Spin wave modes in Pacman-shaped disks with perpendicular uniaxial anisotropy

Magnetic nanostructures with broken symmetry offer new opportunities for tailoring spin-wave excitations through geometric design. In this work, we investigate the combined effects of geometric asymmetry and perpendicular magnetic anisotropy on the equilibrium states and spin-wave modes of Pacman-shaped Permalloy nanodisks using micromagnetic simulations. The degree of asymmetry is controlled by the aperture angle and the displacement of the opening, while the perpendicular anisotropy is varied over a wide range. Phase diagrams reveal that disk asymmetry promotes transitions from vortex states to in-plane and vortex-like configurations, whereas increasing anisotropy favors the emergence of skyrmion-like states and perpendicular single-domain configurations. The dynamic response, analyzed via broadband excitation and Fourier analysis, shows that both geometry and anisotropy strongly affect the number, frequency, and spatial character of the spin-wave modes. Edge-dominated, central, and mixed azimuthal–radial modes are identified, with increasing asymmetry and anisotropy leading to mode splitting and enhanced spatial localization near the aperture region. These results demonstrate that Pacman-shaped nanodisks provide a versatile platform for controlling spin-wave spectra through the interplay of geometry and anisotropy, offering promising perspectives for tunable magnonic and spintronic devices.