The coercive force and rotational hysteresis of elongated ferromagnetic particles

2014 The coercive force of an infinite ferromagnetic cylinder is calculated as a function of the radius and of the inclination of the axis to the applied field. For this calculation it is assumed that only curling and rotation in unison take place ; and that whenever the curling is associated with a discontinuous jump, the magnetization is brought to the lower energy state given by Stoner and Wohlfarth. Using the same assumptions, the rotational hysteresis loss and integral are calculated both for an aligned and for a random assembly of cylinders. The results are found to be in fair agreement with the measurements of Jacobs and Luborsky on elongated ferromagnetic particles. LE JOURNAL DE PHYSIQUE ET LE RADIUM TOME 20, FÉVRIER-MARS 1959, Recently, a new theory of magnetization changes in ferromagnetic particles was developed [11, [2], [3] and was used to calculate the hystérésis curve of an infinite ferromagnetic cylinder whose axis is parallel to the applied field [4], [5]. In the following the former calculations are extended to the case in which the cylinder is not parallel to the field. The dependence of the coercive force on the angle between the cylinder and the applied field and the rotational hysteresis loss are evaluated and found to be in rough agreement with results of experiments made by Jacobs and Luborsky [6] on elongated ferromagnetic fine particles. The nucleation field. Consider the descending hysteresis loop of an infinite cylinder inclined at an angle il to the applied field. Up to a certain negative field the nucleation field the magnetization changes reversibly by rotation in unison in accordance with the calculations of Stoner and Wohlfarth [7]. Following Brown [2] it can be shown that, neglecting the magnetocrystalline anisotropy, this nucleation field, Htn, is the least eigenvalue Ht of the set of equations