Micromagnetic Simulation of Domain Structure Transition in Ferromagnetic Nanospheres under Zero External Field

In this work, we investigated the domain structure transition in ferromagnetic nanospheres at the ground-state conditions under zero external magnetic field by micromagnetic simulation. Four basic ferromagnetic materials, nickel (Ni), permalloy (Py), iron (Fe), and cobalt (Co), with variation in diameters from 20 to 100 nm were modeled in the simulation. It was observed that a transition of domain structure occurs from a single-domain to a multi-domain structure at a specific diameter based on the magnetization energy profile. Interestingly, a vortex– core orientation in the multi-domain regime was related to the magnetocrystalline axis of the material, which first aligns with the hard-axis direction, and then changes to the easy-axis direction for low-anisotropy materials (Ni, Py, and Fe). In contrast, only hard-axis orientation exists for highanisotropy materials (Co). Furthermore, it is also observed that the transition of domain structure was related to the critical diameter. Below the critical diameter, a single-domain structure is exhibited in which the demagnetization energy was larger than the exchange energy. A multidomain structure emerged above the critical diameter where the exchange energy was larger than the demagnetization energy. The comparable values of critical diameter were also calculated based on the Kittel and Brown equations. The results of the critical diameter from the micromagnetic simulation agreed with the theoretical calculations. Therefore, an interpretation of these magnetization dynamics is an important step in the material selection for granular magnetic-based storage.