Dynamics of a longitudinal-and-transverse acoustic wave in a crystal with paramagnetic impurities

The evolution of longitudinal-and-transverse acoustic pulses propagating along an external magnetic field through a system of resonant paramagnetic impurities with effective spin S=1/2 is studied theoretically. It is shown that, when the group velocities of longitudinal and transverse waves are equal and the impurity concentration is sufficiently small, the initial system of equations is reduced to new evolution equations, which are integrable within the framework of the inverse scattering problem approach. These equations qualitatively describe the new coherent dynamics of acoustic pulses.     

Nonlinear acoustic transparency for longitudinal-transverse picosecond pulses in a paramagnetic crystal at low temperatures

Nonlinear propagation of longitudinal-transverse acoustic pulses of duration shorter than one oscillation period (video pulses) is studied theoretically in a system of paramagnetic centers with effective spin S=1. It is shown that, depending on the relationship between the magnitudes of the longitudinal and transverse strain components and on the detuning of their linear velocities, various regimes of propagation corresponding to different dynamics of the field and the medium can occur. In the case where the velocities of longitudinal and transverse hypersonic waves differ only slightly, an effect similar to self-induced transparency is analyzed. For substantial velocity detuning, propagation in the form of rational solitons is possible. If the transverse component is dominant, these solitons can produce full population inversion of Zeeman sublevels. In the opposite limit, the populations remain practically unchanged.     

Effects of soliton dynamics of acoustic pulses in a paramagnetic crystal

Nonlinear dynamics of longitudinal-transverse acoustic pulses in the deformed cubic crystal containing a paramagnetic impurity with effective spin S = 1 is theoretically investigated. Soliton solutions of systems of equations describing the propagation of extremely short and ultrashort pulses at an arbitrary angle to the direction of external deformation parallel to the crystal symmetry axis are obtained. Classification of longitudinal-transverse soliton types and resonant acoustic transparency regimes is given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 31–36, August, 2007.     

On the soliton-like dynamics of ultrashort acoustic pulses in a paramagnetic crystal

A system of nonlinear equations describing the dynamics of the longitudinal and transverse components of an acoustic pulse in a cubic crystal containing paramagnetic impurities has been obtained. On the basis of this system, the dynamics of a two-component ultrashort acoustic pulse propagating under the Zakharov-Benney resonance conditions has been analytically investigated.     

The evolution of longitudinal and transverse acoustic waves in a medium with paramagnetic impurities

We study the bipartial interaction of longitudinal and transverse acoustic pulses with a system of paramagnetic impurities with an effective spin S=1/2 in a crystalline layer or on a surface in the presence of an arbitrarily directed external constant magnetic field. We derive a new system of evolution equations that describes this interaction and show that, in the absence of losses, for equal phase velocities of these acoustic components, and under the condition of their unidirectional propagation, the original system reduces to a new integrable system of equations. The derived integrable system describes the pulse dynamics outside the scope of the slow-envelope approximation. For one of the reductions of the general model that corresponds to the new integrable model, we give the corresponding equations of the inverse scattering transform method and find soliton solutions. We investigate the dynamics and formation conditions of the phonon avalanche that arises when the initial completely or incompletely inverted state of the spin system decays. We discuss the application of our results to describing the interaction dynamics of spins and acoustic pulses in various systems with an external magnetic field.     

Electrically driven spin dynamics of paramagnetic impurities

The spin dynamics of dilute paramagnetic impurities embedded in a semiconductor GaAs channel of a conventional lateral spin valve has been investigated. It is observed that the electron spin of paramagnetic Mn atoms can be polarized electrically when driven by a spin valve in the antiparallel configuration. The transient current through the MnAs/GaAs/MnAs spin valve bears the signature of the underlying spin dynamics driven by the exchange interaction between the conduction band electrons in GaAs and the localized Mn electron spins. The time constant for this interaction is observed to be dependent on temperature and is estimated to be 80 ns at 15 K.     

Nonlinear effects of resonance transparency for two-frequency acoustic pulses in a paramagnetic crystal

Two modes of nonlinear propagation of two-frequency acoustic pulses in a low-temperature crystal containing paramagnetic resonance impurities with an effective spin S = 1 in an external magnetic field and a field of the static strain are considered. It is shown that the spin-phonon transitions occurring within spin triplets according to the V scheme are responsible for two-frequency self-induced acoustic transparency. When the spin-phonon transitions follow the Λ scheme, there can arise an acoustic effect similar to electromagnetically induced transparency in a pulsed mode, which is accompanied by trapping of the population of the spin sublevels.     

Soliton-like propagation modes of picosecond acoustic pulses in a paramagnetic crystal

The nonlinear propagation of picosecond acoustic pulses at an arbitrary angle to an external magnetic field is studied in an elastically isotropic paramagnetic crystal at low temperatures. Various soliton-like propagation modes arising due to spin-phonon interaction and acoustic anharmonicity are revealed, and the stability of these modes with respect to transverse perturbations is analyzed. In the case of defocusing cubic nonlinearity, the crystal can support the propagation of compression pulses, which undergo defocusing, and rarefaction pulses can propagate in the self-channeling mode. In the case of focusing cubic nonlinearity, only compression pulses can propagate if the conditions of stability with respect to self-focusing are satisfied.     

Quasi-solitonic propagation modes of two-component acoustic video pulses in a paramagnetic crystal

Nonlinear propagation of longitudinal-transverse acoustic pulses down to a length of one cycle (video pulses) in a low-temperature paramagnetic crystal in the direction parallel to an external magnetic field is investigated theoretically. The case of a crystal with paramagnetic impurity ions with effective S=1/2 spin is considered. It is shown that, due to spin-phonon interaction, two-component acoustic pulses can propagate in the form of high-power quasi-solitons. Conditions are determined for the formation of exponentially localized subsonic rational solitons which propagate with a velocity higher than the velocity of transverse sound and which have a transverse component with a rotating plane of polarization.     

Amplification oand absorption of an electromagnetic wave in a moderating structure with a paramagnetic crystal

Conclusions An analysis of the paramagnetic amplification G_e and absorption L_e of an electromagnetic wave in a moderating structure shows that the effects of saturation in some cases are significantly different. In consequence of this, the saturation threshold in the crystal in the amplification mode is lower than the saturation threshold in the absorption mode approximately by a factor of G_eM/2L_att. This conclusion must be borne in mind when investigating paramagnetic crystals in distributed structures, in particular when investigating the invesion characteristics of potentially active substances for lasers.It follows from the analysis that the investigation of the invesion properties of the crystal must be conducted on small samples of the crystal, as the possible error in measuring the inversion coefficient will be less for lower values of the paramagnetic amplification factor (all conditions being equal).A moderating structure with a radiating paramagnetic crystal is an example of an active medium, in which the wave propagation process can be described and analyzed by means of Eq. (1). As E_p. (1) postulates the solution in analytic form, and all the parameters of the equation have a clear physical meaning and can be monitored easily during the experimental investigation, then the structure considered here obviously can be a suitable model for studying the propagation of waves in other active media (see, e. g., [9]).Institute of Radiophysics and Electronics, Academy of Sciences of the Ukrainian SSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 22, No. 7, pp. 819–825, July, 1979.     

The theory of nuclear spin diffusion due to paramagnetic impurities in a diamagnetic crystal

The diffusion of nuclear magnetization inside a diffusion barrier, due to modulation of the fluctuation spin operator of a magnetic ion by the interaction between nuclei, is treated to third order of perturbation theory. Cross-relaxation transitions of two types are being modulated. These are the transitions in which a pair of nuclei is mutually reoriented either due to a dipole-dipole interaction between them or by the coupling of each nucleus to the electron spin. The relative effectiveness of these processes depends on the experimental conditions.Translated from Izvestiya Vysskikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 76–80, November, 1975.The author is grateful to B. I. Kochelaev for discussing the results of this work.     

Statics and dynamics of “soft” impurities in a crystal

We investigate the effect of an impurity on the local static and dynamic behaviour of a crystal undergoing a displacive phase transition. It is shown that in mean-field approximation there may occur a freezing-out of local order driven by a soft local mode above the phase transition of the host. For a crystal containing a dilute impurity concentration, the impurity contribution to the static structure factor is calculated. The results are discussed in detail for the specific cases of a displacive and an Ising-type impurity.Work supported by the Swiss National Science FoundationThe results of this paper were presented at the Spring Meeting of the German Physical Society, Münster 1977 (Verhandlungen DPG (VI) 12, 1977)     

Dielectric response of a crystal with a damaged surface layer in the longitudinal-transverse splitting region

A model of the dielectric function of a surface layer formed under the mechanical treatment of the crystal surface is considered in the range of the lattice optical vibrations. An approach is proposed based on the continuous distribution of the dipole-active modes in order to take into account the dislocation effect. It is demonstrated that the model used allows one to describe satisfactorily the decrease in the reflectivity of polished SiC6H samples in the vicinity of the frequency of the transverse optical phonon.     

Translational-rotational interaction in dynamics and thermodynamics of a two-dimensional atomic crystal with molecular impurities

The interaction between the rotational degrees of freedom of a diatomic impurity molecule and phonon excitations of a two-dimensional atomic matrix commensurate to the substrate is investigated theoretically. It is shown that the translational-rotational interaction leads to renormalization of the crystal field constants and a change in the form of the operator for the rotational kinetic energy as compared to the corresponding expression for a free rotator. The contribution from the rotational degrees of freedom of impurities to the low-temperature heat capacity of a diluted solution of diatomic molecules in the two-dimensional atomic matrix is calculated. The possibility of experimentally observing the predicted effects is discussed.     

声表面波在压电晶体表面上的聚焦特性

研究了压电晶体表面上圆弧形叉指换能器产生的声表面波的聚焦现象。用作者提出的压电晶体表面激发的严格矢量场理论来计算会聚的表面波声场,取代了比较流行的源于光学的标量角谱理论。理论分析表明介质的各向异性对声束的会聚特性有很大的影响,如焦长和焦点附近声场的对称性。在实验中可以用光学暗场法来观察声表面波场的会聚。尽管各向异性介质或各向异性压电晶体上表面波声场的会聚都非常复杂,实验的结果和理论分析比较一致。     

Analysis of a monolithic crystal plate acoustic wave filter

We study thickness–shear and thickness–twist vibrations of a finite, monolithic, AT-cut quartz plate crystal filter with two pairs of electrodes. The equations of anisotropic elasticity are used with the omission of the small elastic constant c₅₆. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and the vibration confinement due to the electrode inertia are calculated and examined.     

Soliton generation via continuous stokes acoustic self-scattering of hypersonic waves in a paramagnetic crystal

A new mechanism is proposed for continuous frequency down-conversion of acoustic waves propagating in a paramagnetic crystal at a low temperature in an applied magnetic field. A transverse hypersonic pulse generating a carrier-free longitudinal strain pulse via nonlinear effects is scattered by the generated pulse. This leads to a Stokes shift in the transverse hypersonic wave proportional to its intensity, and both pulses continue to propagate in the form of a mode-locked soliton. As the transverse-pulse frequency is Stokes shifted, its spectrum becomes narrower. This process can be effectively implemented only if the linear group velocity of the transverse hypersonic pulse equals the phase velocity of the longitudinal strain wave. These velocities are renormalized by spin-phonon coupling and can be made equal by adjusting the magnitude of the applied magnetic field. The transverse structure of the soliton depends on the sign of the group velocity dispersion of the transverse component. When the dispersion is positive, planar solitons can develop whose transverse component has a topological defect of dark vortex type and longitudinal component has a hole. In the opposite case, the formation of two-component acoustic “bullets” or vortices localized in all directions is possible.     

The influence of transverse perturbations on the propagation of picosecond acoustic pulses in a paramagnetic crystal

The influence of transverse perturbations on the dynamics of a picosecond soliton-like acoustic pulse in a paramagnetic crystal in an external magnetic field is investigated. The nonlinear and dispersion effects are governed by the intrinsic properties of the crystal and the spin-phonon interaction. The effect of different nonlinear mechanisms and an external magnetic field on the stability against transverse perturbations is analyzed. It is shown that, in the absence of paramagnetic impurities, there can exist only a compression pulse that propagates in a defocusing regime. In the presence of paramagnetic ions in the crystal, there can arise rarefaction pulses that, under specific conditions, can propagate in self-focusing and self-channeling regimes.     

Time-dependent Ginzburg-Landau equations for rotating superconductors with paramagnetic impurities

The time-dependent Ginzburg-Landau equations for rotating superconducting alloys with paramagnetic impurities are derived. The simultaneous occurrence of a homogeneous magnetic field (London moment) and an inhomogeneous electric field, created by inertial forces, is taken into account. The equation describing constant electric field penetration into a rotating superconductor is derived. The dissipative function is obtained as well.