On the temperature dependence of the sound attenuation maximum as a function of frequency and magnetic field in a spin-1 Ising model near the critical region

The crystal field effects on sound attenuation for a spin-1 Ising model on the Bethe lattice

“…wτ 1 1 and wτ 2 1. Such a frequency dependence for the attenuation coefficient has been observed in ultrasonic experimental studies of some magnetic systems [1,8] and theoretical studies [17]- [19], [26]. In the high frequency range (wτ 1 1 and wτ 2 1), the attenuation is independent of the sound wave frequency w and crystal field D/J.…”

“…The critical properties of the sound attenuation in a spin-1 Ising system with bilinear and biquadratic interactions have been investigated within the framework of the cluster variation method (CVM) and the Onsager theory of irreversible thermodynamics and it was found that the maxima of the attenuation was shifted to lower temperatures with increasing frequency and Onsager coefficients [18]. Similarly, the calculation of sound attenuation near critical points in a spin-1 Ising model has been performed by using the lowest approximation of the CVM and Onsager theory simultaneously at different frequencies and magnetic fields and a shift in temperature of the attenuation maximum was detected [19]. The effect of an external magnetic field on the sound attenuation coefficient in a spin-1 Ising system containing biquadratic interaction has been investigated and a quadratic field dependence of the attenuation coefficient on the external magnetic field was found in low field [20].…”

Magnetic relaxation in a spin-1 Ising model near the second-order phase transition point

“…For the dynamical aspects of phase transitions we have used the linear kinetic equations for the long-range order parameters to derive relaxation times on the basis of Onsager theory of irreversible thermodynamics [30][31][32][33]. We have also derived the sound attenuation coefficient and velocity dispersion relation to investigate the properties of ultrasound propagation near the phase transition temperatures [34][35][36][37]. Recently, Keskin and co-workers [38][39][40][41][42] have studied the stationary states of the kinetic spin-1 Ising systems in the presence of a time-dependent oscillating external magnetic field within mean-field approach and used the Glaubertype stochastic dynamics to describe the time evolution of the system.…”

Magnetic Field Influence on Critical Sound Attenuation and Velocity Variation in Ferromagnets

“…The scaling functions need to be determined theoretically as well as experimentally. So far only some mean-field results have been obtained [1,[14][15][16] and the measurements far from critical temperature were carried out in MnP [2]. However, some results can be immediately guessed from the formulae (2) and (3).…”