Theory of Critical Sound Attenuation in Ising-Type Magnets

Abstract

The critical behaviour of sound attenuation has been studied in an elastically isotropic Ising system above the critical point on the basis of a complete stochastic model including both spin-energy and lattice-energy modes linearly coupled to the longitudinal sound mode. The effect of spin-lattice relaxation on the ultrasonic attenuation is investigated. The crossover between Kawasaki behaviour and Murata-Iro-Schwabl behaviour is studied as dependent on the values of ultrasonic frequency, reduced temperature, relaxation times, etc. A new high-frequency regime is discussed in the magnetic systems. This new regime corresponds to an adiabatic sound propagation and is very similar to the ones in binary mixture and liquid helium. A new frequency-dependent specific heat being the harmonic average of the bare lattice and critical spin specific heats is introduced. It was shown that such specific heat describes the process of equilibration between spin and lattice subsystems and includes the most important features of critical sound attenuation.

Critical sound propagation in MnF2

“…Many experimental works have been devoted to the critical sound propagation in the manganese fluoride [3][4][5][6][7][8][9][10] and perhaps it the best known magnet from the experimental point of view but the nature of the critical singularities in the sound attenuation coefficient in MnF 2 is still far from being understood. Recently a general theory of sound propagation near the critical temperature in magnets has been proposed [11,12]. The theory introduces the coupling of the longitudinal sound mode both to bilinear function of spin operators as well as a linear coupling of the sound to the spin-energy density.…”

Acoustic Signatures of the Phases and Phase Transitions in the Blume Capel Model with Random Crystal Field

“…Further, the temperature at which attenuation maxima take place moves to lower temperatures with rising frequency. The frequency shift of the attenuation maxima is also observed in the experimental and theoretical studies of the ultrasonic investigation of liquid helium [56,57] and Rb 2 ZnCl 4 and K 2 SeO 4 [58] as well as other Ising models [37][38][39][40] and elastically isotropic Ising system above the critical point on the basis of a complete stochastic model [59].…”

Critical Sound Propagation in Magnetic Metals and Bottleneck Phenomena

“…As the sound wave strongly couples with the order parameter fluctuations the critical dynamics of sound is a research field where we can test modern concepts of the phase transition theory such as the universality of critical exponents, scaling or the crossover to another universality class etc. Sound attenuation and velocity in magnetic systems have been extensively studied both experimentally and theoretically [1]- [10] . Whereas, the temperature behavior of these quantities has been relatively well recognized during last decades [2,7,8,[11][12][13] using mean-field theories, scaling theory and renormalization group framework a relatively little attention has been paid so far to the problem of critical attenuation in the presence of the ordering magnetic field [14,[16][17][18][19][20].…”

“…Sound attenuation and velocity in magnetic systems have been extensively studied both experimentally and theoretically [1]- [10] . Whereas, the temperature behavior of these quantities has been relatively well recognized during last decades [2,7,8,[11][12][13] using mean-field theories, scaling theory and renormalization group framework a relatively little attention has been paid so far to the problem of critical attenuation in the presence of the ordering magnetic field [14,[16][17][18][19][20].…”

“…It is a crucial parameter determining whether the sound attenuation coefficient reveals a strong or a weak singularity in a given material. In this paper we will focus on the class of metallic ferromagnets which are characterized by strong anomaly of the sound attenuation coefficient (sometimes called Murata-Iro-Schwabl singularity [6,21]) connected with short spinlattice relaxation times [8,10]. In these magnetic materials the maximum in the sound attenuation coefficient occurs in the ordered phase for vanishing magnetic field due to the domination of the magnetic analogue of the Landau-Khalatnikov sound damping near the superfluid transition of liquid 4 He [22].…”