Expanding the Lorentz concept in magnetism

Abstract

In 1878, the Dutch physicist Hendrik Antoon Lorentz first addressed the calculation of the local electric field at an atomic site in a ferroelectric material, generated by all the other electric dipoles within the sample. This calculation, which applies equally well to ferromagnets, is taught in Universities around the World. Here we demonstrate that the Lorentz concept can be used to speed up calculations of the local dipolar field in square, circular, and elliptical shaped monolayers and thin films, not only at the center of the film, but across the sample. Calculations show that long elliptical and rectangular films should exhibit the narrowest ferromagnetic resonance (FMR) linewidth. In addition, discrete dipole calculations show that the Lorentz cavity field $\left({\mu }_{0}M/3\right)$ does not hold in tetragonal films. Depending on the ratio (b/a), the local field can be either less/greater than $\left({\mu }_{0}M/3\right):$ an observation that has implications for FMR. 3D simple cubic (SC) systems are also examined. For example, while most texts discuss the Lorentz cavity field in terms of a Lorentz sphere, the Lorentz cavity field still holds when a Lorentz sphere is replaced by a the Lorentz cube, but only in cubic SC, FCC and BCC systems. Finally, while the primary emphasis is on the discrete dipole–dipole interaction, contact is made with the continuum model. For example, in the continuous SC dipole model, just one monolayer is required to generate the Lorentz cavity field. This is in marked contrast to the discrete dipole model, where a minimum of five adjacent monolayers is required.