Adiabatic sound velocity in the vicinity of phase transition in magnets

Abstract

PACS 05.70.Jk, 62.65.+kThe Ginzburg-Landau Hamiltonian of a magnetic system, containing magneto-elastic as well as entropoelastic interactions in addition to usual magnetic ones, is considered in detail. Adiabatic longitudinal sound velocity is defined by the pressure correlation function and is found to be finite at the phase transition temperature in contrast to the behaviour of the isothermal sound velocity which goes asymptotically to zero. A weakly-singular contribution to adiabatic sound velocity is also found. We show that it can be expressed entirely in terms of the static spin-energy vertex function evaluated with an effective spin Hamiltonian. For the Ising-type magnets the vertex function is found to exhibit a ðT À T C Þ a singularity.Introduction It is well known that the static isothermal and adiabatic elastic moduli are related to the corresponding sound velocities in the zero frequency limit [1]. Experiments on the sound velocity in the magnetic substances show that the low-frequency velocity change shows a weak singularity near the critical temperature. The asymptotic behaviour of the sound velocity is still unclear, however.Is it finite at T C like in a binary mixture [2] or equal zero like at the liquid-gas critical point [3,4]? This controversy is difficult to be resolved by experiment mainly because of very small magnetoelastic coupling constant and small the critical exponent characterising the critical anomaly. In this paper we show that the adiabatic sound velocity is finite at the critical point of a magnet. Our analysis is addressed to both the magnetic insulators like RbMnF 3 ; MnF 2 ; FeF 2 ; Y 3 Fe 5 O 12 and to metallic substances like Ni, Gd, Dy, Tb and so on [5]. Below we establish a connection between the static longitudinal sound velocities and the corresponding correlation functions of our model. The thermodynamic potential GðT; P; BÞ, in the theory of phase transitions, is given by

Critical thermal diffusivity in anisotropic magnets

“…The expressions ͑18͒ and ͑29͒ for the sound velocities are found from analogous considerations of the acoustic mode. 8,17,18 The relation ͑28͒ is a finite-frequency generalization of the known thermodynamic formula 19 ‫)ץ/‪p‬ץ(‬ C v ϭ(‫ץ‬p/‫)ץ‬ T C p .…”

“…8,17 For ͑strongly dumped͒ thermal waves 19,20 with real frequency and complex wave vector k ϭk th wav ()ϩi Ϫ1 (), where k th wav ()ϭ Ϫ1 ()ϭ2D T /, the parameter () has a simple interpretation: neglecting the correction from the bare sound dumping coefficient ⌰, it can be rewritten as…”

Magnetic Field Effect on Sound Propagation in Antiferromagnets

“…T N (H) is the reduced temperature measuring the distance to the critical point, ρ s is the sound attenuation critical exponent and f, g are scaling functions [7][8][9] (which can be different above and below the Néel temperature); c 0± are background sound velocities. Generally, the sound attenuation exponent takes different values for two classes of magnetic materials.…”