Cylindrical Blume-Capel Nanotube with core/shell structure: compensation temperature and hysteresis loops

Abstract

Abstract The critical, compensation and hysteresis behaviors of the Blume-Capel model with mixed spins <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mo>±</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>0</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mo>±</mml:mo> <mml:mn>3</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:math> , on a cylindrical nanotube with core–shell structure were studied using the mean-field approximation based on the Gibbs-Bogoliubov inequality. The effects of the single-ion anisotropies and the exchange coupling on phase diagrams, magnetizations and hysteresis loops were investigated. The first-order and second-order phase transitions and critical end-point were found, therefore, the system does not give any tricritical point. Furthermore, the model’s results anticipate the presence of the compensation phenomena and multi-cycle hysteresis behaviors.