  The energy source powering the X-ray emission from anomalous X-ray pulsars
(AXPs) and soft gamma-ray repeaters (SGRs) is still uncertain. In one scenario,
the presence of an ultramagnetized neutron star, or ``magnetar'', with B on the
order of 10^{14} - 10^{15} G is invoked. To investigate this hypothesis, we
have analyzed archival ASCA data for several known AXPs and SGRs, and fitted
them with a model in which all or part of the X-ray flux originates as thermal
emission from a magnetar. Our magnetar spectral model includes the effects of
the anisotropy of the heat flow through an ultramagnetized neutron star
envelope, reprocessing by a light element atmosphere, and general relativistic
corrections to the observed spectrum. We obtain good fits to the data with
radii for the emitting areas which are generally consistent with those expected
for neutron stars, in contrast to blackbody (BB) fits, which imply much smaller
radii. Furthermore, the inclusion of atmospheric effects results in inferred
temperatures which are lower than those implied by BB fits, but however still
too high to be accounted by thermal cooling alone. An extra source of heating
(possibly due to magnetic field decay) is needed. Despite the harder tail in
the spectrum produced by reprocessing of the outgoing flux through the
atmosphere, spectral fits still require a considerable fraction of the flux to
be in a power-law component.
