A continuous model of magnetic moment distribution in a system with bilinear and biquadratic coupling

Abstract

In this paper, we present a continuous model as an analog to the discrete atomic model often used in the interpretation/analysis of magnetometry studies of magnetic structures with bilinear and/or biquadratic coupling. For a typical set of parameters, the continuous model is shown to be nearly indistinguishable from its discrete counterpart; validating it for data analysis purposes. Furthermore, we also find a very simple analytic expression which can approximately solve the continuous model and also provides insight into the behaviors of the magnetic moment within the magnetic structure. The main advantage of the continuous model is that numerically it can be solved as a boundary value problem, which can be significantly faster than the energy minimization required for the discrete model improving computational speed and allowing for much more rapid data analysis.