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. T c and 2D

2 Quantum well with Mn delta layer 2D GaAs, nm -layer Mn spacer GaAs, 3 nm QW InGaAs, 9-10 nm -layer С Buffer layer GaAs, 0.5 μm cap-layer GaAs, nm Substrate i-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 Sapega et al Buffer GaAs, 25 нм cap-layer GaAs, нм δ-layer Mn spacer GaAs, 1-5 нм QW InGaAs, 9-10 нм GaAs, 5 нм δ-Be Substrate GaAs, (100) B.N. Zvonkov et al. N. Novgorod Y. Furdyna et al. Buffalo Parametes of the samples

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

Transport proofs for ferromagnetism 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. ? Metal - insulator transition under rise of Mn content ? Resistivity Anomalous Hall effect Hall resistance dependes on spin-orbit interaction and carrier polarization R H d= yx = R 0 B + R s M

Formation of charge carrier puddles in the quantum well (QW) from competition of doping disorder and nonlinear screening. z0z0 Partially ionized Mn dopants Typical potential fluctuation V fluc Location of holes in the transverse direction Hole wavefunction in transverse direction After Gergel and Suris paper and Shklovskii and Efros Fluctuation potential Schematic of the quantum well potential (shown inverted). Dashed (blue) line represents the quantum well potential in the absence of fluctuations and the solid (red) line shows the potential well with an attractive fluctuation potential. The dotted line indicates the Mn dopants at a distance from the left face of the quantum well.

Model of nanoscale inhomogeneities z0z0 RMS potential fluctuation: n a - Density of ionized Mn atoms Screening length corresponds to carrier density p: [Kennett, Tripathi, PRB (2006)] PRB, 2011

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

Observed temperature dependence of resistance for (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 percolation threshold and Sample 1 is well-insulating. The fits were made using Eq. (13). Parameters such as the activation energy E A and the droplet separation D 1 were chosen close to the values obtained from the droplet model. The magnetic parameters J and T C were then varied to obtain the above fits. In both cases, the best fit value of T C was significantly larger than the temperature, at which the resistance anomaly (hump or shoulder) was observed. Resistivity PRB, 2011 Two phase system TcTc T с – local transition in magnetic islands

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

10 Noise fit: Frequency dependence The long-time dependence of the resistivity autocorrelation functionS ρ (t) extracted from the noise data at T = 4.0 K together with fits. The red curve is a fit to S ρ (t)=A/t Bln(t/t 0 ), blue curve is a fit to S ρ (t) = A/t 2/5 + Bln(t/t 0 ). In 2D, S ρ (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 S ρ A Bf 2 and S ρ A B lnf Cf, respectively. At the high-frequency end, the fit is to S ρ Af PRB, 2012

Noise fit: Temperature dependence Sample 4 f = 150Hz Fit to T C = 52K PRB, 2012

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

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

Models M=0 GaAs Mn GaMnAsGaInAs GaAsGaMnAsGaInAs Itinerant FM ordering in GaMnAs layer. (S.Caprara et al. PRB (2011)). Averkiev et al. – resonance tunneling. PRB (2012). EFEF Mn layer – GaMnAs T с – local transition in magnetic islands Two phase system TcTc L Meilikhov et al. – overlapping of the wave function tails with GaMnAs layer. JETP Letters (2008)

15 THANKS FOR YOUR ATTENTION! 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. Conclusion

Model of nanoscale inhomogeneities z0z0 Assume Gaussian white noise distribution for ionized dopants: Fluctuation charge in circle of radius R: Disorder screened by holes in QW: PRB, 2011

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

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.

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)

A (GaAs) 1-y Mn y a /a, % In х Ga 1-х As y Mn B (GaAs) 1-y Mn y In х Ga 1-х As z, nм y Mn Sample 4831 sample 4834 Mn content 40 GaAs, nm 50 -layer Mn spacer GaAs, 3 nm QW InGaAs, 9-10 nm -layer С Buffer layer GaAs, 0.5 μm cap-layer GaAs, nm Substrate i-GaAs (100) z, nm Profile of the deviation of the lattice constant from its value for GaAs along the sample depth (z) X-ray diagnostics of the samples 2D J. Appl. Phys. 107, (2010 )

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

GaInAsGaAsGaAs(Mn) 2D conductivity channel z E0E0 Mn L 0 Carrier-mediated FM via carriers in the quantum well. U(z)U(z) (z) GaAs GaInAs E.Z. Meilkhov and R.M. Farzetdinova, JETP Letters (2008) M

23 Mn (z) Mn GaAs GaInAs There is 2D spin – polarized collective state in the GaMnAs aria. The corresponding wave function is expanded inside quantum well and acts on carriers causing their spin-polarization. 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) FM ordering inside Mn layer M From Lucev et al. PRB 2009

Модель M=0 GaAs Mn GaMnAsGaInAs GaAsGaMnAsGaInAs 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 слоя возникает 2D спин – поляризованное состояние. Волновая функция проникает 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 EFEF Mn – содержащий слой GaMnAs T с – локальный ФМ в островках Двухфазная среда TcTc L

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

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

28 Намагниченность Малое содержание Mn Magn JETP Letters, 2007

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

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

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

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

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

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

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

AHE temperature dependence AHE change sign with T Two contributions intrinsic and side-jump AHE

37 2D расчет S.Y. Liu, X.L. Lei, Phys. Rev. B 72, (2005). V.K. Dugaev, P. Bruno, M. Taillefumier, B. Canals, C. Lacroix, Phys. Rev. 71, (2005). AHE J. Phys. Cond. Matt. 2008, JAP2010 Аномальный эффект Холла Холловское сопротивление R H d= yx = R 0 B + R s M Аномальный вклад пропорционален намагниченности и зависит от S-O взаимодействия и спиновой поляризации носителей.

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

Geometry of the droplets

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

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

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

Two-dimensionality 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)] Sample 3 (metallic)

Photolumiscence InGaAs/GaAs:Mn P c (B) dependences for EL and PL of sample 2 and of the reference sample 5 without δ-Mn layer. Inset shows polarized EL spectra; (b) P c (9 T) values vs. d s in LEDs with x = 0.1. Zaitsev, Kulakovskii et al. Jetp letters 90,730 (2009) P sat (9 T) values vs. d s

45 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. T c and 2D Outline