  In the present paper, we prove an improved Combes-Thomas estimate, i.e., the
Combes-Thomas estimate in trace-class norms, for magnetic Schr\"{o}dinger
operators under general assumptions. In particular, we allow unbounded
potentials. We also show that for any function in the Schwartz space on the
reals the operator kernel decays, in trace-class norms, faster than any
polynomial.
