Quadrupole relaxation enhancement--application to molecular crystals

A general theory of field dependent spin-lattice relaxation for nuclei of the spin quantum number 1/2 (1H, 19F, 13C) caused by dipole-dipole interactions with neighboring quadrupolar nuclei (nuclei possessing a quadrupolar moment) is presented. The theory is valid for arbitrary motional conditions and should be treated as a quadrupolar counterpart of the paramagnetic relaxation enhancement theory. When the energy level splitting of the dipolar spin (I=1/2) matches one of the transition frequencies of the quadrupolar nuclei one can observe a local enhancement of the dipolar spin relaxation (referred to as "quadrupolar peaks"). To see such effects the dynamics modulating the spin interactions has to be relatively slow. This brings the system beyond the validity range of perturbation approaches and requires the stochastic Liouville equation to be applied. The presented theory describes the quadrupolar relaxation enhancement (QRE) for an arbitrary spin quantum number of the quadrupolar nuclei and includes the asymmetry of the quadrupolar coupling. It has been applied to interpret the shape of magnetization curves (amplitude of 1H magnetization versus magnetic field) for the molecular crystal [C3N2H5]6[Bi4Br18] ([C3N2H5]-imidazolium). The magnetization curves show several dips (local minima) attributed to 1H-14N quadrupolar relaxation enhancement effects. In addition, as a limiting case a perturbation approach to QRE has been presented and its validity conditions have been discussed.     

The thermodynamic one-particle Green function in the renormalized spin wave approximation for isotropic cubic ferromagnets

The thermodynamic one-particle Green function in the renormalized spin wave approximation for isotropic cubic ferromagnetic insulators with Dyson's spin wave theory as a base is derived. In quantitative respect, dynamic and kinematic effects of spin waves are approximated by the graphs deficient in the energy denominators, wherefore at low temperature kinematic interaction turns out to be too strong. As against the one-particle Green function for independent spin waves, dynamic interaction of ferromagnons is shown to effect the renormalization of the spin wave energy, whereas kinematic interaction directly modifies the average ferromagnon population numbers. In the matter of magnetization, its formula based on the Green function assumes a similar form as in the spin wave theory without interactions on the understanding that it remains valid within the entire range of temperatures from absolute zero up to the critical point.     

Refraction of surface spin waves in spatially inhomogeneous ferrodielectrics with biaxial magnetic anisotropy

The refractive index of surface spin waves propagating in a ferromagnetic medium with a nonuniform distribution of the parameters of uniaxial and orthorhombic magnetic anisotropies and exchange coupling is determined within the spin-density formalism. The coefficients of reflection and transmission of spin waves at the interface between two homogeneous magnets with different constants of uniaxial and orthorhombic magnetic anisotropies, exchange coupling, and saturation magnetization are calculated. The dependences of the intensity of a reflected wave and the refractive index on the wave frequency and the strength of an external dc homogeneous magnetic field are determined.     

The quantum effects of the spin and the Bohm potential in the oblique propagation of magnetosonic waves

We study the quantum corrections to the oblique propagation of the magnetosonic waves in a warm quantum magnetoplasma composed by mobile ions and electrons. We use a fluid formalism to include quantum corrections due to the Bohm potential and to the spin magnetization energy of electrons. The effects of both quantum corrections are shown in the dispersion relation for perpendicular, parallel and oblique propagation. We find that the quantum contributions to the low frequency depend on the type in the oblique propagation with respect to the background magnetic field. The relevance in astrophysical scenarios is exemplified.     

Nonequilibrium spin transport through a diluted magnetic semiconductor quantum dot system with noncollinear magnetization

The spin-dependent transport through a diluted magnetic semiconductor quantum dot (QD) which is coupled via magnetic tunnel junctions to two ferromagnetic leads is studied theoretically. A noncollinear system is considered, where the QD is magnetized at an arbitrary angle with respect to the leads’ magnetization. The tunneling current is calculated in the coherent regime via the Keldysh nonequilibrium Green’s function (NEGF) formalism, incorporating the electron–electron interaction in the QD. We provide the first analytical solution for the Green’s function of the noncollinear DMS quantum dot system, solved via the equation of motion method under Hartree–Fock approximation. The transport characteristics (charge and spin currents, and tunnel magnetoresistance (TMR)) are evaluated for different voltage regimes. The interplay between spin-dependent tunneling and single-charge effects results in three distinct voltage regimes in the spin and charge current characteristics. The voltage range in which the QD is singly occupied corresponds to the maximum spin current and greatest sensitivity of the spin current to the QD magnetization orientation. The QD device also shows transport features suitable for sensor applications, i.e., a large charge current coupled with a high TMR ratio.     

Diverse solid and supersolid phases of bosons in a triangular lattice

We investigate the ground state of bosons with long-range interactions in the large U limit on a triangular lattice. By mapping this system to the spin-1/2 XXZ model in a magnetic field, we can apply the spin wave theory to this study. We demonstrate how to construct the phase diagrams within the spin wave theory. The phase diagrams are given in an extensive parameter region, where, besides the superfluid phase, diverse solid and supersolid phases are shown to exist in this model. Especially, we find that the phase diagram obtained in this method is consistent with the one obtained previously using numerical techniques in the Ising limit. This confirms the effectiveness of our method. We analyze the stability of all the obtained supersolids and show that they will not be ruined by the quantum fluctuations. We observe that the quantum fluctuations in the stripe supersolid phase could be enhanced by the external field. We also discuss the relevance of our result with the experiment that may be realized with ultracold bosonic polar molecules in a triangular optical lattice.     

Spin-potential functional formalism for current-carrying noncollinear magnetic systems

We develop a formalism dual to spin-current-density functional theory (CDFT) where minimization with respect to the scalar and vector spin potentials is used. In this way we circumvent the issues surrounding the nonuniqueness of the mapping between spin potentials and ground-state wave functions, and the v representability issue of current-density functionals. The approach applied within the Kohn-Sham formalism provides the foundations for the optimized effective potential method for CDFT.     

Field-induced magnetic reorientation and effective anisotropy of a ferromagnetic monolayer within spin wave theory

The reorientation of the magnetization of a ferromagnetic monolayer is calculated with the help of many-body Green's function theory. This allows, in contrast to other spin wave theories, a satisfactory calculation of magnetic properties over the entire temperature range of interest since interactions between spin waves are taken into account. A Heisenberg Hamiltonian plus a second-order uniaxial single-ion anisotropy and an external magnetic field is treated by the Tyablikov (Random Phase Approximation: RPA) decoupling of the exchange interaction term and the Anderson-Callen decoupling of the anisotropy term. The orientation of the magnetization is determined by the spin components (), which are calculated with the help of the spectral theorem. The knowledge of the orientation angle allows a non-perturbative determination of the temperature dependence of the effective second-order anisotropy coefficient. Results for the Green's function theory are compared with those obtained with mean-field theory (MFT). We find significant differences between these approaches. Received 6 April 1999 and Received in final form 9 July 1999     

Reducing influence of antiferromagnetic interactions on ferromagnetic properties of p-(Cd,Mn)Te quantum wells

In order to explain the absence of hysteresis in ferromagnetic p-type (Cd,Mn)Te quantum wells (QWs), spin dynamics was previously investigated by Monte Carlo simulations combining the Metropolis algorithm with the determination of hole eigenfunctions at each Monte Carlo sweep. Short-range antiferromagnetic superexchange interactions between Mn spins—which compete with the hole-mediated long-range ferromagnetic coupling—were found to accelerate magnetization dynamics if the layer containing Mn spins is wider than the vertical range of the hole wave function. Employing this approach it is shown here that appreciate magnitudes of remanence and coercivity can be obtained if Mn ions are introduced to the quantum well in a delta-like fashion.     

Quantum spin dynamics of the bilayer ferromagnet La Sr Mn O

We construct a theory of spin wave excitations in the bilayer manganite La_1.2Sr_1.8Mn₂O₇ based on the simplest possible double-exchange model, but including leading quantum corrections to the spin wave dispersion and damping. Comparison is made with recent inelastic neutron scattering experiments. We find that quantum effects account for some part of the measured damping of spin waves, but cannot by themselves explain the observed softening of spin waves at the zone boundary. Furthermore a doping dependence of the total spin wave dispersion and the optical spin wave gap is predicted. Received 15 January 2002 Published online 6 June 2002     

Many-body Green's function theory for the magnetic reorientation of thin ferromagnetic films

The field-induced reorientation of the magnetization of ferromagnetic films is treated within the framework of many-body Green's function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green's functions. This formulation allows a straightforward extension of the monolayer case to thin films with many layers and for arbitrary spin and moreover provides a practicable procedure for numerical computation. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. We utilize the Tyablikov (RPA) decoupling for the exchange interaction terms and the Anderson-Callen decoupling for the anisotropy terms. The dipole coupling is treated in the mean-field approximation, a procedure which we demonstrate to be a sufficiently good approximation for realistic coupling strengths. We apply the new method to monolayers with spin and to multilayer systems with S=1. We compare some of our results to those where mean-field theory (MFT) is applied to all interactions, pointing out some significant differences. Received 19 June 2000 and Received in final form 2 August 2000     

Spin precession and electron spin polarization wave in [001]-grown quantum wells

We theoretically study the spatial behaviors of spin precessions modulated by an effective magnetic field in a two-dimensional electron system with spin-orbit interaction. Through analysis of interaction between the spin and the effective magnetic field, we find some laws of spin precession in the system, by which we explain some previous phenomena of spin precession, and predict a controllable electron spin polarization wave in [001]-grown quantum wells. The shape of the wave, like water wave, mostly are ellipse-like or circle-like, and the wavelength is anisotropic in the quantum wells with two unequal coupling strengths of the Rashba and Dresselhaus interactions, and is isotropic in the quantum wells with only one spin orbit interaction.     

Effect of kinematic interaction in the renormalized spin wave theory for isotropic ferromagnet

The procedure of calculating within the frame-work of renormalized spin wave approximation the contribution from kinematic interaction of ferromagnons to the partition function and magnetization of the isotropic cubic ferromagnet is established. The investigation seen here through extends Dysons's spin wave approach to higher temperatures up to the critical point. In contradistinction to the graphs due to dynamic interaction of spin waves which effect the renormalization of the energy of non-interacting ferromagnons, the diagrams resulting from kinematic interaction are shown to correct the average spin wave population numbers only. That correction proves to be a solution of an integral equation and its quantity depends both on the temperature and the atomic spin quantum numberS, and it tends to zero with increasingS.     

Electromagnetic solitons in a system of quantum dots taking into account the Hubbard interaction

We consider the Maxwell equations for an electromagnetic field propagating in a solid with a three-dimensional superlattice of quantum dots linked by strong tunneling along one axis, where electrons with different spin projections are affected by the strong Coulomb repulsion at a single site. We obtain a phenomenological equation in the form of the classical 1+1-dimensional sine-Gordon equation. Electrons are considered within the framework of quantum formalism taking into account the changes in the dispersion law provided by the presence of Coulomb interactions. The phenomenological equation is solved numerically, and the influence of Coulomb repulsion and the degree of band population on the propagation of ultra-short optical pulses is analyzed.     

The generating functions formalism for the analysis of spin response to the periodic trains of RF pulses. Echo sequences with arbitrary refocusing angles and resonance offsets

The generating functions (GF) formalism was applied for calculation of spin density matrix evolution under the influence of periodic trains of RF pulses. It was shown that in a general case, closed expression for the generating function can be found that allows in many cases to derive analytical expressions for the generating function of spin density matrix (magnetization, coherences). This approach was shown to be particularly efficient for the analysis of multi-echo sequences, where one has to average over various frequency isochromats. The explicit analytical expressions for the generating function for echo amplitudes in a Carr–Purcell–Meiboom–Gill (CPMG) echo sequence, a multiecho sequence with incremental phase of refocusing pulse, a gradient echo sequence including transient period were obtained for an arbitrary flip angle and an arbitrary resonance offset. Comparison of the theory and the spin-echo experiments was done, demonstrating a good agreement.     

Spin-wave excitation by direct current in obliquely magnetized nanostructures

The magnetization dynamics of magnetic nanostructures magnetized at an arbitrary out-of-plane angle is investigated with the spin-wave formalism. The magnetic excitations driven by a spin-polarized direct current are considered to be standing spin-wave modes appropriate for nanopillar structures. The spin waves grow exponentially above a certain critical value of the current density and their post-threshold nonlinear dynamics leads to magnetization oscillations in the microwave range. Due to demagnetizing fields, the current-driven excitation strongly depends on the direction of the applied external magnetic field. In order to calculate the microwave oscillation frequency we derive an equation of motion for the spin-wave amplitude as a function of the out-of-plane angle of the applied field. The results are compared with recent experimental data as well as with another theoretical approach.     

Formalism of Quantum Number Polynomials

Theoretical aspects of the recent perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. By the example of a biatomic molecule, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Hermann-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 58–68, September, 2005.     

Path integrals with arbitrary generators and the eigenfunction problem

We generalize the path integral formalism of quantum mechanics to include the use of arbitrary infinitesimal generators, thus providing explicit expressions for solutions of a wide class of differential equations. In particular, we develop a method of calculating the eigenfunctions of a large class of operators.     

Theory of diluted magnetic semiconductor ferromagnetism

We present a theory of carrier-induced ferromagnetism in diluted magnetic semiconductors ( III1-xMnxV) which allows for arbitrary itinerant-carrier spin polarization and dynamic correlations. Both ingredients are essential in identifying the system's elementary excitations and describing their properties. We find a branch of collective modes, in addition to the spin waves and Stoner continuum which occur in metallic ferromagnets, and predict that the low-temperature spin stiffness is independent of the strength of the exchange coupling between magnetic ions and itinerant carriers. We discuss the temperature dependence of the magnetization and the heat capacity.