Exact Solution for a Stoner–Wohlfarth Particle in an Applied Field and a New Approximation for the Energy Barrier

This paper revisits the classical problem first laid out and analyzed by Stoner and Wohlfarth in their remarkable paper from 1948. While it is straightforward to solve the inverse problem and determine the field required to produce a given magnetization angle, the direct problem of finding the magnetization angle resulting from a given field is more difficult. This paper presents a reasonably compact analytic solution to the direct problem. Within a certain range of applied fields, there exist two stable solutions separated by an energy barrier. The height of the energy barrier can be computed exactly from the solutions for the magnetization. However, as an alternative, a simple approximation for the energy barrier is developed from the known boundary conditions. This approximation is slightly more accurate than the earlier Pfeiffer approximation.