# Spin order and dynamics in the diamond-lattice Heisenberg antiferromagnets CuRh2O4 and CoRh2O4

## TL;DR

This study characterizes the magnetic properties of diamond-lattice antiferromagnets CoRh2O4 and CuRh2O4, revealing classical and incommensurate magnetic orderings, providing foundational insights for exploring quantum phenomena in these materials.

## Contribution

It provides detailed experimental and theoretical analysis of magnetic order and excitations in CoRh2O4 and CuRh2O4, establishing them as reference models for diamond-lattice antiferromagnets.

## Key findings

- CoRh2O4 is a canonical S=3/2 diamond-lattice Heisenberg antiferromagnet with Neel order below 25 K.
- CuRh2O4 exhibits an incommensurate spin helix with reduced ordered moment due to quantum effects.
- The materials serve as benchmarks for studying exotic quantum behaviors in diamond-lattice antiferromagnets.

## Abstract

Antiferromagnetic insulators on the 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 CoRh2O4 (cobalt rhodite) and CuRh2O4 (copper rhodite) by means of thermo-magnetic and neutron scattering measurements and perform group theory analysis, Rietveld refinement, mean-field theory, and spin wave theory calculations to analyze the experimental results. Our investigation reveals that cubic CoRh2O4 is a canonical S=3/2 diamond-lattice Heisenberg antiferromagnet with a nearest neighbor exchange J = 0.63 meV and a Neel ordered ground-state below a temperature of 25 K. In tetragonally distorted CuRh2O4, competiting 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 = (0,0,0.79). Strong reduction of the ordered moment is observed for the S=1/2 spins in CuRh2O4 and captured by our 1/S corrections to the staggered magnetization. Our work identifies CoRh2O4 and CuRh2O4 as reference materials to guide future work searching for exotic quantum behavior in diamond-lattice antiferromagnets.