Ab initio calculations of erbium crystal field splittings in oxide hosts

We present an effective ab initio method to calculate the crystal field coefficients of an erbium (Er³⁺) ion experiencing different local site symmetries in several wide-band-gap oxides, and then evaluate crystal field splittings of these Er³⁺ ions for their ground and excited states. The optical transitions between the ground state (Z) and excited state (Y) manifolds of the environmentally shielded 4f states of these Er³⁺ ions have wavelengths ∼ 1.5 μm and thus have potential applications to quantum communications and quantum memories. These results are in excellent agreement with recent low-temperature measurements, provided the inadequate calculation of the 4f shell screening is adjusted by reducing the radial extent of the 4f wavefunctions by approximately a factor of 2.