Frustration on a centred pyrochlore lattice in metal-organic frameworks

Geometric frustration inhibits magnetic systems from ordering, opening a window beyond Landau's paradigm into topological matter and emergent gauge fields, with potential applications to quantum computing. In most systems frustration stems from one of only two elementary units of spins: either triangles or tetrahedra. Here we explore an alternative route for frustration via molecular design in the metal-azolate framework [Mn(II)(ta)2], whose units are centred tetrahedra made of five spins. Despite a Curie-Weiss temperature of -21 K indicating the energy scale of magnetic interactions, [Mn(II)(ta)2] orders only at 0.43 K, putting it firmly in the category of highly frustrated magnets. Using a combination of simulations and field theory, we show that this material is proximate to a spin liquid described as a three-dimensional "slab" of a four-dimensional emergent electric field. The large degeneracy and robustness of this spin liquid, and additional chemical possibilities in the metal-organic frameworks beyond the pyrochlore structure, unlock a new door in frustrated magnetism.