Hysteresis loops in a mixed-spin (3/2, 3) nanotube with core-shell structure

This work investigates a ferrimagnetic Ising nanotube with a spin-3/2 core and a spin-3 shell. The Blume-Capel model and the mean-field approach based on the Gibbs-Bogoliubov inequality are used to examine numerically the hysteresis behavior of this system as a function of various parameters, namely exchange interactions, crystal fields, and temperature. Although the mean-field method, derived from statistical mechanics, neglects fluctuations, it has been successfully applied to describe various phase transition phenomena, particularly hysteresis. This nanotube exhibits first-order phase transitions for low values of magnetic field h, which disappear for higher values. The absolute increase in the crystal field \(D_C\) in the core causes deformation of the hysteresis loops (splitting and lateral broadening) and a significant decrease in remanent magnetization and coercive field, accompanied by the appearance of stability levels. Moreover, increasing the absolute value of \(D_S\) in the shell transforms the tri-loops into a single loop, and for \(D_S \le -3\), the loop becomes rectangular, displaying a well-defined and stable coercive field. Increasing the exchange interaction \(J_S\) in the shell leads to more complex loops, evolving from a single loop to multiple loops up to nine. Beyond \(J_S = 0.4\), the system stabilizes with clear tri-loops. Concerning the increase in the absolute value of the interfacial exchange interaction \(J_{int}\), a single hysteresis loop with weak fluctuations is observed at low \(|J_{int}|\), which transforms into multi-loops (three then five), then these loops merge into a broadened loop, with an area that continues to grow by increasing \(|J_{int}|\). In addition, the remanent magnetization and coercive field increase with \(|J_{int}|\). Finally, at low temperatures T, the system exhibits tri-loops, however, hysteresis decreases with rising temperature and vanishes beyond the critical temperature. Both remanent magnetization and coercive field gradually decrease with increasing T.