Mean Field Study of a Cylindrical Ferrimagnetic Nanotube with Different Anisotropies

Abstract

In this paper, the ferrimagnetic mixed spins (1, 5/2) Blume-Capel model is proposed to investigate the phase diagrams and hysteresis behaviors of a magnetic cylindrical nanotube with a core-shell structure using the mean-field approximation based on the Bogoliubov inequality for the Gibbs free energy. The core sites are occupied by σ= ±1, 0 spins, whereas the shell sites are filled by S= ±5/2, ±3/2, ±1/2 spins. The effects of exchange couplings (Jin, JS) and single-ion anisotropies (DC, DS) on core, shell, and total magnetizations are investigated, as well as hysteresis behaviors. The entropy, free energy, and specific heat are analyzed to establish the stability of the solutions. The presentation and discussion of phase diagrams is detailed. The system shows a first-order and second-order phase transitions, as well as tricritical and critical end- points. In addition, the system shows compensation and reentrant behaviors. Various multiple hysteresis loop behaviors are seen according on the Hamiltonian parameters, such as the presence of triple, quintuple, and septuple hysteresis loops.