Magnonic dispersion of Er₂O₃

Rare-earth magnets may provide useful magnetic properties for quantum technologies, including quantum transduction and quantum memories. Here we calculate the band structure of magnons in antiferromagnetic Er₂O₃.

We consider zero temperature Er₂O₃ in an antiferromagnetic state that hosts magnons and approximate the interaction of the spins as exchange interaction and magnetic dipole-dipole interaction. The symmetry axes of the spins are considered in the exchange interaction and the external magnetic field. This model is valid when the external magnetic field is below 1.5 Tesla at which the spin-flop occurs. Similar models will describe other dipole-dipole interactions of spins, such as ensembles of molecular spins. The Holstein-Primakoff representation and paraunitary diagonalization are employed to quantize the Hamiltonian. Er₂O₃ has 32 erbium atoms in a non-primitive cubic unit cell. The long-range nature of magnetic dipole-dipole interaction poses a challenging issue for considering magnonic structure from dipole-dipole interactions. The dipole-dipole interaction drops as a cube power of the separation between spins. If these long-distance neighbors are ignored the magnonic dispersion will change.