  The observed upper bound on the spin down rate of the otherwise typical Soft
Gamma-ray Repeater SGR 0418+5729 has challenged the interpretation of this
source as a neutron star with ultrastrong magnetic fields. Current limits imply
a dipole magnetic field strength of less than 7.5 x 10^{12} G (Rea et al.
2010), which is significantly smaller than that of a typical SGR. Independent
of the properties inferred from X-ray timing, the X-ray spectra of neutron
stars allow a measurement of their magnetic field strengths because they are
distorted from pure blackbodies due to the presence of a magnetic field in a
radiative equilibrium atmosphere. In this paper, we model high signal-to-noise
XMM-Newton spectra of SGR 0418+5729 to place constraints on the strength of the
magnetic field at the surface of the neutron star. Our analysis shows that
neutron star atmosphere models with moderate magnetic field strengths
(10^{12-13} G) cannot fit the X-ray spectra, whereas, models with stronger
magnetic fields are able to account for the observations. We find that the
strength of the magnetic field at the surface is 1.0 x 10^{14} G. This value,
although lower than all of the other SGRs analyzed to date, is still high
enough to generate the observed X-ray bursts from the source. In connection to
the spindown limits, it also implies a significantly non-dipolar structure of
the magnetic field. We discuss the results of our spectral modeling and compare
them with other SGRs.
