Experimental observations of rare-earth ions doped into an antiferromagnetic crystal show an enriched optical spectrum. In this paper we present a cluster-based model to describe erbium ions doped into a gadolinium vanadate (Er:GdVO
4) host crystal, wherein the erbium ion couples directly to its four nearest neighbour gadolinium ions, which in turn couple to the mean field of the rest of the crystal. Compared to previous models in the literature, the parameters used to fit this model are fewer in number, with clearer physical origins. Agreement with the experimentally observed optical spectrum of Er:GdVO
4 suggests that our model succeeds in capturing the most important interactions of the system, suggesting that it may be useful for predicting microwave-to-optical transduction in future experiments.
Rare-earth-ion doped crystals are a promising platform for applications in microwave-to-optical transduction. Erbium is of special interest because of its telecom wavelength optical transitions. This work investigates the optical and electron-spin properties of Er
3+:YVO
4. An initial transduction of classical microwave signal using this material is demonstrated. The measured strong optical dipole moment and narrow ensemble inhomogeneities make Er
3+:YVO
4 a promising material for microwave-to-optical transduction.