Zeeman effect in α-quartz

The helical crystal structure in α-quartz acts as the natural micro-solenoids for an electromagnetic wave passing through them, producing a longitudinal magnetic field in the direction of the optical axis. The longitudinal magnetic field further induces the Larmor frequency for the rotation of the bound electrons. The calculated Larmor frequency was experimentally confirmed by monitoring a line splitting of the infrared OH-band in the transmission spectra of α-quartz. A shift in the resonance frequency of the OH-band is equal to the Larmor frequency induced by the natural Zeeman effect.     

Dynamics of magnetization in ferromagnet with spin-transfer torque

We review our recent works on dynamics of magnetization in ferromagnet with spin-transfer torque. Driven by constant spin-polarized current, the spin-transfer torque counteracts both the precession driven by the effective field and the Gilbert damping term different from the common understanding. When the spin current exceeds the critical value, the conjunctive action of Gilbert damping and spin-transfer torque leads naturally the novel screw-pitch effect characterized by the temporal oscillation of domain wall velocity and width. Driven by space- and time-dependent spin-polarized current and magnetic field, we expatiate the formation of domain wall velocity in ferromagnetic nanowire. We discuss the properties of dynamic magnetic soliton in uniaxial anisotropic ferromagnetic nanowire driven by spin-transfer torque, and analyze the modulation instability and dark soliton on the spin wave background, which shows the characteristic breather behavior of the soliton as it propagates along the ferromagnetic nanowire. With stronger breather character, we get the novel magnetic rogue wave and clarify its formation mechanism. The generation of magnetic rogue wave mainly arises from the accumulation of energy and magnons toward to its central part. We also observe that the spin-polarized current can control the exchange rate of magnons between the envelope soliton and the background, and the critical current condition is obtained analytically. At last, we have theoretically investigated the current-excited and frequency-adjusted ferromagnetic resonance in magnetic trilayers. A particular case of the perpendicular analyzer reveals that the ferromagnetic resonance curves, including the resonant location and the resonant linewidth, can be adjusted by changing the pinned magnetization direction and the direct current. Under the control of the current and external magnetic field, several magnetic states, such as quasi-parallel and quasi-antiparallel stable states, out-of-plane precession, and bistable states can be realized. Th     

Coherent optical control of the spin of a single hole in an InAs/GaAs quantum dot

We demonstrate coherent optical control of a single hole spin confined to an InAs/GaAs quantum dot. A superposition of hole-spin states is created by fast (10-100?ps) dissociation of a spin-polarized electron-hole pair. Full control of the hole spin is achieved by combining coherent rotations about two axes: Larmor precession of the hole spin about an external Voigt geometry magnetic field, and rotation about the optical axis due to the geometric phase shift induced by a picosecond laser pulse resonant with the hole-trion transition.     

Larmor labeling development

The first applications of polarized neutrons were to distinguish magnetic from nuclear scattering amplitudes. Much later the first set-ups for measuring the precession phase of the polarization passing a magnetic field were realized. This phase, determined by the field strength and interaction time, could label magnetic fields, wavelength of the neutrons and length over which the field is present. The latter could be used by proper shaping of the magnetic field to label also the direction of transmitted neutrons. The advantage of this labeling is that high precision measurements are possible without strong confinement of the beam by diaphragms. An overview of the use of Larmor labeling of polarized neutrons is given for applications in magnetism, in inelastic neutron scattering and small angle scattering.     

Larmor precession and dwell time of a particle scattered by a quantum well

The Larmor precession of a neutral spin- particle in a uniform constant magnetic field confined to the region of a one-dimensional rectangular potential well is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle dwelling at a potential well. With the help of a general spin coherent state it is explicitly shown that the spin precession time is equal to the dwell time. The comparison of the time in a potential well with that in free space shows apparent superluminality.     

The Larmor nutation

The classical non-relativistic problem of the motion of a charged particle in an external central force field and a weak uniform magnetic field is revisited to show that the motion of the kinetic angular momentumL = r × p of the particle, in the so-called Larmor approximation, is not a simple precession but is actually a composite motion involving precession as well as a high frequency nutation. The precession-nutation motion ofL is discussed in the Larmor approximation when the Larmor-frame-orbit of the charged particle is an ellipse (or a circle) for the case of the two central forces namely the Coulomb and the Hooke-law-force, which are the only two central forces known to permit closed orbits.     

Wave propagation in a rarefied plasma with finite Larmor radius

Wave propagation in a rarefied two-component plasma immersed in a uniform constant magnetic field has been discussed wherein the plasma pressure is assumed to be anisotropic owing to finite Larmor radius effect. It is shown that, for propagation along the external magnetic field, there exist two modes of wave propagation, namely, the gravitational mode and the hydromagnetic mode. The former is found to be independent of the magnetic field and hence of the Larmor radius, while the latter is appreciably influenced by the finite Larmor radius. On the other hand, for transverse propagation, there are three modes of wave propagation viz. the ion-sound mode, the electron-sound mode and the electromagnetic mode. It is shown that only the lowfrequency ion-sound mode is affected by the finite Larmor radius.     

Electronic spin precession and interferometry from spin-orbital entanglement in a double quantum dot

A double quantum dot inserted in parallel between two metallic leads can entangle the electron spin with the orbital (dot index) degree of freedom. An Aharonov-Bohm orbital phase can be transferred to the spinor wave function, providing a geometrical control of the spin precession around a fixed magnetic field. A fully coherent behavior occurs in a mixed orbital-spin Kondo regime. Evidence for the spin precession can be obtained, either using spin-polarized metallic leads or by placing the double dot in one branch of a metallic loop.     

The Effect of Finite Larmor Radius on Gravitational Instability of a Finitely Conducting Magnetised Hall Medium in Presence of Suspended Particles

The problem of stability of a self-gravitating, infinite homogeneous gas in the presence of suspended particles is investigated. The medium is assumed conducting and effect of external magnetic field, Hall current and finite Larmor radius corrections are also considered. The equations of the problem are linearized and from linearized equations a general dispersion relation for a dusty gas-particle medium is obtained. The dispersion relation is reduced for two special cases of wave propagations: Parallel and perpendicular to the direction of uniform magnetic field. The effect of suspended particles on the medium is investigated in both the cases. It is found that in the presence of finite Larmor radius corrections and suspended particles the condition of instability is determined by Jeans's criterion for a self gravitating finitely conducting magnetised Hall medium.     

Effect of Conductivity on Magneto-Gravitational Instability of a Medium with Finite Larmor Radius and Suspended Particles

The self-gravitational instability of an infinite homogeneous magnetised and finitely conducting gas-particle medium is considered to include the finite Larmor radius effect in the presence of suspended particles. The equations of the problem are linearized and from linearized equations a general dispersion relation for dusty-gas is obtained. The dispersion relations are also obtained for propagation, parallel and perpendicular to the direction of uniform magnetic field. The Jeans, criterion is discussed for these two different directions of wave propagation. It is found that in the presence of finite Larmor radius corrections and suspended particles the condition of instability is determined by Jeans' criterion for a self gravitating, finitely conducting, magnetized gas-particle medium.     

Methods for spin injection managing in inGaAs/GaAs/Al<Subscript>2</Subscript>O<Subscript>3</Subscript>/CoPt spin light-emitting diodes

Spin injection in CoPt/Al₂O₃/(Al)GaAs spin light-emitting diodes (SLEDs) was studied. The oscillations of the degree of circular polarization upon variation of a distance between the active region of the SLED and a CoPt ferromagnetic injector were observed. The oscillations depend neither on a SLED material (GaAs or AlGaAs), nor on the type of injected spin-polarized carriers (electrons and holes) and are related to the action of a perpendicular magnetic field on the injected spin-polarized carriers that causes their precession. During the transfer to the active region through a distance of 50–100 nm from the injector, a z–component of a spin changes a phase that is detected experimentally as the change in sign of the degree of circular polarization of luminescence. Conceivably, a source of the internal magnetic field leading to spin precession is the magnetic field of the nonuniformly magnetized CoPt contact.     

Wigner Rotations and Precession of Polarization

An easy and direct derivation of Thomas precession is obtained from infinitesimal Wigner rotations arising in unitary representations of the Poincaré group. For spin > 1/2, multipole parameters are studied from this point of view. The canonical 3-component definition of polarization arising naturally in this context is compared with formalisms which start form a pseudo 4-vector and an antisymmetric tensor respectively. The full Thomas equations, including Larmor precession, is derived using time derivatives of finite Wigner rotations. Exact solutions, with arbitrary initial conditions, are presented for constant magnetic fields and for orthogonal constant electric and magnetic fields. For a class of plane wave external fields exact solutions are obtained for the Dirac equation generalized by the inclusion of anomalous magnetic moment (Pauli) and electric dipole moment terms. Using the front form of dynamics, well-adapted to this context and coinciding with proper time dynamics, expectation values are calculated. The polarization pseudo 4-vector thus obtained is shown to satisfy the BMT equation, which is equivalent to the Thomas equation. This shows that the validity of the classical precession equations is not necessarily restricted to slowly varying external fields. These solutions can also be of interest in the study of spin 1/2 particles in laser fields and in the study of electric dipole moments.     

Analysis of magnetization instability patterns in spin-transfer nano-oscillators

The stability of large precessional magnetization motions induced by spin-polarized currents in spin-transfer nano-oscillators is discussed. Quantitative analytical predictions are obtained for the critical values of spin-polarized injected current and external magnetic field at which the oscillator magnetization precession becomes unstable. It is shown that the mechanism leading to instability is parametric resonance of well-defined pairs of magnetostatically coupled perturbation modes. The amplitude of these modes grows to large non-thermal values when the oscillator frequency matches the mean of the natural frequencies of the two coupled modes. Analytical predictions are obtained for the space-time structure and symmetry of the magnetization patterns that are formed at the instability. Analytical results are compared with numerical simulations of spin-transfer-driven magnetization dynamics.     

Larmor spin precession and neutron optics

We consider the neutron-optical phenomena that emerge during the coherent interaction of a neutron with a sample when the neutron spin precesses in a magnetic field. As follows from general considerations, such an interaction gives rise to an extra precession phase, which is added to the Larmor precession phase. This phenomenon can be interpreted as a manifestation of the time delay due to a finite time of the neutron-sample interaction. The Larmor neutron spin precession with a constant frequency serves as a clock for measuring this time delay. We used such a clock to directly measure the difference between the neutron velocity in matter and its vacuum value. We also present the results of the first experiments in which Larmor clocks were used to measure the neutron tunneling time in the resonance of a quasi-bound state and the Bragg diffraction time. Prospects for further applications of the method are discussed.     

Self-Diffusion Imaging by Spin Echo in Earth's Magnetic Field

The NMR of the Earth's magnetic field is used for diffusion-weighted imaging of phantoms. Due to a weak Larmor field, care needs to be taken regarding the use of the usual high field assumption in calculating the effect of the applied inhomogeneous magnetic field. The usual definition of the magnetic field gradient must be replaced by a generalized formula valid when the strength of a nonuniform magnetic field and a Larmor field are comparable (J. Stepišnik,Z. Phys. Chem.190, 51–62 (1995)). It turns out that the expression for spin echo attenuation is identical to the well-known Torrey formula only when the applied nonuniform field has a proper symmetry. This kind of problem may occur in a strong Larmor field as well as when the slow diffusion rate of particles needs an extremely strong gradient to be applied. The measurements of the geomagnetic field NMR demonstrate the usefulness of the method for diffusion and flow-weighted imaging.     

Zero-field and Larmor spinor precessions in a neutron polarimeter experiment

We present a neutron polarimetric experiment where two kinds of spinor precessions are observed: one is induced by different total energy of neutrons (zero-field precession) and the other is induced by a stationary guide field (Larmor precession). A characteristic of the former is the dependence of the energy-difference, which is in practice tuned by the frequency of the interacting oscillating magnetic field ωR. In contrast the latter completely depends on the strength of the guide field, namely Larmor frequency ωL. Our neutron-polarimetric experiment exhibits individual tuning as well as specific properties of each spinor precession, which assures the use of both spin precessions for multi-entangled spinor manipulation.     

GaAs中电子g因子的温度和能量依赖性的飞秒激光吸收量子拍研究

采用时间分辨椭圆偏振光抽运-探测光谱研究磁场作用下本征GaAs中电子自旋弛豫动力学，观察到吸收量子拍现象.这种吸收量子拍起源于电子自旋的拉莫尔进动，因而其拍频成为高精度测量电子g因子的一种新方法.利用这种新方法研究了本征GaAs中电子g因子的温度和能量依赖特性，发现g因子随电子的温度和能量增加而增加，但与k·p理论预测相差甚大.基于实验结果拟合，我们给出了一个g因子的温度和能量依赖的经验公式. 关键词： 椭圆偏振光抽运-探测光谱 自旋量子拍 g因子 GaAs     

Analytical treatment of synchronization of spin-torque oscillators by microwave magnetic fields

An analytical approach is presented for the study of synchronization effects in spin-transfer-driven nanomagnets subjected to radio-frequency magnetic fields. The conditions are derived and discussed under which the current-induced magnetization precession is synchronized by the radio-frequency field. Exact analytical results are obtained for the case when the problem exhibits uniaxial symmetry around the axis perpendicular to the device plane. It is demonstrated that the magnetization dynamics under nonzero current and nonzero rf field is identical in structure to that under zero current. On this basis, analytical predictions are obtained for: the existence of phase-locking between current-induced magnetization precession and rf field oscillations; the frequency pulling effect in proximity of phase locking; the occurrence of hysteresis effects in phase-locking as a function of the spin-polarized current. The proposed approach is valid for arbitrary rf field amplitude and current intensity.     

Average transient period for precession regimes in magnetic films with dynamic bistability

The average transient time of regular regimes corresponding to the dynamic bistability state is studied using analysis of uniform precession of magnetization of a thin magnetic film. The possibility of controlling the transient process parameter by an additional ac magnetic field in the form of a harmonic of noise signal is established. A new type of stochastic resonance is detected, which corresponds to the probability of high-amplitude precession and is manifested during a short noise action.