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.     

Dynamics of vector acoustic solitons under nonlinear interaction between long and short waves

Propagation of a longitudinal-transverse pulse through a statically strained crystal containing paramagnetic impurities and placed in an external magnetic field is investigated. It is shown that the nonequilibrium distribution of the populations of impurity spin sublevels allow us to create the conditions for effective interaction between the longitudinal (longwave) and transverse (shortwave) components of the pulse.     

On the propagation of hypersonic solitons in a strained paramagnetic crystal

Nonlinear dynamics of a subnanosecond transverse elastic pulse in a low-temperature paramagnetic crystal placed into a magnetic field and statically strained in the same direction is investigated. Paramagnetic impurities implanted into the crystal have an effective spin of 3/2, and the pulse propagates at right angles to the magnetic field. In the general case, the structure of the pulse is such that the approximation of slowly varying envelopes, which is standard for quasi-monochromatic signals, is inapplicable. Under certain conditions, the pulse propagation in the 1D case is described by the Konno-Kameyama-Sanuki integrable wave equation for strain, which is transformed into the Hirota equation for the envelope of the given strain in the quasi-monochromatic limit. The effect of transverse perturbations on extremely short and quasi-monochromatic solitons is studied in detail. The conditions and features of self-focusing and defocusing of acoustic solitons in the form of extremely short pulses and envelope solitons are revealed. The propagation of an extremely short “half-wave” hypersonic pulse in the “acoustic bullet” regime in the medium with a quasiequilibrium population of quantum sublevels of effective spins is predicted.     

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.     

Self-induced acoustic transparency in the long-short-wave resonance mode

The effect of self-induced acoustic transparency for transverse-longitudinal pulses propagating along an external magnetic field in a system of resonance paramagnetic impurities with the effective spin S=1/2 is theoretically investigated. In this case, the short-wave transverse component of the pulse causes quantum transitions, and the longitudinal long-wave component dynamically shifts the frequency of those transitions. When the speeds of the longitudinal and transverse acoustic waves in the crystal matrix are close to each other, both components interact in the mode of the long-short-wave resonance, which is described by a system of nonlinear integro-differential equations. It is shown that this interaction results, in particular, in the modulation of the carrier frequency of the circular-polarized component of the pulse. More precisely, the frequency in the neighborhood of the signal’s maximum is less than in the vicinity of its edges. Solutions in the form of traveling 2π-pulses are analyzed analytically and numerically. It is shown that there exist solutions that include a longitudinal component and cannot be reduced to well-known transverse solitons of the sinus-Gordon equation.     

Acoustic activity effect for picosecond soliton-like pulses

A theoretical analysis is made of the acoustic activity for interfering picosecond acoustic soliton-like pulses of down to a single oscillation period. An analysis is made of the case where these pulses propagate parallel to an external magnetic field and one of the acoustic axes in a cubic crystal containing paramagnetic impurities having effective spin S = 1. Allowance is made for natural, magnetic (Faraday), and cross acoustic activity. This cross activity is caused by the significant spatial nonlocality of the spin-phonon interaction for such short pulses in crystals having no center of inversion in the presence of paramagnetic impurities. A system of nonlinear equations is obtained for the transverse and longitudinal components of the strain in the form of a coupling between the “differentiated” nonlinear Schrödinger equation (with nonlinearity after the derivative sign) and the Korteweg-de Vries equation which generalizes the known systems of long-short-wavelength resonance to the case where the slowly varying envelope approximation is not valid. An approximate solution of this system is used to study the structure of an elastic soliton-like pulse whose transverse component has a rotating plane of polarization, which propagates under conditions of nonlinear coupling with the longitudinal strain.     

Soliton mechanism of acoustic pulse frequency conversion to the red region

Self-scattering of a transverse acoustic pulse from a longitudinal strain video pulse (induced by an acoustic pulse) in a paramagnetic crystal in a magnetic field is predicted. This effect is accompanied by a continuous frequency shift of the hypersonic pulse to the red region; this shift is proportional to the pulse intensity.     

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.     

Acoustic self-induced transparency for transverse waves in a system with resonant and quasi-resonant transitions

A theoretical analysis of acoustic self-induced transparency is presented for transverse elastic waves propagating perpendicular to an applied magnetic field through a crystal with spin-3/2 paramagnetic impurities. The interaction between an acoustic pulse and magnetic field is described by Maxwell-Bloch-type equations for a system with transitions inhomogeneously broadened because of a quadrupole Stark shift. If the pulse carrier frequency is resonant with one transition and quasi-resonant with another transition, then the evolution of a one-dimensional pulse is described by an integrable Konno-Kameyama-Sanuki (KKS) equation. The underlying physics of its soliton solution and the corresponding behavior of the medium are analyzed. Self-focusing and self-trapping conditions are found for a pulse of finite transverse size. In the latter regime, the pulse stretches along the propagation direction, transforming into a “hollow bullet,” while its transverse size remains constant.     

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.     

Quantum spin glass and the dipolar interaction

Anisotropic dipolar systems are considered. Such systems in an external magnetic field are expected to be a good experimental realization of the transverse field Ising model. With random interactions, this model yields a spin glass to paramagnet phase transition as a function of the transverse field. We show that the off-diagonal dipolar interaction, although effectively reduced, induces a finite correlation length and thus destroys the spin-glass order at any finite transverse field. We thus explain the behavior of the nonlinear susceptibility in the experiments on LiHo(x)Y(1-x)F(4), and argue that a crossover to the paramagnetic phase, and not quantum criticality, is observed.     

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.     

Electromagnetic activity of a pulsating paramagnetic neutron star

The fact that neutron star matter possesses the capability of maintaining a highly intense magnetic field has been and still is among the most debatable issues in pulsar astrophysics. Over the years, there were several independent suggestions that the dominant source of pulsar magnetism is either the field-induced or the spontaneous magnetic polarization of the baryon material. The Pauli paramagnetism of degenerate neutron matter is one of the plausible and comprehensive mechanisms of the magnetic ordering of neutron magnetic moments, promoted by a seed magnetic field inherited by the neutron star from a massive progenitor and amplified by its implosive contraction due to the magnetic flux conservation. Adhering to this attitude and based on the equations of magnetoelastic dynamics underlying continuum mechanics of single-axis magnetic insulators, we investigate electrodynamics of a paramagnetic neutron star undergoing nonradial pulsations. We show that the suggested approach regains a recent finding of Akhiezer et al. [1] that the spin-polarized neutron matter can transmit perturbations by low-frequency transverse magnetoelastic waves. We found that nonradial torsional magnetoelastic pulsations of a paramagnetic neutron star can serve as a powerful generator of a highly intense electric field producing the magnetospheric polarization charge whose acceleration along the open magnetic field lines leads to the synchrotron and curvature radiation. Analytic and numerical estimates for periods of non-radial torsional magnetoelastic modes are presented and are followed by a discussion of their possible manifestation in currently monitored activity of pulsars and magnetars.     

Picosecond acoustic solitons anisotropically coupled to a spin system

An integrable model developed by the author is used to analyze the evolution of longitudinal-transverse acoustic pulses propagating parallel to an external magnetic field in a paramagnetic crystal with spin-1/2 impurities. Acoustic pulse propagation in a medium with orthorhombic spin-phonon coupling symmetry is described without invoking the slowly varying envelope approximation. A solution to the model is found by a modified inverse scattering method based on an analysis of the Riemann-Hilbert problem taking into account the problem symmetry.     

Rayleigh-Taylor instability experiments with precise and arbitrary control of the initial interface shape

In a Rayleigh-Taylor instability a dense fluid sits metastably atop a less dense fluid, a configuration that can be stabilized using a magnetic field gradient when one fluid is highly paramagnetic. On switching off the magnetic field, the instability occurs as the dense fluid falls under gravity. By affixing appropriately shaped magnetically permeable wires to the outside of the cell, one may impose arbitrarily chosen and well-controlled initial perturbations on the interface. This technique is used to examine both the linear and nonlinear growth regimes for which the perturbation amplitudes, growth rates, and nonlinear growth coefficients are obtained.     

Numerical simulation of optical bi-stability in antiferromagnetic sandwich structure

The magnetically optical bi-stability, a third-order nonlinear response, is investigated on an antiferromagnetic (AF) sandwich structure, where an AF film is sandwiched between two dielectric films. The configuration with the AF anisotropy axis and external static magnetic field both in the interfaces and normal to the incident plane is used. The incident wave is taken as a TE wave with its electric component transverse to the incident plane. We find that bistable switches can appear only in a finite frequency range and an incident angle range for a given regime of incident power, which means that there are the critical incident angle and frequency. The power threshold value for the bi-stability increases with the incident angle. In addition, the bi-stability also easily is modulated by the external magnetic field.     

Magnetic and Magneto-Optical Properties in Paramagnetic NdF3 Under High Magnetic Field

In this paper, we first theoretically report the magnetic and magneto-optical properties in paramagnetic media under high external magnetic field. Considering the action of the external magnetic field H_e and indirect exchange interaction H_v, the characteristic of the magnetic saturation and the property of the Faraday rotation to be nonlinear with external magnetic field are presented in paramagnetic NdF₃. In terms of our theory, the indirect exchange interaction plays an important role in the magnetization M and the Faraday rotation θ in NdF₃ under high external magnetic field. The theory is in good agreement with experimental results. On the other hand, a reasonable explanation for the temperature dependence of the ratio of the Verdet constant to the magnetic susceptibility V/χ is obtained.     

Primary acoustic echo during excitation of a paramagnetic crystal by picosecond elastic video pulses

The primary acoustic echo formed during excitation of a paramagnetic crystal with effective spin S=1 by two transverse picosecond elastic video pulses is investigated theoretically. Both exciting video pulses are applied perpendicular to the external magnetic field. It is shown that the primary acoustic echo in the general case consists of six longitudinal and transverse signals at the frequencies of the transitions within a Zeeman triplet. The optimal parameters of the exciting video pulses for the appearance of different echo signals are determined. Fiz. Tverd. Tela (St. Petersburg) 41, 623–628 (April 1999)     

Dissipative Solitonic Objects of Transverse Ultrasound in a Deformed Paramagnetic Crystal

JETP Letters - It has been demonstrated that a deformed nonequilibrium paramagnetic crystal in an external magnetic field allows the existence of microsecond dissipative solitonic pulses of...     

Stability of the collisional plasma flow in a magnetic field

A collisional plasma flow moving along a magnetic field at a velocity lower than the speed of sound is considered. It has been found that stationary small perturbations increase downstream in the flow. The mechanism of the increase is related to the fact that subsonic ideal-plasma flows respond to external perturbations primarily by a change in the pressure of the plasma. As a result, the pressure under perturbation of the velocity changes so that the stationary flow is decelerated and accelerated if the force is directed along and against the velocity, respectively. This phenomenon can be explained under the assumption that the effective mass of the plasma is negative. If the velocity of the flow is inhomogeneous in the transverse direction, the viscosity force plays a role of the external perturbing force. In this case, the effective transverse viscosity coefficient, which should be treated as negative, can be renormalized instead of the effective mass. The sign of the effective specific heat or the effective transverse thermal conductivity coefficient changes similarly if the velocity of the flow is lower than the speed of sound but is higher than the thermal velocity of ions calculated from the sum of the ion and electron temperatures. A downstream increase in the stationary perturbations is called in this work spatial instability. The downstream growth rate has been determined. The numerical analysis of the evolution of perturbations illustrates the development of the spatial instability of subsonic collisional plasma flows moving along the magnetic field.