Spin order and dynamics in the diamond-lattice Heisenberg antiferromagnets CuRh 2 O 4 and CoRh 2 O 4
Here, antiferromagnetic insulators on a diamond lattice are candidate materials to host exotic magnetic phenomena ranging from spin-orbital entanglement to degenerate spiral ground states and topological paramagnetism. Compared to other three-dimensional networks of magnetic ions, such as the geometrically frustrated pyrochlore lattice, the investigation of diamond-lattice magnetism in real materials is less mature. In this work, we characterize the magnetic properties of model A-site spinels CoRh 2 O 4 (cobalt rhodite) and CuRh 2 O 4 (copper rhodite) by means of thermomagnetic and neutron-scattering measurements, and we perform group theory analysis, Rietveld refinement, mean-field theory, and spin-wave theory calculations to analyze the experimental results. Our investigation reveals that cubic CoRh 2 O 4 is a canonical S = 3/2 diamond-lattice Heisenberg antiferromagnet with a nearest-neighbor exchange J = 0.63 meV and a Néel ordered ground state below a temperature of 25 K. In tetragonally distorted CuRh 2 O 4 , competing exchange interactions between up to third-nearest-neighbor spins lead to the development of an incommensurate spin helix at 24 K with a magnetic propagation vector k m = (0,0,0.79). Strong reduction of the ordered moment is observed for the S = 1/2 spins in CuRh 2 O 4 and captured by our 1/ S corrections to the staggered magnetization. Our work identifies CoRh 2 O 4 and CuRh 2 O 4 as reference materials to guide future work searching for exotic quantum behavior in diamond-lattice antiferromagnets.