A Cluster-Based Model of the Spectrum of Erbium-Doped GdVO$_4$
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.