  We study superconductivity on the surface of a topological insulator,
mediated by magnetic fluctuations in an adjacent ferromagnetic or
antiferromagnetic insulator. Superconductivity can arise from effective
interactions between helical fermions induced by interfacial fermion-magnon
interactions. For both ferromagnetic and antiferromagnetic insulators, these
fermion-fermion interactions have the correct structure to facilitate pairing
between particles located on the same side of the Fermi surface, also known as
Amperean pairing. In antiferromagnets, the strength of the induced interactions
can be enhanced by coupling the topological insulator asymmetrically to the two
sublattices of the antiferromagnet. This effect is further amplified by next
nearest neighbor frustration in the antiferromagnetic insulator. The
enhancement makes the induced interactions significantly stronger in the
antiferromagnetic case, as compared to the ferromagnetic case. These results
indicate that an uncompensated antiferromagnetic interface might be a better
candidate than a ferromagnetic interface for proximity-induced magnon-mediated
superconductivity on the surface of a topological insulator.
