Metastability of Magnetic Nanoparticles in Magnetization Relaxation with Different Dynamics and Distributions of Magnetic Anisotropy

We study the metastability of magnetic nanoparticles with size distributions. We simulate an array of magnetic nanoparticles with a spin S = 1 ferromagnetic Blume-Capel model on a square lattice. Studying decays of the metastable state in the Blume-Capel model at low temperatures requires an extremely long computational time in kinetic Monte Carlo simulations. Therefore, we use an advanced algorithm adapted from the Monte Carlo with absorbing Markov chain algorithm for the Ising model in order to study the Blume-Capel model with size distributions. We modeled the particle size distributions as distributions of magnetic anisotropy. We compute the low-temperature average lifetime of the magnetization relaxation using kinetic Monte Carlo simulations with the advanced algorithms. We also calculate the lifetime using the absorbing Markov chains method for analytical results. Our results show that the lifetime of the metastable state follows a modified-Arrhenius law where the energy barrier has a dependency on temperature and standard deviation of the distributions in addition to magnetic field and magnetic anisotropy. The magnetic anisotropy barrier is determined by the smallest particle within a given distribution. We also study magnetization relaxation in different single critical droplet regions using different dynamics: Glauber and phonon-assisted dynamics. We find that the lifetime follows the modified-Arrhenius law for both dynamics, and an explicit form of the lifetime differs in different regions for different dynamics. For the Glauber dynamics, the Arrhenius prefactor does not depend on the standard deviation of the distribution of the magnetic anisotropy. For the phonon-assisted dynamics, however, even the prefactor of the lifetime depends on the standard deviation and is significantly reduced for a wide distribution of magnetic anisotropy. Furthermore, the phonon-assisted dynamics forbids transitions between degenerate energy states and results in an increase of the energy barrier at the single critical droplet region boundary compared to that for the Glauber dynamics. We find that the spin system with a distribution of magnetic anisotropy finds lower-energy relaxation pathways to avoid degenerate state, and the energy barrier becomes the same for both dynamics.