Multiple crossover in the decay of metastable volume fraction of a Blume-Capel ferromagnetic needle

TL;DR

This study uses Metropolis Monte Carlo simulations of a spin-1 Blume-Capel model on a quasi-one-dimensional needle to explore metastability and relaxation. It reveals that the decay of the metastable volume fraction deviates from the classic Avrami law by exhibiting multiple crossovers, with cross-section and anisotropy affecting the effective exponents and crossover times. The reversal time is shown to decrease exponentially with positive anisotropy and remain nearly unchanged for negative anisotropy, while the paramagnetic relaxation remains exponential but shows no clear D-dependence. Overall, the work highlights rich, geometry-driven metastable dynamics in a low-dimensional magnetic system with single-site anisotropy, offering insights for nucleation and relaxation in quasi-1D materials.

Abstract

The transient behaviours of a Blume-Capel ferromagnetic needle have been studied extensively by Monte-Carlo simulation. The needle has an elongated length in one direction compared to its cross-section. In the context of transient behaviour, we have captured the decay of the metastable state and the magnetic relaxation behaviours in our study. The dependence of metastable behaviour with anisotropy (single site) has been studied. \emph{Interestingly, we have observed multiple (different values of $n$ in different time domains) crossover in the decay of metastable volume fraction (obeying Avrami's law $β\sim {\rm exp}(-Kt^n)$). We have identified the crossover time, and the values of $n$ are estimated precisely.} The mean (magnetic) reversal time has been studied as a function of anisotropy. It is observed to be almost independent of anisotropy for its negative value; however, it is found to decrease exponentially with positive anisotropy. The exponential relaxation behaviour (in the corresponding paramagnetic phase) is observed. The relaxation time was found to depend on the strength of anisotropy.

Figures (15)

• Figure 1: Temperature dependences of thermodynamic quantities; (a) Magnetisation, (b) Susceptibility, (c) averaged energy density, and (d) Specific heat in a Blume-Capel ferromagnetic needle of size $L_x = 4, ~ L_y=4,$ and $L_z=200$. Represented for different values of magnetic anisotropy $D =$-2.0, -1.0, 0.0, +1.0 and +2.0. Here, $h_{ext}=0$.
• Figure 2: Phase diagram of a Blume-Capel ferromagnetic needle of size $L_x = 4, ~ L_y=4,$ and $L_z=200$, on the $D-T_c^p$ plane. Here, $h_{ext}=0$.
• Figure 3: Temperature dependences of the (a) magnetisation and (b) susceptibility for different values of $L_x=L_y$ with fixed $L_z=200$, $D=+1$ and $h_{ext}=0$.
• Figure 4: Variation of pseudo-critical temperature $T_c^p$ with cross-sectional dimensions $L_x$ and $L_y$ (where $L_x = L_y$), for fixed values of $L_z=200$, $D=+1$ and $h_{ext}=0$. The pseudocritical temperature increases as the cross -sectional area ($L_x \times L_y$) of the BC needle increases. The red arrow in right-top corner indicates the numerical estimates of pseudocritical temperature for Blume-Capel cubeozkankutlu.
• Figure 5: Top: Variation of magnetisation with time (in unit of MCSS) for two different values of positive anisotropy $D=$+1.50 and +2.50. The BC ferromagnetic needle kept at a fixed temperature $T=0.8T_c^p$ in the presence of an external magnetic field $h_{ext}=-0.25$. Bottom: Densities of spin $S_i^z =$+1, 0 and -1 ($\rho_{1}$, $\rho_{0}$ and $\rho_{-1}$) evolve with time. The vertical line in each figure indicates the reversal time for a single sample only.