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

Rare-earth magnets may provide useful magnetic properties for quantum technologies, including quantum transduction and quantum memories. Erbium(III) oxide (Er2O3) may be able to host magnons because of the localized f shell electrons. Out of the 32 Erbiums in Er2O3 non primitive unit cells, 24 have C2 symmetry and 8 have C3i symmetry. At zero temperature, Er2O3 is in non collinear antiferromagnetic state and the site symmetry plays an important role in exchange interaction in this state. Here we analyze the site symmetry of the crystal and show how C3i sites do not provide exchange coupling that influences the magnon dispersion. Then the Holstein-Primakoff representation and paraunitary diagonalization are employed to quantize the Hamiltonian. Er2O3. The effect of the dipolar interaction in the magnons is presented and the energy gap between the dipolar magnons and exchange magnons is calculated.