Analytic description of spin waves in dipolar/octupolar pyrochlore magnets

We derive analytic forms for spin waves in pyrochlore magnets with dipolar-octupolar interactions, such as Nd₂Zr₂O₇. We obtain full knowledge of the diagonalized magnonic Hamiltonian within the linear spin wave approximation. We also consider the effect of a 'breathing mode' as a perturbation of this system. The breathing mode lifts the degeneracy of the upper band of the spin wave dispersion along the directionX→Wink-space.