Effect of void geometry and magnetic anisotropy in controlling the vortex in sub-micron annular Permalloy disc

Ferromagnetic rings, particularly asymmetric Permalloy (Py) rings are recognized as promising configurations for spintronic devices, offering additional degrees of freedom for manipulating magnetic states, especially in vortex configurations. Through micromagnetic simulations, our study explores the impact on magnetization states and spin configuration concerning ring symmetry, aligning with the interest in controlling vortex states for information storage. We initially obtained zero-field spin configurations by varying ring thickness (t), observing a 360° domain wall in rings with t < 12 nm and bi-vortex wall in rings with t ∼36 nm during magnetization reversal. Notably, an extended stability of the global-vortex state was observed in rings with t > 36 nm, indicating the dominance of global-vortex nucleation in thick asymmetric rings during domain wall movement. We investigate the hysteresis loops and spin configurations by varying the in-plane and out-of-plane anisotropy values. Our findings reveal the presence of multiple vortex cores with different polarities and sense of rotations in the ring for the in-plane anisotropy ∼30 to ∼40 kJ m−3. Additionally, a global-vortex with two vortex cores was formed due to demagnetization energy. We analysed the energy profile of stable magnetization states for various t and anisotropy values. Interestingly, the shape of the hysteresis loop changes significantly for the disc containing different shapes of void. Circular and square-shaped geometries suggest that the bi-vortex state is a stable configuration during magnetization reversal in both cases. The study also indicates the stability of the vortex with a square-shaped void geometry up to a sufficiently large field. For the case of triangular-shaped voids, the global-vortex state was favored with even the small fields. The estimated spin canting angles are found to be correlated with the presence of vortex spin configurations. Overall, these results are important for the development of magnetization vortex-based spintronics devices.