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В.В. Вальков, С.В. Аксенов , Е.А. Уланов Лаборатория теоретической физики ИФ СО РАН,

Влияние процессов многократного рассеяния на квантовый транспорт электронов в магнитном поле через анизотропный атом. В.В. Вальков, С.В. Аксенов , Е.А. Уланов Лаборатория теоретической физики ИФ СО РАН, Сибирский аэрокосмический университет.

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В.В. Вальков, С.В. Аксенов , Е.А. Уланов Лаборатория теоретической физики ИФ СО РАН,

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  1. Влияние процессов многократного рассеяния на квантовыйтранспорт электронов в магнитном поле через анизотропный атом В.В. Вальков, С.В. Аксенов, Е.А. Уланов Лаборатория теоретической физики ИФ СО РАН, Сибирский аэрокосмический университет XX Уральская международная зимняя школа по физике полупроводников 17 - 22 февраля 2014 г. 1

  2. Outline Experiments on quantum transport through magnetic atomic structures: manifestation of many-body interactions Fano resonances in transport characteristics of spin structures and the magnetoresistance connected with them Effects of multiple inelastic scattering on transport properties of a single anisotropic magnetic impurity with nonequilibrium Green functions and Keldysh diagram technique 2

  3. H.B. Heersche et al., PRL96, 206801 (2006) Transport through individual atoms and molecules in break junction Mn12 molecule T=3 K T≤0.3K 3 Tunnel regime: a). Coulomb-blockade-like behavior b). Negative differential conductance Differential conductance map • M.-H. Jo, et al., NanoLett.6, 2014 (2006) • C. Timm, F. Elste, PRB 73, 235204 (2006) - theory

  4. W. Liang et al., Nature417, 725 (2002) T=0.3 K T=20K 4 Transport through individual atoms and molecules in break junction Strong coupling:Kondo resonance V2– based molecule • L.I. Glazman and M.E. Raikh, JETP Lett. 47, 452 (1988) – theory of the effect • M. N. Kiselev, K. Kikoin, and L. W. Molenkamp, PRB 68, 155323 (2003) – double QDs

  5. T=0.6 K Differential conductance measurements of single manganese atoms Geometry of the experiment Images obtained by scanning tunneling microscope (STM) (I=50 pA, V=100 mV) The reason of step in the conductance spectrum for H≠0 is availability of additional transport channel which is defined by lesser value of Mn spin projection Sz. • A.J. Heinrich et al., Science 306, 466 (2004). 5

  6. T=0.6 K, B=0 T Scanning tunneling spectroscopy (STS) of manganese chains adsorbed on thin insulating layer Conductance spectra STM images of 2-9 Mn chains on CuN (I=0.1 nA, V=10 mV, SMn=5/2) • C.F. Hirjibehedin, C.P. Lutz, A.J. Heinrich, Science 312,1021 (2006). 6

  7. 7 T=0.6 K Spin dimer – the simplest spin configuration is formed by… • …magnetic atoms 2 Mn: • C.F. Hirjibehedin, C.P. Lutz, A.J. Heinrich, Science 312,1021 (2006). I=5.9-6.4мэВ, gD=2.1±0.1

  8. Spin-averaging spectra of a Mn atom on a Cu2N/Cu(100) surface Manifestation of multiple scattering processes Spin-polarized spectra of a Mn atom Energy splitting of the Mn spin states and their lifetimes • S. Loth etal., Nature Physics 6, 340 (2010). 8

  9. Spin dimer – the simplest spin configuration is formed by… • …magnetic molecules STM image (I=0.03 nA, V=0.9 V) Cobalt phthalocyanine (CoPc) molecule(S=1/2) Third layer T=0.4 K • X. Chen et al., PRL101, 187208 (2008) 9

  10. Kondo effect and the role of magnetocrystalline anisotropy M. Ternes, et al., J. Phys.: Condens. Matter 21 053001 (2009) A.F. Otte, et al., Nature Phys. 4, 847 (2008) T=4.7 K T=0.5 K Theory: • J. Fernandez-Rossier, PRL 102, 256802 (2009); • J. Fransson, et al., PRB 81 115454 (2010). The dependence of the conductance steps’ shifts on the magnetic field direction is caused by strong magnetocrystalline anisotropy of an individual atom 10

  11. Antiferromagnetic Fe chain as information bit T=0.5 K Why aren’t Mn chains suitable? The magnetic anisotropy is ~50 times stronger in Fe than in Mn onCu2N surface. The strong easy-axis anisotropy of Fe evidently stabilizes the two Neel states as observable magnetic states. Structures with more atomsremain stable tohighertemperatures • S. Loth etal., Science 335, 196 (2012). 12

  12. Possible experimental situation: Nanoobject having the dimer configuration of its spins is situated in mechanically controllable break-junction Theoretical description by tight binding method 13

  13. System Hamiltonian where Hamiltonian of spin dimer in external magnetic field Hamiltonian of sf-exchange interaction 14

  14. Спиновый димер с обменным взаимодействием антиферромагнитного типа Состояния спинового димера классифицируются по значению суммарного спинового момента Синглетное состояние спинового димера 15

  15. Зависимость энергий состояний спинового димера от магнитного поля E H 1) 2) 3) 16

  16. Случай коллинеарной спиновой конфигурации: магнитное поле больше критического Зависимость от энергии коэффициента прохождения электрона с проекцией спина +1/2 соответствует хорошо известной зависимости для случая туннелирования квантовой частицы через двухбарьерную структуру 17

  17. Неколлинеарная спиновая конфигурация: магнитное поле больше критического Зависимость общего коэффициента прохожденияТ и его компонент T00, T10, T11 от E при EH=15, EI=1.5, A=30 дляосновного состояния: 18

  18. 1) 2) 3) 2) 2) Неколлинеарная спиновая конфигурация: магнитное поле больше критического 19

  19. Зависимость общего коэффициента прохожденияТ и его компонент T00, T10, T11 от E при EH=15, EI=1.5, A=30 дляосновного состояния: Видна важная роль спин-флип процессов для спин-зависящего транспорта 20

  20. Индуцирование магнитным полемпиковрезонансного туннелирования для EI=15, A=30. Пунктир: EH=0. Сплошная линия: EH=6 (~ 106 Э) . 23

  21. Fano effect for electron transport through spin dimer The electron with wave vectorkincidents upon dimer being in the ground singlet state and … 24

  22. Fano effect for electron transport through spin dimer First transport channel: by using ground state of the system, , which belongs to continuous energy spectrum. 25

  23. Second transport channel: by using excited states, , which belong to discrete energy spectrum when E<I. Fano effect for electron transport through spin dimer Interference of waves referred to different paths gives rise to Fano resonances. • U.Fano,Phys. Rev. 124, 1866 (1961). 26

  24. Fig.3. Dependences T(E), T00(E), T10(E) и T11(E) for parameters of fig.1, εD=-0.09 eV, μBH=0.25 meV.Inset: Fano peak is induced by magnetic field. 27

  25. Fano effect for electron transport through spin dimer New path occurs when the magnetic field is turned on. Consequently, additional Fano resonances of the transmission coefficient obtain. 28

  26. ! H=0:p=q Коэффициент прохождения и поведение антирезонансов Фанов случае полного s-f-взаимодействия Упрощения: где ! При H≠0 может возникнуть 4 антирезонанса, два из них исчезают при H=0 29

  27. Volt-amperecharacteristic (VAC) calculations by Landauer method 30 Magnetoresistance • S. Datta, Electronic transport in mesoscopic systems, 1995. The influence of magnetic field on Fano resonances

  28. εD≠0 Anomalously high magnetoresistancedue toFano effect Transmission The dependence of the antiresonance energies onAsf Вальков В.В., Аксенов С.В., ЖЭТФ 140, 305 (2011)Val’kov V.V., Aksenov S.V., arXiv:1109.0391v1 (2011) 31

  29. STM geometry 2 Suggested model 32

  30. E H=0 D 0 Electron transport through single magnetic impurity Energy spectrum of magnetic impurity with spin moment S=1 Solution of Schrodinger equation 34

  31. Transport through magnetic impurity 37

  32. Spectrum of the system 38

  33. Possible transitions from zero-fermion to one-fermion sector 39

  34. Possible transitions from one-fermion to two-fermion sector 40

  35. Atomic representation and Hubbard operators Зайцев Р.О., ЖЭТФ, 1975, 1976 41

  36. General relations theory of quantum transport using atomic representation for device • L.V.Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964); • A.L. Ivanov, S.G. Tikhodeev, (Eds.),Problems of Condensed Matter Physics, Clarendon Press, Oxford (2008); • R.O. Zaitsev, Lekciipokvantovoikinetike (2009); • P.I. Arseev, N.S. Maslova, Phys. Usp. 53, 1151 (2010) The spectral function of device 43

  37. The spectral function of tunnel coupling between device and left contact The spectral function of tunnel coupling between device and right contact 44

  38. Keldysh contour С Zoo nonequilibrium Green's functions mixed Green’s functions Green’s functions of the device Green’s functions of contacts Indices a, b = ± marks the branches of Keldysh contour 45

  39. Keldysh contour С 46

  40. Calculation of the spectral functions Effective interaction The components of the effective interaction 47

  41. Graphic form of the system of equations for nonequilibrium device functions • Зайцев Р.О., ЖЭТФ, 1975, 1976 The matrix elements of the effective interaction are split in the indices of the root vectors • Вальков В.В.,Овчинников С.Г. Квазичастицы в сильно коррелированных системах, Новосибирск, 2001 47

  42. P.I. Arseev, N.S. Maslova, Phys. Usp. 53, 1151 (2010) I~tL2 tR2 52

  43. The spectral function Wσ +- has maxima at transition energies 49 H=0 Parameters: ξd=A=5 meV, D=3 meV, U=10 meV, eV=50 meV,tL=tR=t/10, t=-1 eV, T=1K.

  44. The influence of magnetic field on the spectral functions 50

  45. The influence of magnetic field on the spectral functions 51

  46. Electrical current • В.В. Вальков, С.В. Аксенов, Е.А. Уланов, Письма в ЖЭТФ 98, 459 (2013); 53

  47. Main contribution in Iαα is near ω=-Eα, whereas the one for Iαβ is out this ω region and Iαα >> Iαβ for tunnel regime (Γ<<Eα, eV). Low temperatures limit, T<< Eα, eV Quantum kinetic equations for occupation numbers Low temperatures limit, T<< Eα, eV 55

  48. Nonequilibrium occupation numbers of the system Parameters: ξd=A=5 meV, D=3 meV, U=10 meV, μBH=0,tL=tR=t/100, t=-1 eV, T= 1K. 56

  49. The magnetic field influence on occupation numbers Parameters: ξd=A=5 meV, D=3 meV, U=10 meV, μBH=0.5meV, g=2, tL=tR=t/100, t=-1 eV, T= 1K. 57

  50. The magnetic field influence on occupation numbers Parameters: ξd=A=5 meV, D=3 meV, U=10 meV, μBH=2.5meV, g=2, tL=tR=t/100, t=-1 eV, T= 1K. 58

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