Spin-state ice in geometrically frustrated spin-crossover materials.

Frustration, the inability to simultaneously minimise competing interactions, can produce macroscopically degenerate classical states and long-range entangled quantum states, most notably topological spin-liquids. Spin ices are important examples where local constraints, called ice rules, lead to an extensive residual entropy and low-energy physics described by an emergent gauge field. Local violations of the ice rules lead deconfined magnetic monopoles. But it is not known how commonly such physics is realised in other classes of materials. Spin crossover materials contain molecules with two thermodynamically accessible spin-states: one low-spin (LS) and the other high-spin (HS). Here we show that frustrated magneto-elastic interactions can give rise to spin-state ices. The low-energy physics exhibits an emergent divergence-less field with a gap to topological excitations that are deconfined quasi-particles with spin fractionalised midway between the LS and HS spin.