Can magnetic fields stabilize or destabilize twin stars?

Sharp phase transitions described by stiff equations of state allow for the existence of a third family of stable compact stars (besides white dwarfs and neutron stars), twin stars. In this work, we investigate for the first time the role of strong magnetic fields on non-magnetic twin stars sequences and the case in which magnetic fields themselves give rise to a third family of stable stars. We use three sets of equations of state to study such effects from a more general point of view: the Quark-Hadron Chiral Parity-Doublet (Q$χ$P) model for both hadronic and quark phases, and the Many-Body Forces (MBF) model connected to either the MIT Bag model with vector interaction (MIT) or to the Constant-Sound-Speed (CSS) approximation for the quark phase, through a Maxwell construction. Magnetic field effects are introduced in the structure of stars through the solution of the Einstein-Maxwell equations, assuming a poloidal magnetic field configuration and a metric that allows for the description of deformed stars. We show that strong magnetic fields can destabilize twin star sequences, with the threshold intensity being model dependent. On the other hand, magnetic fields can also give rise to twin stars in models that did not predict these sequences, up to some point when they are again destabilized. In this sense, magnetic fields can play an important role on the evolution of neutron stars.