  We study the pulse morphologies and pulse amplitudes of thermally emitting
neutron stars with ultrastrong magnetic fields. The beaming of the radiation
emerging from a magnetar was recently shown to be predominantly non-radial,
with a small pencil and a broad fan component. We show that the combination of
this radiation pattern with the effects of strong lensing in the gravitational
field of the neutron star yields pulse profiles that show a qualitatively
different behavior compared to that of the radially-peaked beaming patterns
explored previously. Specifically, we find that: (i) the pulse profiles of
magnetars with a single hot emission region on their surface exhibit 1-2 peaks,
whereas those with an antipodal emission geometry have 1-4 peaks, depending on
the neutron star compactness, the observer's viewing angle, and the size of the
hot regions; (ii) the energy dependence of the beaming pattern may give rise to
weakly or strongly energy-dependent pulse profiles and may introduce phase lags
between different energy bands; (iii) the non-radial beaming pattern can give
rise to high pulsed fractions even for very relativistic neutron stars; (iv)
the pulsed fraction may not vary monotonically with neutron star compactness;
(v) the pulsed fraction does not decrease monotonically with the size of the
emitting region; (vi) the pulsed fraction from a neutron star with a single hot
pole has, in general, a very weak energy dependence, in contrast to the case of
an antipodal geometry. Comparison of these results to the observed properties
of anomalous X-ray pulsars strongly suggests that they are neutron stars with a
single hot region of ultrastrong magnetic field.
