  The effects of strong magnetic fields on the deconfinement phase transition
expected to take place in the interior of massive neutron stars are studied in
detail for the first time. For hadronic matter, the very general
density-dependent relativistic mean-field (DD-RMF) model is employed, while the
simple, but effective vector-enhanced bag model (vBag) model is used to study
quark matter. Magnetic-field effects are incorporated into the matter equation
of state and in the general-relativity solutions, which also satisfy Maxwell's
equations. We find that for large values of magnetic dipole moment, the maximum
mass, canonical mass radius, and dimensionless tidal deformability obtained for
stars using spherically symmetric Tolman-Oppenheimer-Volkoff (TOV) equations
and axisymmetric solutions attained through the LORENE library differ
considerably. The deviations depend on the stiffness of the equation of state
and on the star mass being analyzed. This points to the fact that, unlike what
was assumed previously in the literature, magnetic field thresholds for the
approximation of isotropic stars and the acceptable use of TOV equations depend
on the matter composition and interactions.
