Dynamic Hysteresis in Molecular-Based Magnetic Systems (I): Application of the Path Probability Method to the Mixed-Spin (1,7/2) Blume-Capel Ising Model

This study systematically investigates the non-equilibrium magnetic loop responses (DMHBs) of a mixed-spin (1, 7/2) Blume-Capel Ising system (BCIS) on a hexagonal lattice under an sinusoidal magnetic stimuli using the PPM framework (PPM). We explore the effects of the system parameters: exchange interaction parameters (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${J}_{\sigma S}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${J}_{SS}$$\end{document}), temperature (T), oscillating magnetic field frequency (omega), crystal field parameter (d), and kinetic rate constants (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{2}$$\end{document}). Our findings reveal complex and varied hysteresis loop morphologies, including triple, double, and elliptical loops, for both individual sublattices (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${m}<^>{A}$$\end{document} ,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${m}<^>{B}$$\end{document}) and total magnetization (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${m}<^>{T}$$\end{document}). We analyzed the corresponding coercive fields (CFs) and remanent magnetizations (RMs). The results demonstrate how changes in these parameters significantly influence the DMHBs, leading to characteristics indicative of both hard and soft magnetic materials. Notably, the kinetic rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{2}$$\end{document} is found to play a crucial role, analogous to wheel speed in rapid solidification processes, affecting the loop area and thus the "hardness" of the simulated magnet. While our theoretical predictions generally align with existing theoretical literature, some interesting discrepancies with experimental observations are noted. These differences may arise from practical limitations in experimental setups, such as the achievable wheel speed in melt spinning, or variations in the compositional concentrations of magnetic alloys. This research provides valuable insights into the non-equilibrium dynamics of molecular-based spin-configured molecular systems and extends the application of the PPM to complex mixed-spin systems.

Journal

JOURNAL OF SUPERCONDUCTIVITY AND NOVEL MAGNETISM

Year

2025

Volume

38

Issue

6

ISSN

1557-1939

eISSN

1557-1947

DOI

10.1007/s10948-025-07080-w

WoS UID

WOS:001629048100001