Perpendicular magnetic anisotropy in thin films enables extraordinary spin-wave phenomena: anti-Larmor precession, negative reflection and refraction, multi-reflection and multi-refraction

We present a theoretical and numerical investigation of the role of perpendicular magnetic anisotropy (PMA) in shaping spin-wave (SW) dynamics under low magnetic fields in thin and ultrathin magnetic films. PMA introduces an in-plane torque that counteracts exchange, dipolar, and Zeeman contributions, fundamentally modifying SW dispersion and inducing a local minimum that, under specific conditions, becomes the lowest frequency across all geometric configurations. This results in a sombrero-shaped dispersion in ultrathin films and a cowboy-hat-like shape in thicker films, where dipolar interactions dominate. Using isofrequency contour (IFC) analysis, we demonstrate that these PMA-induced dispersion shapes enable nontrivial wave phenomena unprecedented in uniform media: bireflection and negative reflection in ultrathin films, and trireflection in thicker films--where a single incident beam splits into three reflected components, two with negative angles. Most remarkably, we predict and demonstrate tri-refraction, where one incident beam generates three refracted beams with two exhibiting negative refraction angles. We further show anti-Larmor precession of magnetization near the dispersion minimum in thicker films, arising from the interplay between PMA-induced and dipolar torques. Systematic simulations across diverse material systems--metallic films, ferrimagnetic garnets, hybrid structures, and multilayers--confirm the universal nature of these phenomena in any PMA system supporting stripe domain transitions. These results open new opportunities to explore wave phenomena beyond magnonics.