Exact formulation for hysteresis loops and energy loss in Stoner–Wohlfarth systems

We propose an exact expression to describe the hysteresis loops of an ensemble of Stoner–Wohlfarth particles undergoing an alternating quasi-static magnetic field. A statistical approach, which treats the quantities characterizing each particle as random variables, is adopted to get the orientation distribution of the local polarizations with respect to the applied field direction and the constitutive equation of the whole particle assembly. The hysteresis loop area gives the energy loss figure, but we have also obtained a straightforward integral expression for this quantity. The analytical relationships for the symmetric loops and the losses are successfully tested against numerical results, and the mathematical method adopted also displayed the ability to reproduce the “elemental loop” associated with any given particle of the system. While having a fundamental character, the proposed approach bears applicative interest, representing a versatile tool as the core of codes that simulate the behavior of devices employing magnetic components.