  The fermionic self-energy on the surface of a topological insulator proximity
coupled to ferro- and antiferromagnetic insulators is studied. An enhanced
electron-magnon coupling is achieved by allowing the electrons on the surface
of the topological insulator to have a different exchange coupling to the two
sublattices of the antiferromagnet. Such a system is therefore seen as superior
to a ferromagnetic interface for the realization of magnon-mediated
superconductivity. The increased electron-magnon-coupling simultaneously
increases the self-energy effects. In this paper we show how the inverse
quasiparticle lifetime and energy renormalization on the surface of the
topological insulator can be kept low close to the Fermi level by using a
magnetic insulator with a sufficient easy-axis anisotropy. We find that the
antiferromagnetic case is most interesting from both a theoretical and an
experimental standpoint due to the increased electron-magnon coupling, combined
with a reduced need for easy-axis anisotropy compared to the ferromagnetic
case. We also consider a set of material and instrumental parameters where
these self-energies should be measurable in angle-resolved photoemission
spectroscopy experiments, paving the way for a measurement of the interfacial
exchange coupling strength.
