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Disorder effects in 2D ferromagnetic semiconductor structures:

Disorder effects in 2D ferromagnetic semiconductor structures: GaAs / InGaAs / GaAs quantum well with remote Mn delta-layer B. Aronzon , A . Davydov, K. Kugel, V. Tripathi, K. Dhochak, A. Lashkul and E. Lahderanta. 1 . Introduction.

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Disorder effects in 2D ferromagnetic semiconductor structures:

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  1. Disorder effects in 2D ferromagnetic semiconductor structures: GaAs/InGaAs/GaAs quantum well with remote Mn delta-layer B. Aronzon, A. Davydov, K. Kugel, V. Tripathi, K. Dhochak, A. Lashkul and E. Lahderanta 1.Introduction. Structure description. Proofs of 2D and ferromagnetic ordering. 2. Disorder effects. Resistivity. 3. Disorder effects. Noise. 4. The nature of ferromagnetic ordering. Models. 5. Conclusion. Semiconductor spintronics. 2 problems. Tc and 2D

  2. Quantum well with Mn delta layer 2D cap-layer GaAs, 60-80 нм δ-layer Mn spacer GaAs, 1-5 нм cap-layer GaAs, 30-40 nm QW InGaAs, 9-10 нм -layer Mn spacer GaAs, 3 nm QW InGaAs, 9-10 nm GaAs, 5 нм GaAs, 15-18 nm δ-Be -layer С Buffer GaAs, 25 нм Buffer layer GaAs, 0.5 μm Substrate i-GaAs (100) Substrate GaAs, (100) Awshalom et al., 2004 Zaicev, et al., 2009 Aronzon et al., 2006, 2009, 2010, 2011, 2012 Wegscheider et al., 2007, 2010 Dietl et al. 2010 Sapega et al. 2012 Y. Furdyna et al. Buffalo B.N. Zvonkov et al. N. Novgorod Parametes of the samples 2

  3. Quantum Hall Effect 2D Mn 0.5ML 3 J. Appl. Phys. 107, 023905 (2010)

  4. Transport proofs for ferromagnetism Anomalous Hall effect Resistivity Hall resistance dependes on spin-orbit interaction and carrier polarization RHd= yx = R0B + RsM ? Metal - insulator transition under rise of Mn content ? • Pure carbon doping (Sample 5) shows no resistance anomaly. • Samples 1 and 4 show hysteresis in magnetisation curve. • [ JETP Lett. (2008)] • Anomalous Hall effect observed in all samples doped with Mn.

  5. Fluctuation potential After Gergel’ and Suris paper and Shklovskii and Efros Formation of charge carrier puddles in the quantum well (QW) from competition of doping disorder and nonlinear screening. z0 Location of holes in the transverse direction Hole wavefunction in transverse direction Typical potential fluctuation Vfluc Schematic of the quantum well potential(shown inverted). Dashed (blue) line represents thequantum well potential in the absence of fluctuations and thesolid (red) line shows the potential well with an attractive fluctuationpotential. The dotted line indicates the Mn dopantsat a distance from the left face of the quantum well. Partially ionized Mn dopants

  6. Model of nanoscaleinhomogeneities RMS potential fluctuation: z0 [Kennett, Tripathi, PRB (2006)] Screening length corresponds to carrier density p: n’a- Density of ionized Mn atoms PRB, 2011

  7. EA + J(1-cos θi j ) θi j Vb a r r i e r Di j Extra energy cost due to spin orientation i j Electrical resistance: Role of ferromagnetic correlations PRB, 2011 Resistivity anomaly corresponds to rapid change of magnetic contribution. Cosine term changes appreciably when magnetic correlation length becomes of the order of droplet separation.

  8. Resistivity Two phase system Tc PRB, 2011 Tс– local transition in magnetic islands Observed temperature dependence of resistancefor (a) Sample 4, in units of the resistance at 70 K, and (b)Sample 1, in units of the resistance at 90 K (points), and theoretical fits (solid lines). Sample 4 is near the percolationthreshold and Sample 1 is well-insulating. The fits were madeusing Eq. (13). Parameters such as the activation energy EAand the droplet separation D1 were chosen close to the valuesobtained from the droplet model. The magnetic parametersJ and TC were then varied to obtain the above fits. In bothcases, the best fit value of TC was significantly larger thanthe temperature, at which the resistance anomaly (hump orshoulder) was observed.

  9. Power spectral density of electrical noise Percolation transition in magnetic subsystem? There are no transitions in transport properties. 9 PRB, 2012

  10. Noise fit: Frequency dependence The long-time dependenceof the resistivity autocorrelation functionSρ(t) extracted from the noise data at T = 4.0 K together with fits. The red curve is a fit to Sρ(t)=A/t1.05 + Bln(t/t0), blue curve is a fit to Sρ(t) = A/t2/5 + Bln(t/t0). In 2D, Sρ(t ) ∼ t−1 behavior is expected for a disordered RKKY ferromagnet and Sρ (t ) ∼ t−2/5 for double-exchange ferromagnets. The logarithmic time dependence indicates 1/f noise contributions. The fit to the RKKY model is better than to the double exchange. Frequency dependence of noise at T = 4 K (solid curve) together with fits to the low- and high-frequency regimes. At the low-frequency end, the dashed curve and the dotted curve are fits to Sρ∼ A − Bf2 and Sρ∼ A − B lnf − Cf, respectively. At the high-frequency end, the fit is to Sρ∼Af−1.53. PRB, 2012

  11. Noise fit: Temperature dependence Sample 4 f = 150Hz Fit to TC= 52K PRB, 2012

  12. Curie temperature dependence on the depth of quantum well Mn 110 meV GaAs GaAs GaAs U=180 meV U=140 meV U=100 meV 55 and 57 set 48 set Mn 0.5 Ml J. Phys. Conf. Ser. 2013

  13. Curie temperature dependence on the spacer thickness cap-layer GaAs, 60-80 нм δ-layer Mn spacer GaAs, 1-5 нм cap-layer GaAs, 30-40 nm QW InGaAs, 9-10 нм -layer Mn spacer GaAs, 3 nm QW InGaAs, 9-10 nm GaAs, 5 нм GaAs, 15-18 nm δ-Be -layer С Buffer GaAs, 25 нм Buffer layer GaAs, 0.5 μm Substrate i-GaAs (100) Substrate GaAs, (100) Mech CVD MBE 13 J. Phys. Conf. Ser. 2013

  14. Models Mn M=0 GaMnAs GaAs GaInAs Two phase system Tc Itinerant FM ordering in GaMnAs layer. (S.Caprara et al. PRB (2011)). Averkiev et al. – resonance tunneling. PRB (2012). Meilikhov et al. – overlapping of the wave functiontails with GaMnAs layer. JETP Letters (2008) EF Tс– local transition in magnetic islands L Mn layer –GaMnAs GaMnAs GaAs GaInAs

  15. Conclusion Disorder and magnetic interactions affect strongly both transport and magnetic properties of the structures and could explain the temperature dependence of resistance and noise quantitatively. THANKS FOR YOUR ATTENTION! 15

  16. z0 Model of nanoscale inhomogeneities Assume Gaussian white noise distribution for ionized dopants: Fluctuation charge in circle of radius R: Disorder screened by holes in QW: PRB, 2011

  17. Ferromagnetic correlations: models I. Isotropic 2D Heisenberg ferromagnet No long-range magnetic order at finite temperature. II. Uniaxial 2D Heisenberg ferromagnet M. Bander, D. Mills, PRB (1988) for Ising

  18. Voltage noise: magnetic fluctuations Resistivity noise from magnetic fluctuations Autocorrelation function of magnetisation Autocorrelation function contains information on dynamics, and can shed light on the mechanism of ferromagnetism.

  19. Magnetic correlations: dynamics Resistivity noise is sensitive to the dynamics of the ferromagnet: Interested in two broad universality classes depending on whether the dynamics has a hydrodynamic description: Model A: No conserved order parameter e.g. anisotropic Heisenberg Model B: Conserved order parameter e.g. Isotropic Heisenberg Hohenberg, Halperin, RMP (1977)

  20. 2D a/a, % InхGa1-хAs yMn A (GaAs)1-yMny Sample 4831 .0 InхGa1-хAs yMn cap-layer GaAs, 30-40 nm 50 -layerMn spacer GaAs, 3 nm 55 B (GaAs)1-yMny QW InGaAs, 9-10 nm sample 4834 60 GaAs, 15-18 nm -layer С Buffer layer GaAs, 0.5 μm z, nm Substrate i-GaAs (100) z, nм X-ray diagnostics of the samples Profile of the deviation of the lattice constant from its value for GaAs along the sample depth (z) J. Appl. Phys. 107, 023905 (2010) Mn content 40

  21. Noise fit: Frequency dependence Sample 4 T=4K (Model B) (Model A) Model A: Model B: Model A: Random Telegraph Model B: Diffusive spin dynamics

  22. U(z) (z) 0 E.Z. Meilkhov and R.M. Farzetdinova, JETP Letters (2008)  L M Carrier-mediated FM via carriers in the quantum well. 2D conductivity channel GaAs(Mn) GaInAs GaAs GaInAs GaAs GaAs E0 (z) Mn z   

  23. (z) Mn M FM ordering inside Mn layer FM ordering occurs in GaMnAs layer due to itinerant mechanism. Carriers in the quantum well do not invoolved. V.V. Tugushev et al. PRB (2009) From Lucev et al. PRB 2009 There is 2D spin – polarized collective state in the GaMnAsaria. The corresponding wave function is expanded inside quantum well and acts on carriers causing their spin-polarization. Mn GaInAs GaAs 23

  24. Модель Mn M=0 GaMnAs GaAs GaInAs Двухфазная среда Tc ФМ упорядочение в GaMnAs слое обусловлено обменом спинов Mn через носители в этом же слое.Носители из квантовой ямы в обмене почти не участвуют (S.Caprara et al.PRB (2011)).Вблизи дельта слоявозникает 2D спин – поляризованное состояние.Волновая функцияпроникает из дельта слоя в квантовую яму, вызывая спиновую поляризацию дырок. Аверкиев и др. – резонансное туннелирование, Мейлихов и др. – перекрытие хвостов волновой функции из КЯ в слой GaMnAs EF Tс– локальный ФМ в островках L Mn – содержащий слой GaMnAs GaMnAs GaAs GaInAs

  25. Voltage noise: frequency dependence Sample 4 Characteristic frequency Freq. dependence of the voltage noise for temperatures below resistivity anomaly. Freq. dependence is not 1/f. Random telegraph? Griffiths?

  26. Conclusions • At low carrier density, competition of disorder and nonlinear • screening causes formation of charge puddles in 2DHG. • Resistance anomaly arises when magnetic correlation length • becomes comparable with a relevant length scale. Anomaly • not evidence for a phase transition. • In 2D (unlike 3D) resistance anomaly may occur far below • Curie temperature. • Noise is non-1/f over a large window of frequencies. • Data in reasonable agreement with both Model A • (Random Telegraph) and Model B (Diffusive spin dynamics).

  27. намагниченность Magn Диэлектрический образец Загадка 3 В чем причина необычного вида гистерезиса? Exchange bias of hysteresis loop Известен для двухвазных систем с ферро- и антиферромагнитными включениями, например, в манганитах. 27 JETP Letters, 2008

  28. Magn НамагниченностьМалое содержание Mn 28 JETP Letters, 2007

  29. Magn Model Mn rich lake Jf-af Mn delta layer M spacer Ferromagnetic region Antiferromagnetic region 2DEG Jf QW, high carrier concentration Magnetic moment of the lake is pinned by Jf-af The percolation transition in magnetic system affect scattering and results in decrease of resistance – reason of the noise. Due to quantization spin of heavy holes aligns perpendicularly Due to shape anisotropy magnetic moment of Mn layer aligns along Is the exchange possible? Yes, due to high Fermi energy and disorder. dqw=10 nm, rloc= 20-30 nm, K in plane is about Kz JETP Letters, 2008 PSS, 2008 29

  30. Magn Nature for AFM regions Fig from Lutcev et al. PRB (2009) Tugushev et al. PRB (2009)

  31. Magnetization Mag Metallic sample Low Mn content Insulator sample High Mn content What is the reason for unusual hysteresis loop? Exchange bias of hysteresis loop Known for two phase systems with ferro - and anti-ferro inclusions, for example, phase separation in manganites 31 JETP Letters, 2008

  32. Model of nanoscale inhomogeneities 1 Formation of charge carrier puddles in the quantum well (QW) from competition of doping disorder and nonlinear screening. (Gergel' & Suris, JETP (1978)) Typical potential fluctuation Partially ionized Mn dopants

  33. Estimate of the droplet sizes Virial theorem: Droplet charge distributed over subbands: Solve these nonlinear equations to get droplet size

  34. Results of the calculations T= 77 K T= 5 K

  35. Флуктуационный потенциал и температурная зависимость сопротивления Вслед за работой Гергель, Сурис, ЖЭТФ (1978) Загадка 1 Расчетная температура не совпадает с максимумом R(T). Две температуры? PRB 2011

  36. AHE AHE temperature dependence AHE change sign with T Two contributions intrinsic andside-jump

  37. АномальныйэффектХолла AHE Холловское сопротивлениеRHd= yx = R0B + RsM Аномальный вклад пропорционален намагниченностии зависит от S-O взаимодействия и спиновой поляризации носителей. 2D расчет S.Y. Liu, X.L. Lei, Phys. Rev. B 72, 195329 (2005). V.K. Dugaev, P. Bruno, M. Taillefumier, B. Canals, C. Lacroix, Phys. Rev. 71, 224423 (2005). 37 J. Phys. Cond. Matt. 2008, JAP2010

  38. Fluctuation potential After Gergel’ and Suris paper and Shklovskii and Efros Schematic of the quantum well potential(shown inverted). Dashed (blue) line represents thequantum well potential in the absence of fluctuations and thesolid (red) line shows the potential well with an attractive fluctuationpotential. The dotted line indicates the Mn dopantsat a distance from the left face of the quantum well.

  39. Geometry of the droplets

  40. Voltage noise: charge fluctuations Fluctuations in inter-droplet tunnelling A. L. Rakhmanov et al., PRB (2001) [phase-separated manganites] Random-telegraph type (consistent with experiment) Different from characteristic time associated with resistivity. Temperature dependence not in agreement with data. Need to look at magnetic contribution to noise.

  41. FM transition in the Mn layer affects the conductivity in QW Mech GaAs  L U(z) GaInAs GaAs Mn V-band z

  42. FM transition in the Mn layer affects the conductivity in QW Mech U(z) 5569 GaInAs FM transition occurs GaAs GaAs Mn V-band z  L

  43. Two-dimensionality Sample 3 (metallic) • Negative magnetoresistance consistent with 2D weak • localisation corrections. • Observation of Shubnikov-de Haas oscillations for fields • perpendicular to plane of hole gas. • Quantum Hall effect in all samples, including Sample 1. • [B. A. Aronzon et al., J. Appl. Phys. (2010)]

  44. Photolumiscence InGaAs/GaAs:Mn Zaitsev, Kulakovskii et al.Jetp letters 90,730 (2009)

  45. Outline 1.Introduction. Structure description. Proofs of 2D and ferromagnetic ordering. 2. Disorder effects. Resistivity. 3. Disorder effects. Noise. 4. The nature of ferromagnetic ordering. Models. 5. Conclusion. Semiconductor spintronics. 2 problems. Tc and 2D

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