We investigate the prospect of achieving negative permittivity and permeability at optical frequencies in a dielectric crystal containing stoichiometric rare-earth ions. We derive the necessary transition linewidth, ion density and electric and magnetic oscillator strengths using a simplified model of non-interacting dipoles. We identify Erbium crystals in a magnetically ordered phase as the most promising material to meet these conditions, and describe initial optical measurements of two potential candidates, \ercl{} and 7\lierf{}, which display linewidths of 3~GHz and 250~MHz, respectively. The properties of 7\lierf{} satisfied our criterion for negative permeability.
@article{arxiv.2205.02739,
title = {Negative refractive index in dielectric crystals containing stoichiometric rare-earth ions},
author = {Matthew C. Berrington and Henrik M. Rønnow and Matthew J. Sellars and Rose L. Ahlefeldt},
journal= {arXiv preprint arXiv:2205.02739},
year = {2022}
}