Recent Developments in Molecular Spin Gyroid Research

Gyroid is a type of 3D periodic structure that is ubiquitous in nature on scales ranging from macro to micro, and is attracting much attention in various research fields such as geometry, physics, chemistry, biology and even architecture. Along with honeycomb and diamond structures, gyroid is one of the three structures mathematically recognized as having a strong isotropic property. Microscopic gyroidal materials with magnetic spin centers, known as molecular spin gyroids, have been investigated for more than twenty years, but the peculiar electronic and magnetic properties arising from their exotic structures are still poorly understood, in contrast to extensively studied microscopic honeycomb materials such as graphene. In this review, we describe the geometrical and physical aspects of gyroids, and introduce various microscopic gyroidal materials in accordance with a classification of the interactions that constitute the gyroidal structures. Then, we report our recent investigations on a molecular spin gyroid formed by a polyhedral organic pi-conjugated molecule. A unique 3D spin frustration forming a spin liquid state is also discussed.