Temperature-induced collapse of spin dimensionality in magnetic metamaterials

Spin and spatial dimensionalities are universal concepts, essential for describing both phase transitions and dynamics in magnetic materials. Lately, these ideas have been adopted to describe magnetic properties of metamaterials, replicating the properties of their atomic counterparts as well as exploring properties of ensembles of mesospins belonging to different universality classes. Here, we take the next step when investigating magnetic metamaterials not conforming to the conventional framework of continuous phase transitions. Instead of a continuous decrease in the moment with temperature, discrete steps are possible, resulting in a binary transition in the interactions of the elements. The transition is enabled by nucleation and annihilation of vortex cores, shifting topological charges between the interior and the edges of the elements. Consequently, the mesospins can be viewed as shifting their spin dimensionality, from 2 (XY-like) to 0 (vortices), at the transition. The results provide insight into how dynamics at different length scales couple, which can lead to thermally driven topological transitions in magnetic metamaterials.