  The presence of quark-hadron phase transitions in neutron stars can be
related to several interesting phenomena. In particular, previous calculations
have shown that fast rotating neutron stars, when subjected to a quark-hadron
phase transition in their interiors, could give rise to the backbending
phenomenon characterized by a spin-up era. In this work, we use an equation of
state composed of two phases, containing nucleons (and leptons) and quarks. The
hadronic phase is described in a relativistic mean field formalism that takes
many-body forces into account, and the quark phase is described by the MIT bag
model with a vector interaction. Stationary and axi-symmetric stellar models
are obtained in a self-consistent way by solving numerically the
Einstein-Maxwell equations by means of a pseudo-spectral method. As a result,
we obtain the interesting backbending phenomenon for fast spinning neutron
stars. More importantly, we show that a magnetic field, which is assumed to be
axi-symmetric and poloidal, can also be enhanced due to the phase transition
from normal hadronic matter to quark matter on highly magnetized neutron stars.
Therefore, in parallel to the spin-up era, classes of neutron stars endowed
with strong magnetic fields may go through a "magnetic-up era" in their lives.
