Magnetic Configurations and Phase Diagrams of Sub-100-nm NiFe Nanorings

Using the micromagnetics package MAGPAR, we study the ground states of NiFe nanorings with sub-100-nm lateral dimensions, in zero external field. We solve the Landau-Lifschitz-Gilbert equation for three different initial magnetizations (in plane, out of plane, and vortex) to obtain the lowest energy state. Plotting the total energy as a function of thickness, along with its corresponding magnetostatic and exchange energies, we are able to identify various phase transitions and derive phase diagrams as a function of thickness and outer radius, normalized to the exchange length, for rings with different inner to outer radius ratios. We discuss the results in terms of shape anisotropy and its effect on the magnetostatic and exchange energies. We also compare the results of our numerical method to the phase diagram of a nanodot and the phase diagrams of rings obtained by analytical models. Finally, we present a new ground state configuration, the helix, found along the boundary between the vortex and out of plane phases, where the magnetization is vortex like, but with moments canted along the z direction