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Self-localization of magnons and magnetoroton in a binary Bose-Einstein condensate

We consider a two-component Bose-condensed mixture characterized by positive s-wave scattering lengths. We assume equal densities and intra-species interactions. By doing the Bogoliubov transformation of an effective Hamiltonian we obtain the lower energy magnon dispersion incorporating the superfluid entrainment between the components. We argue that p-wave pairing of distinct bosons should be accompanied by self-localization of magnons and formation of a magnetoroton. We demonstrate the effect on a model system of particles interacting via step potentials.