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Aronzon B.A.

Mechanisms of ferromagnetic ordering and anomalous Hall effect in 2D GaAs/InGaAs/GaAs structures with Mn delta layer. Rylkov V.V. Lagutin A.S. Davydov A.B. Pankov M.A. Meilikhov E.Z. Pashaev E.M. Zvonkov B.N. Danilov Yu. A. Vikhrova O.V. Laiho R. Lashkul A. Kulbachinskii V.A.

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Aronzon B.A.

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  1. Mechanisms of ferromagnetic ordering and anomalous Hall effect in 2D GaAs/InGaAs/GaAs structures with Mn delta layer Rylkov V.V. Lagutin A.S. Davydov A.B. Pankov M.A. Meilikhov E.Z. Pashaev E.M. Zvonkov B.N. Danilov Yu. A. Vikhrova O.V. Laiho R. Lashkul A. Kulbachinskii V.A. Aronzon B.A. RRC “Kurchatov Institute”, Moscow, Russia NIFTI, N. Novgorod , Russia Vihuri Lab., Turku, Finland MSU, Moscow, Russia

  2. Outline 1 Motivation 2 2D DMS structure 3 Transport properties, FM ordering 4 Mechanisms 5 Anomalous Hall effect 6 Magnetization, magnetic structure 7 Conclusion

  3. Motivation Application Incorporation of magnetism into modern electronics - spintronics Basic Research Incorporation of magnetism into physics of semiconductors Coulomb interaction, disorder, e-e interaction, electron – phonon interaction, + strong exchange interaction Mechanism of the exchange interaction; Effects of the disorder, Coulomb and exchange interactions interplay; Peculiarities of the 2D quantum effects in the presence of the ferromagnetism; AHE origin; Magnetic structure.

  4. Possible interaction mechanism Exchange via free electrons RKKY interaction Indirect exchange via empty states above the Fermi energy in the heavy hole band. Impurity spins are parallel. Zener Fermi-energy Mn Mn

  5. Quasi 2D DMS ? .0 cap-layer GaAs, 30-40 nm 50 -layer Mn spacer GaAs, 3 nm 55 QW InGaAs, 9-10 nm 65 GaAs, 15-18 nm -layer С Buffer layer GaAs, 0.5 μm z, nm Substrate i-GaAs (100) A.M. Nazmul, M. Tanaka et al.; T. Wojtowicz, J.K. Furdyna et al. Low mobility structures (< 10 cm2/(V s)) 2D structures Парфеньев и др. 2009 Зайцев, Кулаковскийи др., 2009 Аронзон и др., 2006 Quantum well with Mn delta layer 40 Table 1. Structure parameters 5

  6. 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, нм Crystal structure X- Ray characterization Depth (z) profiles of the lattice mismatch related to GaAs evaluated from fitting the experimental X-ray rocking curves. Mn content 40

  7. 2D Mn 0.5ML

  8. Methods spin-dependent scattering < Temperature dependence of resitance R GMR effect Tc T Anomalous Hall Effect The Hall resistance RHd= yx = R0B + RsM AHE is proportional to magnetization and is due to S-O interaction . skew–scattering: Rs R1xx ; side-jump: Rs R2xx For both mechanisms AHE depends on the strength of the S-O interaction and spin polarization of carriers. AHE current arises due to scattering asymmetry Renewed interest in AHE nature T.Jungwirth et al.(2002), T. Dietl et al.(2003), A.A. Burkov et al. (2003) 2D case: S.Y. Liuet al. (2005), V.K. Dugaevet al. (2005) Berry phase v(k) = grad [ε(k)]/h + (e/h)E(k) z(k) = 2Im[<u/ky|u/kx>]  - does not depend on scattering 8

  9. Temperature dependence of the sample resistance spin-dependent scattering < Main feature – Hump or Shoulder. Mn doped samplesonly. J. Phys. Cond. Matt. 2008

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

  11. Mn 110 meV GaAs GaAs GaAs U=180 meV U=140 meV U=100 meV Curie temperature dependence on the depth of quantum well 55 set 57 set Mn 0.15 Ml JAP 2010

  12. (z) Mn 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) 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 12

  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) CVD MBE 13

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

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

  16. Anomalous Hall Effect The Hall resistance RHd= yx = R0B + RsM AHE is proportional to magnetization and is due to S-O interaction . skew–scattering: Rs R1xx ; side-jump: Rs R2xx For both mechanisms AHE depends on the strength of the S-O interaction and spin polarization of carriers. AHE current arises due to scattering asymmetry Renewed interest in AHE nature T.Jungwirth et al.(2002), T. Dietl et al.(2003), A.A. Burkov et al. (2003) 2D case: S.Y. Liuet al. (2005), V.K. Dugaevet al. (2005) Berry phase v(k) = grad [ε(k)]/h + (e/h)E(k) z(k) = 2Im[<u/ky|u/kx>]  - does not depend on scattering Condenst-matter physists today have some acquaitance with skew-scattering, but have a harder time recalling what the Luttinger anomalous velocity is

  17. Anomalous Hall Effect ~ 2D calculated 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). 17 JETP Letters 2007; JAP 2010

  18. Эффекты туннелирования InGaAs/GaAs:Mn Квантовая яма  - слой Mn 1.5 eV GaAs InGaAs GaAs 1.3 eV 0.1 eV ~0.08 eV 3-5 nm 10nm Эксперимент: поляризация фотолюминесценциииз квантовой ямы С.В. Зайцев, М.В.Дорохин, А.С.Бричкин, О.В.Вихрова, Ю.А.Данилов, Б.Н.Звонков, В.Д.Кулаковский, Письма в ЖЭТФ 90,730 (2009)

  19. Anomalous Hall Effect 1.2ML 0.5ML Amplitude is negative at low temperatures and change sign at Tc

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

  21. Magnetizationlow Mn content Aronzon, Kulbachinskii et al., JETP letters, 2007

  22. Magnetization Metallic sample Intermediate 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 22 JETP Letters, 2008

  23. 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 23 JETP Letters, 2008

  24. Nature for AFM regions Tugushev et al. PRB (2009)

  25. Conclusion Maximum in the temperature dependence of resistance and anomalous Hall effect are the sign for magnetic ordering in 2D structures with Mn layer separated from the quantum well Anomalous Hall effect was observed in 2D structures with Mn layer separated from the quantum well and with relatively high mobility of carriers. The change of its sign with temperature as well as its value supports the intrinsic mechanisms. The unusual shifted hysteresis loop was observed Disorder and interactions affect strongly both transport and magnetic properties of the structures Spin-polarization of carriers were observed THANKS FOR YOUR ATTENTION 25

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