Energy Minimizers in Thin Ferromagnetic Nanorings with Four-Fold In-Plane Anisotropy

We present results obtained from micromagnetic simulations of thin ferromagnetic nanorings. We investigate annuli made of materials with non-negligible cubic anisotropy. In thin films the crystalline anisotropy favors magnetizations lying in the film plain along $\pm\hat{\mathbf{x}}$ or $\pm\hat{\mathbf{y}}$ directions. The magnetostatic energy separates into boundary and bulk terms. Our previous work provided a classification of remanent states based on the above contributions to the energy [1]. There are three regimes with distinct features of the remanent states depending on the dominant energy term. The magnetization configurations present four distinct domains. Different remanent states coexist in each of these regimes and they are characterized by the behavior of the domain walls spanning the annulus. Here, we compute the energies for these metastable states in a variety of ring dimensions and material parameters. In particular, we attempt to locate the ground state as a function of ring dimensions. This information is of importance for the design of magnetic storage devices based on configurations presenting $2\pi$ domain walls [2]. [1] G.D. Chaves-O'Flynn, C. Muratov. Submitted. IEEE Trans. Mag. [2] C. Muratov and V. Osipov. IEEE Trans. Mag, 45, p.3207 (2008)