The autoresonant approach for the generation of dark solitons by external fields is developed in the context of the effects of mode-locking instabilities which occur in multi-phase driving. The one-phase step-by-step and two-phase drivings are studied for slowly varying frequencies of the drives. Possible scenarios for the stable generation of high-depth dark solitons are found. Adiabatic control of soliton parameters is demonstrated when the driving amplitudes exceed a threshold. The driving amplitude diagrams for preferable scenarios of the generation of high-amplitude dark solitons are presented.

The effects of magnon dissipation on the properties of magnetoelastic waves in ferromagnets in the vicinity of magnetoelastic resonance are investigated. The magnetoelastic waves in this region are strongly anisotropic, and the directions with high intensity (caustic waves) are formed. Dissipation leads to the disappearance of the gap between different magnetoelastic modes, finiteness of amplification factor, and to the damping of caustic waves in some directions. The caustic patterns formed by the caustic waves are transformed due to dissipation. In elastically isotropic and slightly anisotropic ferromagnets, caustics disappear when even a small dissipation is taken into account, while in strongly elastically anisotropic ferromagnets the main features of caustic patterns are retained in a wide region of the external magnetic field.

The vicinities of two resonance points where longitudinal and transverse elastic waves interact with the magnetic mode are considered. The caustic patterns of magnetoelastic waves (MEW) in galfenol crystals Fe1-xGax with two compositions (x = 0.18 and x = 0.086) are calculated. The investigation of MEW focusing and caustic is based on the analysis of constant frequency surfaces, which are obtained in the model of continuous medium. It was found that the caustic patterns significantly depend on the magnitude of external magnetic field and galfenol composition.

The focusing and caustic effects of magnetoelastic waves (MEW) in Galfenol crystals (Fe100−xGax) in the vicinity of magnetoelastic resonance are considered. It is shown that the caustic pattern of magnetoelastic waves differs significantly from the phonon caustic pattern, and the directions of MEW caustics are controlled by the magnitude of the external magnetic field. The region of magnetic field in which the MEW caustics can be observed is determined.

The caustic of magnetoelastic waves (MEW) propagating in thick-film ferromagnets is investigated. The model of continuous medium is employed, and MEW are considered in the long wavelength approximation. It is shown that in thick-film samples the difference between the internal and external magnetic fields leads to a special form of the anisotropy of the MEW spectrum and, accordingly, to the appearance of a caustic. The possibility to control this phenomenon with the frequency of MEW is revealed. In particular, the directions and frequency ranges of the waves where the caustic occurs are obtained.

The focusing features and caustic of magnetoelastic waves in Y3Fe5O12 (YIG) crystals in the long wavelength approximation are investigated. It is shown that the interaction of phonon and magnetic subsystems leads to pronounced anisotropic properties of magnetoelastic waves. Four magnetoelastic eigenmodes are realized in the crystal, and two of them possess a focusing and caustic in the vicinity of magnetoelastic resonance point. The region of frequencies and wavenumbers of magnetoelastic waves is obtained, where the caustic can be observed. The directions of the focusing and caustic are defined.

The features of focusing and caustic of spin waves in antiferromagnetic crystals with body-centered tetragonal (BCT) lattice in the framework of Heisenberg model are investigated. The model takes into account the interaction of an atom's spin with its first and second neighbors. It is shown that magnon focusing picture depends on the ratio between the exchange coupling constants of atom's spin with first (J(1)) and second (J(2)) neighbors. If the value of J(2) is positive then the spin waves focusing occurs in the [1 0 1], [1 1 0], and [1 0 0] directions and if J(2) is negative then the caustic of magnons forms in some directions. The region of frequencies of spin waves where the caustic can be observed is obtained. The dependence of caustic direction on magnon frequency is investigated.

Magnetization dynamics in spheroidal ferromagnetic samples is studied theoretically. It is shown that, in a magnetostatic approximation, electronic-nuclear magnetostatic modes with a discrete spectrum of eigen oscillations exist in such samples. The structure and the field dependence of the frequencies of these oscillations are substantially dependent on the parameter of the spheroid shape that is the ratio of it’s axes and also on the external magnetic field value. In a certain region of values of these parameters, the dependence of the eigenfrequencies of the system on them becomes nontrivial. The external field strength and the sample shape determine not only the eigenfrequencies in the system, but also the number of the eigenmodes. In addition, for each of the eigenmodes, there exists a “forbidden” region of magnetic fields and shape parameters in which this mode cannot be observed.

We present a study of nonlinear NMR and Bose-Einstein condensation (BEC) of nuclear spin waves in antiferromagnetic MnCO3 with coupled electron and nuclear spins. In particular, we show that the observed behavior of NMR signals strongly contradicts the conventional description of paramagnetic ensembles of noninteracting spins based on the phenomenological Bloch equations. We present a theoretical description of the coupled electron-nuclear spin precession, which takes into account an indirect relaxation of nuclear spins via the electron subsystem. We show that the magnitude of the nuclear magnetization is conserved for arbitrary large excitation powers, which is drastically different from the conventional heating scenario derived from the Bloch equations. This provides strong evidence that the coherent precession of macroscopic nuclear magnetization observed experimentally can be identified with the BEC of nuclear spin waves with k = 0.

AbstractMagnetization dynamics in spheroidal ferromagnetic samples is studied theoretically. It is shown that, in a magnetostatic approximation, electronic-nuclear magnetostatic modes with a discrete spectrum of eigen oscillations exist in such samples. The structure and the field dependence of the frequencies of these oscillations are substantially dependent on the parameter of the spheroid shape that is the ratio of it’s axes and also on the external magnetic field value. In a certain region of values of these parameters, the dependence of the eigenfrequencies of the system on them becomes nontrivial. The external field strength and the sample shape determine not only the eigenfrequencies in the system, but also the number of the eigenmodes. In addition, for each of the eigenmodes, there exists a “forbidden” region of magnetic fields and shape parameters in which this mode cannot be observed.

The detailed calculations of dependence of the frequency of oscillations on the external magnetic field and on the shape of ferromagnet sample with interacting electronic and nuclear subsystems were done. Such system possesses a discrete number of eigenfrequencies of precession of magnetization. It is shown that these magnetostatic eigenmodes can be degenerated, i.e. different modes can have the same frequency. The dependence of these degenerated modes on the sample shape is investigated. It is shown that the properties of magnetization precession and even the number of eigenmodes depend on the external magnetic field and on the shape of the sample. These effects may produce specific features on the NMR spectra of magnetic materials.

A physical mechanism responsible for the relaxation of nuclear spins coupled by the hyperfine interaction to relaxed electron spins in materials with spin ordering is proposed. The rate of such induced nuclear spin relaxation is proportional to the dynamic shift of the nuclear magnetic resonance (NMR) frequency. Therefore, its maximum effect on the NMR signal should be expected in the case of nuclear spin waves existing in the system. Our estimates demonstrate that the induced relaxation can be much more efficient than that occurring due to the Bloch mechanism. Moreover, there is a qualitative difference between the induced and Bloch relaxations. The dynamics of nuclear spin sublattices under conditions of the induced relaxation is reduced to the rotation of m 1 and m 2 vectors without any changes in their lengths (m 1 2 ( t ) = m 2 2 ( t ) = m 0 2 ( t )= const). This means that the excitation of NMR signals by the resonant magnetic field does not change the temperature T n of the nuclear spin system. This is a manifestation of the qualitative difference between the induced and Bloch relaxations. Indeed, for the latter, the increase in T n accompanying the saturation of NMR signals is the dominant effect.

We present a new theoretical description of the coupled electron-nuclear spin systems which takes into account an indirect relaxation of nuclear spins via the electron subsystem. In our theory the magnitude of the nuclear magnetization is conserved for arbitrary large excitation powers, similar to the Landau-Lifshitz-Gilbert model of relaxation. This is drastically different from the conventional heating scenario based on the phenomenological Bloch equations. The predictions of our theory are compared with the experimental nonlinear NMR signals obtained in a weakly anisotropic antiferromagnetic MnCO$_3$ sample at temperatures below $1,$K and good quantitative agreement is observed. The proposed theory brings together the properties of magnetic nuclear resonance in, on the one hand, the magnetic systems considered here and, on the other hand, the superfluid ${^3}$He where the magnitude of the nuclear magnetization vector is also conserved.

The structure of the domain wall in a magnetically uniaxial ferromagnetic film placed in an external electric field has been studied. It has been shown that the domain wall has a complex twisted structure whose characteristics (thickness, profile, and limit velocity of steady motion) depend on the film thickness, quality factor, and external electric field. The effect of the electric field on the domain wall is caused by inhomogeneous magnetoelectric coupling taking place in domain walls with a twisted structure.

The micromagnetic structure of the domain wall (DW) with periodically distributed horizontal Bloch lines in a ferromagnetic film in an external electric field has been studied. The effect of the electric field on the internal DW micromagnetic structure is caused by inhomogeneous magnetoelectric coupling. Possible scenarios of the DW internal structure transformations implemented with varying the electric fields strength have been analyzed in detail. For each scenario, static characteristics of the system, such as the energy, DW profile, DW effective thickness, and electric polarization have been calculated.

In this paper we propose a method to generate pure dark solitons by a periodic external field with a slowly varying frequency, which allows to control amplitude of the excited solitons and period of soliton trains. Our approach to generate dark solitons is based on the effect of autoresonance when the excited wave is phase-locked by the drive after the crossing the resonance. The resonant frequency and the threshold condition on the amplitude of the driving were found.