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

Effects of the quark-hadron phase transition on highly magnetized neutron stars