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М. И. Дьяконов Université Montpellier II, France Лекция 1

М. И. Дьяконов Université Montpellier II, France Лекция 1. Введение в спиновую физику. Что такое спин? Историческая справка Спин и магнитный момент электрона Спины и магнитные моменты ядер Последствия (важные и менее важные) Спиновые взаимодействия. Samuel Goudsmit (right)

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М. И. Дьяконов Université Montpellier II, France Лекция 1

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  1. М. И. Дьяконов Université Montpellier II, France Лекция 1 Введение в спиновую физику • Что такое спин? • Историческая справка • Спин и магнитный момент электрона • Спины и магнитные моменты ядер • Последствия (важные и менее важные) • Спиновые взаимодействия

  2. Samuel Goudsmit (right) George Uhlenbeck (left) 1928 Историческая справка Спин - это внутренний момент (количества движения = импульса) частицы Спин электрона открыли Гаудсмит и Уленбек в 1925 г

  3. Историческая справка В то время Паули и многие другие (Лоренц, Крониг ...)считали,что идея спина - это ерудна. Из воспоминаний Гаудсмита (1971): "The one thing I remember is that Ehrenfest said to me: "Well, that is a nice idea, though it may be wrong. But you don't yet have a reputation, so you have nothing to lose". Из письма Томаса Гаудсмиту (1926): "I think that you and Uhlenbeck have been very lucky to have your spinning electron published and talked about before Pauli heard of it."

  4. Историческая справка На самом деле существованиеспина было видно уже в экспериментах Штерна и Герлаха (1921), которые были неправильно интерпретированы

  5. Предсказывает также магнитный момент электрона: Paul Adrien Maurice Dirac Уравнение Дирака (1928) Релятивистское уравнение для электрона, из которого существование спина следует автоматически P. A. M. Dirac В магнитном поле циклотронный период равен периоду прецессии спина! Диалог Дирака и Гейзенберга на корабле по дороге в Японию Dirac: 'Why do you dance?' Heisenberg: 'When there are nice girls, it is a pleasure' Dirac: 'But, Heisenberg, how do you know beforehand that the girls are nice?'

  6. Магнитный момент электрона Связанная с этим энергия в магнитном поле: E = ± μB Проекция спина на любую ось = ±1/2 (в единицахћ). Sz = ± 1/2, и так же для Sx и Sy. В то же времяS2 = 3/4!Не странно ли? T. e.Sx2, Sy2и Sz2всегда существуют одновременно (не может быть Sx2 =0)

  7. Если шар с зарядомe,радиусаrвращается со скоростью на экваторе v, то его магнитный момент порядка Zitterbewegung? Получается, что если v ~ c , то чтобы получить правильное значениеμнужно взятьr ~ħ/mc~ 10‒10cm ("комптоновская" длина) • Zitterbewegung and the Magnetic Moment of the Electron • Basil S. Davis, Arxiv:1307.1490

  8. Спины и магнитные моменты других частиц Протон, нейтрон, и кварки, из которых они состоят, мюон и нейтрино, имеют спин = ½ Магнитный момент протона и нейтрона порядка eћ/mc, где теперь m это массапротона. Их магнитные моменты в ~ 2000 раз меньше магнитного момента электрона Ядра с четным числом протонов+нейтронов как правило имеют спин =0 и не обладают магнитным моментом Ядра с нечетным числом протонов+нейтронов обладают полуцелымспином Примеры: He4 I = 0, He3 I = 1/2, In113 I = 9/2 Спин фотона = 1

  9. Спин электрона полуцелый, S=1/2 Электроны - фермионы Принцип Паули Структура атомов, молекул, вещества Химия Живая материя, хомо сапиенс, общество Наше сегодняшнее заседание Роль спина в Природе

  10. Спиновые взаимодействия 1. Диполь-дипольное взаимодействие 2. Спин-орбитальное взаимодействие 3. Обменное взаимодействие 4. Сверхтонкое взаимодействие со спинами ядер 5. Взаимодействие с внешним магнитным полем

  11. Spin interactions Direct magnetic interaction – the dipole-dipole interaction between the magnetic moments of a pair of electrons. Order of magnitude ~μ2/r 3. Normally negligible for electrons, however important for nuclear spins Exchange interaction – Coulomb interaction between electrons, which becomes spin-dependent because their wavefunction must be anti-symmetric.Is at the origin of ferromagnetism.Important in magnetic semiconductors Spin-orbit interaction – If an observer moves with a velocity v in an external electric field E, he will see a magnetic field B = (v/c)×E. Thus there is an effective magnetic field acting on the magnetic moment (spin) of a moving electron.Stongly enhanced for atoms with large Z. This interaction is responsible for most of the spin-related optical and transport effects Hyperfine interaction with lattice nuclei – Magnetic interaction between the electron and nuclear magnetic moments. Important for bands originating from s-states in atoms with large Z. Leads to spectacular phenomena in the strongly coupled electron ̶ nuclei spin system

  12. Проекция спина на любую ось = ±1/2 (в единицахћ). Sz = ± 1/2, и так же для Sx и Sy. В то же времяS2 = 3/4!Не странно ли? T. e.Sx2, Sy2и Sz2всегда существуют одновременно (не может быть Sx2 =0)

  13. Введение в спиновую физику М. И. Дьяконов Université Montpellier II, France Лекция 2 Я б смотреть на эти спины и за деньги не хотел... Саша Черный (1908)

  14. Спиновая физика: 1) Изучение равновесного состояния спинов 2) Возмущение равновесного состояния 3) Измерение отклика на это возмущение

  15. Историческая справка Atomic physics Polarized luminescence (Wood, 1923)‏ Depolarization by magnetic field (Wood, 1923; Hanle, 1924)‏ Optical pumping (Kastler, Brossel,1950)‏ Magnetic resonances Nuclear magnetic resonance (Rabi, 1938)‏ Electron spin resonance (Zavoisky, 1944)‏

  16. W. Hanle “Über magnetische Beeinflussung der Polarisation der Resonanz-Fluoreszenz” Z. Physik 30, 93 (1924)‏ Wilhelm Hanle (1901-1993) Историческая справка R.W. Wood and A. Ellett “Polarized resonance radiation in weak magnetic fields” Phys. Rev. 24, 243 (1924)‏ Robert Wood (1868-1955)‏

  17. Историческая справка J. Brossel, A. Kastler, “La détéction de la résonance magnétique des niveaux excités – l’effet de depolarization des radiations de résonance optique et de fluorescence” Compt. Rend. Hebd. Acad. Sci. 229, 1213 (1949)‏ Alfred Kastler (1902-1984)‏ Jean Brossel (1918-2003)‏

  18. 1938 - Discovery of the Nuclear Magnetic Resonance Isidor Rabi (1898-1988)‏ 1944 - Discovery of the Electron Spin Resonance Evgeny Zavoisky (1907-1976) Историческая справка

  19. B S +μB ‒μB Уравнение: Спиновыйрезонанс Магнитный момент прецессирует вокруг магнитного поля с частотойΩ = 2μB/ħ

  20. B S B1 Спиновый резонанс Теперь включим переменное магнитное поле B1 (t) перпендикулярное B и вращающееся с частотой ω = Ω (резонанс) Перейдем во вращающуюся с частотой ωсистему координат. В этой системе останется только постоянное поле B1.Магнитный момент прецессирует вокруг магнитного поляB1с частотойΩ1 = 2μB1/ħ Если вначале спин направлен вдоль B, то через времяπ/Ω1 спин перевернется (180° импульс)

  21. Felix Bloch (1905-1983)‏ Уравнение Блоха S0 - равновесное значение спина T2 - поперечное время релаксации T1 - продольное время релаксации

  22. Spin echo

  23. Human brain scanned by NMR Applications come unexpected!

  24. Georges Lampel 2008 First experiment on optical spin orientation of free electrons in a semiconductor‏

  25. l = 0 l = 1 l = 1 Optical transitions between atomic levels with j = 3/2 and j =1/2 under absorption of a right circularly polarized photon The ratio of the two probabilities is 3:1 Band structure of GaAs near Γ point Opticalspin orientation and detection

  26. GaAs P0 P = 1+ /s Opticalspin orientation and detection Excitation by circularly polarized light Detection of the circular polarization of luminescence,P For recombination with non-polarized holes P = S, the average spin per electron whereis the electron lifetime, sis the spin relaxation time

  27. The Hanle effect depolarization of luminescence in magnetic field‏ P(0) Ωis the spin precession frequency in magnetic field, 1/Τ = 1/ + 1/sis the effective spin lifetime P(B) = 1+ (ΩΤ)2 (The Hanle curve)‏ ”It was then observed that the apparatus was oriented in a different direction from that which obtained in earlier work, and on turning the table on which everything was mounted through ninety degrees, bringing the observation direction East and West, we at once obtained a much higher value of the polarization” R. Wood and A. Ellett (1924)‏

  28. Spin relaxation

  29. Spin relaxation Mistification of spin relaxation: “The qubit (spin) gets entangled with the environment…” “The environment is constantly trying to look at the state of a qubit, a process called decoherence” Spin relaxation is a result of the action of fluctuating in time magnetic fields In most cases, these are not real magnetic fields, but rather “effective” magnetic fields originating from the spin-orbit, exchange, or hyperfine interactions Two parameters of a randomly fluctuating magnetic field: a) Its amplitude, or the average spin precession frequency,ω, in this random field b) Its correlation timec, i.e. the time during which the field may be roughly considered as constant

  30. IMPORTANT PARAMETER What happens, depends on the value of the dimensionless parameter ωc which is the typical angle of spin precession during the correlation time Spin relaxation

  31. Spin relaxation TWO LIMITING CASES: a)c << 1(most frequent case)‏ The spin vector experiences a slow angular diffusion b)c >> 1 This means that during the correlation time the spin will make many rotations around the direction of the magnetic field

  32. Spin relaxation a)c << 1 Number of uncorrelated random steps duringt: t/c Squared precession anglefor each step:(c)2 Total squared angle after time t :(c)2t/c Spin relaxation time may be defined as the time at which this angle becomes of the order of 1: 1/s ~ 2c This is essentially a classical formula ! Random walk of the spin vector

  33. Spin relaxation b)c >> 1 During time ~ 1/ the spin projection transverse to the random magnetic field is (on the average) completely destroyed, while its projection along the direction of the field is conserved After time c the magnetic field changes its direction, and the initial spin polarization will disappear. Thus for this case s ~ c , i.e. the spin relaxation time is on the order of the correlation time This consideration is quite general It applies to any mechanism of spin relaxation!

  34. Введение в спиновую физику The electron-nuclear spin system Житьна вершинеголой, Писатьпростыесонеты, Ибратьулюдей издола Хлеб, вино, икотлеты. Саша Черный Spin-related transport phenomena, spin Hall effect М. И. Дьяконов Université Montpellier II, France Лекция 3

  35. The electron-nuclear spin system Electron spin system Electron spin orientation Electron spin detection Effective nuclear magnetic field Dynamic nuclear polarization NMR Nuclear spin system

  36. The electron-nuclear spin system The physics is governed by three basic interactions: Hyperfine interaction between electron and nuclear spins Fermi contact interaction:V = AIS(for an electron in s-state)‏ I- nuclear spin,S- electron spin Consequences: (i) Nuclear spin relaxation(electron spin system in equilibrium)‏ (ii) Dynamic nuclear polarization(electron spin system out of equilibrium)‏ Time scale: from seconds to minutes, to hours (iii) Effectivenuclear magnetic fieldacting on electron spins The field of 100% polarized nuclei in GaAs would be about6 Tesla!

  37. The electron-nuclear spin system b) Dipole-dipole interaction between nuclear spins. Can be characterized by thelocal magnetic field,BL~several Gauss and a precession period of a nuclear spin in this field,N~10-4 s This interaction leads tonuclear spin diffusion(Bloembergen)‏ Diffusion coefficient:DN~a2/N~ 10-12 cm2/s So, spin diffusion on a distance of 100 Åtakes~ 1s and several hours for a distance of 1 μm c) Zeeman interaction of electron and nuclear spins with the external magnetic field N/ B ~ 10-3

  38. The average nuclear spin is given by the thermodynamical formula: I+1 B Iav = always along B ! 3 kΘ Calculation of the spin temperature (Dyakonov, Perel, 1974) gives : B(BS)‏ BN = B0 B2+BL2 The electron-nuclear spin system Nuclear spin temperature The timeN~10‒4 s(also calledT2)gives a characteristic time scale for the nuclear spin system, which is much shorter than the spin-lattice relaxation timeT1 During time~τNthermal equilibrium within this system is established, with a nuclear spin temperatureΘ, which may be very different from the crystal temperature, for example, something like10‒6K

  39. The oblique Hanle effect (manifestation of nuclear magnetic field in the obliqueHanle effect)‏ Dyakonov, Perel, Ekimov, Safarov (1974) The nuclei always get polarized so thatI~ (SB)B HenceBmust be neither parallel, nor perpendicular toS !

  40. The electron-nuclear spin system(Nuclear spin Zoo)‏ Circular polarization of luminescence in AlGaAs in perpendicular magnetic field for different field orientation with respect to crystal axes V.A. Novikov and V.G. Fleisher, Sov. Phys. JETP, 44, 410 (1976)‏

  41. The electron-nuclear spin system(Nuclear spin Zoo)‏ Self-sustained oscillations of the circular polarization of the luminescence inAlGaAsappearing after application of transverse magnetic fieldB=60 G for different angles with [110] V.A. Novikov and V.G. Fleisher, Sov. Phys. JETP, 47, 539 (1978)‏

  42. Oblique Hanle effect in GaAs • θ = 83o • θ = 87o • θ = 90o • B.P. Zakharchenya, V.G. Fleisher et al, • Sov. Phys. Solid State 23, 810 (1981)‏ The electron-nuclear spin system (Nuclear spin Zoo)‏

  43. Spin-related transport phenomena, spin Hall effect

  44. Edwin Hall Joaquin Mazdak Luttinger Robert Karplus Anomalous Hall effect • 1879 Hall Effect • 1881 Anomalous Hall Effect in ferromagnets: Explanation (spin-orbit interaction!): J. Smit (1951,1955) R. Karplus, J.M. Luttinger (1954)

  45. Leningrad 1976 Current-induced spin accumulation (Spin Hall Effect)

  46. j Current-induced spin accumulation

  47. z x Now there is a pure spin currentqxz The charge current is zero:q=0 z x Spin and charge currents qxz - zcomponent of spin is flowing in thexdirection Generally: qij Here the spin current is accompanied by a charge currentqx(electric currentj = – q/e)

  48. Spin-orbit interaction couples the two currents: qi = qi(0) + εijk qij (0) qij = qij(0)– εijk qk(0) M.I. Dyakonov, Phys. Rev. Lett. 99, 126601 (2007) Hereis a dimensionless couplingparameter proportional to the spin-orbit interaction ijkis the unit antisymmetric tensor Coupling of spin and charge currents Charge flow density:q = - j/e( j – electric current density) Spin polarization flow density tensor:qij(flow of the j-component of spin in direction i) Spin polarization density:P = 2S, whereSis the spin density vector. Without taking account of spin-orbit interaction: – normal expression with drift and diffusion – similar expression (spins carried by drift and diffusion) )

  49. Anomalous Hall Effect Inverse Spin Hall Effect Spin Hall Effect Diffusive counterpart of SHE Phenomenological equations (Dyakonov, Perel, 1971)  =,  = D.

  50. First observation of the Inverse Spin Hall Effect( j~ curlP ) Proposal:N.S. Averkiev and M.I. Dyakonov, Sov. Phys. Semicond.17, 393 (1983) Experiment: A.A. Bakun, B.P. Zakharchenya, A.A. Rogachev, M.N. Tkachuk, and V.G. Fleisher, Sov. Phys. JETP Lett.40, 1293 (1984) Circularly polarized light creates spin polarization P, howevercurl P = 0 Byapplying a magnetic field parallel to the surface, one creates the y component of P. This makes a non-zero curlPand hence an electric current in the x direction

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