  We present a theoretical study of interacting electron-hole pairs located on
a magnetized surface of a strong topological insulator (TI). The excitonic
energy levels and the optical absorption on such surface display unique and
potentially measurable features such as (i) an enhanced binding energy for
excitons whose total angular momentum is aligned with the magnetic exchange
field, (ii) a stark dependence of the optical absorption on the direction of
the magnetic exchange field as well as on the chirality of the incident light,
and (iii) a tunable center-of-mass motion of spinful excitons induced by
particle-hole asymmetry in the exchange field. Our predictions are relevant to
surfaces of magnetically doped TIs or surfaces coated with magnetic films, in
addition to TI nanowires placed under longitudinal magnetic fields.
