Site symmetry analysis and magnonic dispersion of Er2O3 including the dipolar interaction

Rare-earth elements possess interesting magnetic properties which make a viable option for emerging quantum technologies, including quantum transduction and quantum memories. $Er^{3+}$ has long spin coherence time and its electrons are optically accessible. $Er_2O_3$ is a non collinear antiferromagnetic material at low temperature. We model its crystal field using Steven's operators which yields the same energy splitting and g-factor. Then we use that to model magnon energy. We consider magnons which are governed by the exchange interaction, magnetic dipolar interaction, and small external magnetic field. The Holstein-Primakoff representation and para-unitary diagonalization are employed to quantize the effective spin Hamiltonian. Finally, I will present the dispersion curve of the magnons in this crystal.