斯通纳-沃尔法斯磁滞回线的近似显式公式
Approximate explicit formulas for Stoner-Wohlfarth hysteresis loops
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中文总结 AI 辅助
研究推导斯通纳-沃尔法斯模型磁滞回线的近似显式公式，考虑单粒子与粒子集合，基于物理假设，通过匹配不同磁场区间函数获一般公式，平均磁滞回线公式与数值计算最大偏差在\(h0 = 0.5\)，对应磁化强度斜率急剧变化。
中文摘要 AI 辅助
本文推导了斯通纳-沃尔法斯模型中磁滞回线的近似显式公式。考虑了易轴方向固定的单个粒子以及各向异性轴随机取向的粒子集合的磁滞回线。推导公式的物理假设是，在低场和高场时，粒子磁矩分别位于易轴或外场方向附近。令人惊讶的是，即使在约化磁场\(h0\)不是很小的斯通纳-沃尔法斯星状线附近，低场公式也近似有效。通过适当匹配在磁场不同区间定义的函数得到一般分段公式，以最大化公式精度。对于平均磁滞回线，公式与数值计算磁化强度的最大偏差（合理小）出现在\(h0 = 0.5\)处，对应于磁化强度斜率的急剧变化。
英文摘要
Approximate explicit formulas for the hysteresis loops in the Stoner-Wohlfarth model are derived. We consider the hysteresis loops both for a single particle with a fixed easy-axis direction and for an ensemble of particles with randomly oriented anisotropy axes. The physical assumption used to derive the formulas is that the particle magnetic moment lies in the vicinity of the easy axis or the external field direction, at low and high fields, respectively. Surprisingly, the low-field formula is approximately valid even near the Stoner-Wohlfarth astroid, where the reduced magnetic field h0 is not very small. The general piecewise formula is obtained by an appropriate matching of the functions defined on different intervals of the magnetic field, which are chosen to maximize the formula accuracy. For the averaged hysteresis loop, the maximal, but reasonably small, deviation of our formula from numerically calculated magnetization occurs at h0 = 0.5, which corresponds to the sharp change in magnetization slope.
