The effect of tilted edges on the shape anisotropy and stray field coupling of uniformly magnetized rectangular elements

Abstract

The influence of tilted edges on the magnetostatic properties of uniformly magnetized thin rectangular elements is studied. To calculate the magnetostatic energy, the Poisson equation is solved. The shape of the magnetic element is approximated by horizontally assembled thin cuboids and the solutions of Rhodes and Rowlands [Proc. Leeds Phil. Soc. 6, 191 (1954)] are utilized. A second approach is the straightforward integration of the Poisson equation taking into account the trapezoidal shape of the side faces due to the tilted edges. For an adequate number of cuboids, both methods agree very well. It is found that the shape anisotropy of a single magnetic element with tilted edges is reduced compared to that of an ideal cuboid. For a two element system the shape anisotropy competes with the magnetostatic interaction favoring a magnetization orientation parallel to the connecting line of the elements. If the elements are oriented in-line with their short axes, the easy magnetization axis switches at a critical distance between the elements. This distance increases when the elements have tilted edges.