Analytical model for shape anisotropy in thin-film nanostructured arrays: Interaction effects

When reducing the size of array elements and interelement separations to the nanoscale, long-range magnetostatic interactions become important. A methodology that extends the study of conventional single-element magnetostatics is presented, adding the effect of stacking nanoelements into close proximity in arrays and the consequent interaction effects. This would be very time consuming to model by micromagnetic simulations that are also very vulnerable to artifacts due to cell or boundary condition selection. The proposed method considers an analytical expression valid for short interelement separations and not very costly to evaluate by computational means. This approach allows the quantitative study of shape anisotropy in non-square-shaped arrays. It is also shown how it can be used to find anisotropy compensation conditions, where an anisotropy due to a magnetic element shape can be compensated by the shape anisotropy due to the array. The obtained results can be used to establish a criterion for the minimum number of elements to be considered for a micromagnetic simulation of an array to be realistic depending on the element size and separation.