Three-dimensional checkerboard spin structure on a breathing pyrochlore lattice

The standard approach to realize a spin-liquid state is through magnetically frustrated states, relying on ingredients such as the lattice geometry, dimensionality, and magnetic interaction type of the spins. While Heisenberg spins on a pyrochlore lattice with only antiferromagnetic nearest-neighbor interactions are theoretically proven disordered, spins in real systems generally include longer-range interactions. The spatial correlations at longer distances typically stabilize a long-range order rather than enhancing a spin-liquid state. Both states can, however, be destroyed by short-range static correlations introduced by chemical disorder. Here, using disorder-free specimens with a clear long-range antiferromagnetic order, we refine the spin structure of the Heisenberg spinel ZnFe2O4 through neutron magnetic diffraction. The unique wave vector (1,0,12) leads to a spin structure that can be viewed as alternatively stacked ferromagnetic and antiferromagnetic tetrahedra in a three-dimensional checkerboard form. Stable coexistence of these opposing types of clusters is enabled by the bipartite breathing pyrochlore crystal structure, leading to a second-order phase transition at 10 K. The diffraction intensity of ZnFe2O4 is an exact complement to the inelastic scattering intensity of several chromate spinel systems which are regarded as model classical spin liquids. Our results challenge this attribution, and suggest instead of the six-spin ring mode, spin excitations in chromate spinels are closely related to the (1,0,12) type of spin order and the four-spin ferromagnetic cluster locally at one tetrahedron.