Magnons and excitons from Bethe-Salpeter equation and its application to graphene-based magnets

Abstract

With the recent isolation of two-dimensional semiconducting magnetic materials, the theoretical study of spin-flip collective excitations (magnons) along with spin-conserving electron-hole bound pairs (excitons) has become particularly relevant. Describing both types of quasiparticles within the same theoretical framework is possible, in principle, but the well-established many-body formalism for the calculation of excitons, based on the intertwined Bethe-Salpeter and Hedin's equations, is not satisfactory for magnons, since the usual approximations produce a spurious gapped Goldstone mode. Here, we show that excitons and magnons can be computed on the same footing under the same Bethe-Salpeter formalism, while respecting the gapless Goldstone mode for magnons. We demonstrate how this can be achieved through the evaluation of the full Bethe-Salpeter equation, beyond the Tamm-Dancoff approximation in model Hamiltonians. As an example, we apply it to ferromagnetic and antiferromagnetic graphene, faithfully represented by the extended Hubbard model. Our results clarify the roles of on-site and non-local interactions in exciton and magnon appearance and identify consistency requirements relevant to extending the approach to first-principles calculations.