High-frequency magnetic field on crystal field diluted S = 1 Ising system: magnetic relaxation near continuous phase transition points

Abstract

Magnetization relaxation and the steady state response of the S = 1 Ising model with random crystal field to a time varying magnetic field with a frequency ω is modelled and studied here by a method that combines the statistical equilibrium theory with the theory of irreversible thermodynamics. The method offers information on the relaxation time (τ) of the system as well as the temperature (θ) and ω dependencies of the complex (AC or dynamical) susceptibility (i.e., χ(ω) = χ′(ω) − iχ″(ω)). The so-called low- and high-frequency regions are separated by τ because τ−1 → 0 as θ approaches the critical temperatures (θc). One can choose to keep the frequency ω fixed and observe the low-frequency behaviors followed by the high-frequency behaviors when θ → θc. It is shown that χ(ω) exhibits different behaviors in low- and high-frequency regimes that are separated by the quantity ωτ: χ′(ω) converges to static susceptibility and χ″(ω) → 0 for ωτ ≪ 1. However, in the high-frequency region where ωτ ≫ 1, χ′(ω) vanishes and χ″(ω) displays a peak at the critical temperature (θc). Besides the above, the logarithm of the susceptibility components versus log(ω) is also plotted. From these plots, one plateau (a step-like) region and a shifted peak with rising temperature is observed for the real and imaginary parts, respectively.