  We present a unified explanation for the observed properties of the isolated
neutron star RX J0720.4-3125 by obtaining, for the first time, a
self-consistent model that accounts simultaneously for the observed X-ray
spectrum and optical excess, the pulsed fraction, the observed spectral feature
around 0.3 keV, and the long--term spectral evolution. By fitting the
parameters of our realistic self--consistent models to all archival XMM--Newton
observations and available optical data, we show that all observed properties
are consistent with a normal neutron star with a proper radius of about 12 km,
a temperature at the magnetic pole of about 100 eV and a magnetic field
strength of 2-3 x 10^{13} G, with no need to invoke additional emission and
absorption components nor exotic internal composition. The observed variability
of the effective temperature, strength of the spectral feature, and pulsed
fraction are in good agreement with the predictions of our model in which the
star is subject to free precession, producing changes in the angle between the
magnetic field and the rotation axis of tens of degrees with a periodicity of 7
years, as pointed out by other authors on the basis of phenomenological models.
In addition to the evidence of internal toroidal components, we also find
strong evidence of non-dipolar magnetic fields, since all spectral properties
are better reproduced with models with strong quadrupolar components.
