Rigorous micromagnetic computation of configurational anisotropy energies in nanoelements

A method combining the nudged elastic band method with finite element micromagnetics is used to calculate minimum energy paths, global minima, metastable states and, most importantly, saddle points between energy minima. We study configurational anisotropy effects in thin permalloy elements, e.g., 5 nm thick squares. For squares with the size of 15–200 nm the ground states are so-called “leaf” states with the average magnetization along one of the diagonals. However a second state (“buckle”) becomes stable with the average magnetization along one edge at sizes larger than ∼80 nm. The superposition of the four easy axes leads to a combination of four and eightfold anisotropy. At ∼200 nm size both states have about the same energy so that the overall picture becomes that of an effective eightfold anisotropy.