<i>Ab-inito</i> and crystal-field calculations of defect properties of Er³⁺ in yttria

Wide band-gap oxides with rare-earth impurities exhibit narrow transitions with long coherence times and high quantum efficiency due to partially filled f orbitals. This allows the fabrication and usage of these materials in highly efficient optical amplifiers, high power lasers, data, and quantum information processing.
We study electronic, structural, and spin properties of trivalent erbium impurities in yttria. First, we perform ab-initio calculations of the structural properties using the generalized gradient approximation and the pseudopotential method. We also calculate the electronic band structure and the density of states of the bulk and doped yttria. Then we proceed to compute the formation energies of erbium impurities. We also compute level splittings and g-tensors using a crystal field Hamiltonian. We show that the g-tensor is highly anisotropic, with a large component in one direction. The presence of an abundant isotope with a non-zero nuclear spin and anisotropic g-tensor suggest that an experimental control of the spin dynamics of this system is possible through the Zeeman and hyperfine interaction.