias U C (for HRS) 12 U =.1V 12 U =.5V R (Ω) 9 8 5mK 3mK 45mK 6mK R (Ω) 9 8 3mK 3mK 45mK 6mK 75mK sweep direction sweep direction sweep direction B - driven MIT decreases with increasing temperatures Existence of jumps dependent on U bias, T, magnetic disorder B

19 Influence of magnetic disorder B - driven MIT depend strongly on ratio between p and Mn ions

20 Orientation of B-field sample A cooling # 6 T = 3mK U =.5V (Ω) sweep direction sweep direction n α B Transition from HRS to LRS depends only on the perpendicular component of the applied B-field

21 Main findings (1) Abrupt current jumps over several orders of magnitude and hysteresis concerning the bias voltage (2) Magnetic hysteresis and colossal magnetoresistance; Transition from HRS to LRS only driven from B Similar findigs in insulating phase of strongly disorderd superconducting materials (InO, TiN,...) Explained by thermal bistability caused by electron phonon decoupling Requirements: Amorphous InO M. Ovadia et al.phys. Rev. Lett. 2, (29) M. Ovadia et al.phys. Rev. Lett. 2, (29), B. L. Altshuler et al. Phys. Rev. Lett. 2, (29) Electrons are strongly interacting; strong enough for electrons being mutually thermalized. -7 Electron-phonon (e-ph) interaction is weak (Disorder suppresses e-ph coupling if wavelength -9 of thermal phonon exceeds the electron elastic mean free path (l h 47 nm) The intrinsic I-V curves are linear for constant electron temperature T -12 el I(A) Mn + M2DHG in InAs apparent nonlinearity is a reflection of electrons being overheated U (V) B = T 3mK 17mK 3mK 45mK 6mK 75mK

22 Model: Thermal bistability due to e-ph decoupling R strong T-dependent at B = T db5/ 2( T, B) R ( B, T ) = R exp( a / db T B 5/2 Brillouin function for S = 5/2; R, a, γ determined by fitting R(T, B =) Use heat balance equation: B. L. Altshuler et al. Phys. Rev. Lett. 2, (29) Comparison Therory Experiment: Abrupt resistance changes Hysteretic behaviour Critical values for B jump differ significantly Jump height opposite behaviour Hysteretic behaviour of R at HRS not decribed ) γ 2 Ubias R( T, B) LW h = F ( T F S (T) energy loss LW, determiend by coupling to accoustic phonons T h(s) hole (substrate) temperature S ) F calculated R - B traces measured R - B traces Jumps only for high el. fields (high U bias ) calculations done by C. Sliwa and T. Dietl h S ( T S ) I (A) U =.5V 5mK mk 15mK 2mK 25mK 3mK 35mK 4mK 45mK 5mK

23 Main findings (1) Abrupt current jumps over several orders of magnitude and hysteresis concerning the bias voltage (2) Magnetic hysteresis and colossal magnetoresistance; Transition from HRS to LRS only driven from B Notes: Compressively strained InAs QW Large energy separation between HH and LH subband HH intraband matrix elements j x, j y very small (MIT immune to in-plane B-field!) Strong antiferromagnetic p-d exchange interaction Removes degeneracy of Mn spin states and hence reduces role of nuclear magnetic moments in the spin relaxation (M. Goryca et al.prl 2, 4648, R. Giraud et al. PRL 87, 5723) Introduces a magnetic anisotropy barrier E a for transitions between s z = 1/2, S z = -5/2 and s z = -1/2, S z = 5/2 barrier E a elongates relaxation time of hole spin τ s by exp(e a /k b T)

24 Theoretical description of hysteresis High resistance state Low resistance state B = E a Magnetic anisotropy barrier B = B c Hysteretic high-resistance state originate from magnetic anisotropy barrier of heavy holes coupled to the localized Mn ions by strong p-d exchange interaction. Results: Very slow spin relaxation of individual bound holes, e.g., relaxation of hole spins reaches s at T =.49 K (calculated) Relaxation of bound holes exceeds time for a B-field sweep hysteresis Model developed by C. Sliwa and T. Dietl UW et al. to accepted for publication in Nature Physics

25 B-field sweep-rates R (Ω) T = 4mK U =.5V.1T/min.1T/min.25T/min.5T/min.75T/min 1T/min Magnetic hysteresis is reduced for lower B-field sweep-rates: confirmation of theoretical picture

26 Minor loops R (Ω) T = 4mK U =.5V up down B=.31 T min 2 min min 2 min 94 min Minor loops starting at HRS: No evidence for ferromagnetic ordering Slow transition from HRS to LRS at fixed B Confirmation of theoretical picture! UW et al. to accepted for publication in Nature Physics

27 Monitoring the relaxation from HRS to LRS 11 without thermal bistability sample B T = 4mK U =.5V with thermal bistability ( jumps ) T = 5 mk B =.3T R (Ω) wait at:.31t.28t 5 1 time (s) R (Ω) sample A cooling # 7.52V.53V.48V.46V.44V.42V.4V 5 1 time (s) Relaxation from HRS to LRS with and without thermal decoupling (jumps). Not fully relaxed after jumps. Relaxation depends on magnetic disorder, U bias, T, B. time (s)

28 time (s) wait at: Relaxation from HRS to LRS U bias =.5 V 5 mk mk 15 mk 2 mk 25 mk 3 mk wait at: U bias =.25 V 5 mk mk 15 mk 2 mk 25 mk Exponential dependence from B, T & (U bias ) for relaxation to thermal decoupling (jumps) Relaxation at B = T exceeds the lifetime of the universe of ~ 4.3 * 17 s for low T year 1 week 1 day 1 h 1 min

29 Anomalous behavior in the QHE regime R xy (1/R xy - e 2 /h) -1 [-1] [1] T = 2 mk R xy (h/e 2 ) Rxx Deviation in Hall slope without hints for parallel conductance (SdH ) Slope can be corrected by subtracting e 2 /h Explanation, origin?

30 Conclusion 2DHG without Mn in the InAs channel: Coexistence of ferromagnetism and weak localization phenomena 2DHG with Mn in the InAs channel Quantized transport phenomena in coexistence with abrupt resistance changes over several orders of magnitude, hysteretic behaviour and long relaxation times. Abrupt resistance jumps caused by thermal bistability. No long-range ordering in the channel. Hysteresis originates from a large magnetic anisotropy of the heavy holes coupled to the Mn acceptors by strong p-d exchange interaction. Unusual quantum Hall traces.

31 Anomalous behavior in the QHE regime T - dependence 3 # B , [-1], [1] ~2mK 2mK 4mK 6mK ~2mK 2mK 4mK 6mK R xy (h/e 2 ) - measured ~2mK 2mK 4mK 6mK Rxy (h/e2 ) - corrected

32 T = 4.2K R xy variation of p via field effect p = 4.4 x 11 cm -2 p = 6.4 x 11 cm p = 4.4 x 11 cm -2 5 p = 6.4 x 11 cm

33 U bias -driven MIT: Dependence of B 1E-6 1E-7 9T B 1E-8 I (A) 1E-9 T 1E- 1E-11 sample A cooling # 2 B QW T = 4mK U (V) U bias - driven MIT and spikes in the current signal minor dependent on B

34 MBE Facility in Regensburg High - Mobility Chamber Spintronic Chamber Source materials: Al, Ga, In, As Dopants: Si, C Source materials: Al, Ga, In, As Dopants: Si, C, Mn acceptor with localized spin of 5/2

35 From weak to strong localization Weak (anti-) localization Localization Strong localization T = 1.6K Rxy (h/e2 ) 12 T = 4.2 K T = 1.6 K Rxy (h/e2 ) p = cm -2 p = cm -2 p = cm Rxy (h/e2 ) InAlAs cap InAlAs:Mn InAlAs spacer InGaAs InAs InGaAs InAlAs buffer Magnetic modulation doped: Mn provides free holes InAlAs cap C-δ-doping InAlAs spacer InGaAs InAs InGaAs InAlAs buffer Non-magnetic modulation doped: C provides free holes; Mn impurities inside the QW InAlAs cap InGaAs InAs InGaAs InAlAs spacer InAlAs:Mn InAlAs buffer Magnetic modulation doped: C provides free holes; Mn impurities inside the QW Interaction of localized Mn ions with S = 5/2 and free 2D holes causes strong localization

36 Longitudinal resistance: h-h interaction correction 3 [-1] 8mK 2 1 SdH oscillations superimposed by a negative parabolic background 5mK [1] 8mK Quantum correction to the classical Drude conductivity due to electronelectron interaction.5 - (B 2 ) (Ω) - (B 2 ) (Ω) 5mK [-1] [1] 5 mk 2 mk 4 mk 6 mk 8 mk After subtraction of a second order polynomial: Strong T-dependence in the low field region T-dependent damping of the SdHs effective mass m* B-dependent damping of the SdHs quantum scattering time τ q

37 Transport coefficients and effective mass 1.4 [1] 1.2 8mK mK values for m* indicate valence band nonparabolicity arising from interaction of hh and lh bands ratio between τ t /τ q close to unity denoting domination of short range scattering potential (high amount of large angle scattering) B 2 (T 2 ) R -2 xx [1] -25 T 6 mk: impurity interaction time τ hh anisotropic T 4 mk: τ hh reduced and isotropic γ UW et al. Phys. Rev. B 79, (29) ln (1/T) (1/K)

38 Weak localization and ferromagnetic transition, [1] sweep direction 5mK mK 4mK 6mK mK 7mK 1.5K sharp transition in the magnetoresistance behavior within mk T 6 mk: weak antilocalisation effect corresponding to strong spin orbit coupling T 6 mk: Hysteretic double maxima that can be explained by superposition of anisotropic magnetoresistance and weak antilocalization Coexistence of ferromagnetism and weak antilocalisation UW et al. Phys. Rev. B 79, (29)

39 Hall effects in the ferromagnetic phase R xy R xy R xy - R hall mK 4mK -.2 6mK 6mK 7mK 1.6K 4.2K T = 2 mk T = 2 mk T 4.2K: regular Hall effect 4K > T > T C : superposition of regular and anomalous Hall effects T T C : Superposition of regular, anomalous and hysteretic planar Hall effects Existence of planar Halleffect confirms spontaneous magnetization lying in the (1) plane ( to the 2DHG) Coexistence of ferromagnetism and high-mobility 2DHGs T < T C : τ hh isotropic and reduced indicating interaction of the aligned 2D (and 3D) holes

40 Weak antilocalization Phasecoherence time τ φ (ps) Spinrelaxation time Elastic scattering time τ so (ps) τ e (ps) Weak antilocalization observed up to 16 K τ so decreased with temperature Dyakonov-Perel can be excluded as dominant spin relaxation mechanism (Elliot-Yaffet, Bir-Aranov-Pikus or a combination) Hikami et al., Prog. Theor. Phys., 63, 2 (198) T(K) 2 e 1 H e 1 Hφ H so 1 1 Hφ 1 Hφ 2H so σ ( B) + + = Ψ 2 2π + Ψ 2 B + 2 B Ψ B + 2 B + Ψ with B external magnetic field, D diff diffusion constant, H e =, Hφ =, H so = 4D characteristic fields of the elastic (H e ), inelastic (H ϕ ) diff eτ e 4Ddiff eτ φ 4Ddiff eτ so and the spin-orbit (H so ) dephasing process. S. Knott et al. in preparation