In spite of its key role in compact star physics, the surface tension of quark matter is not well comprehended yet. In this work we analyze the behavior of the surface tension of three-flavor quark matter in the outer and inner core of cold deleptonized magnetars, proto magnetars born in core collapse supernovae, and hot magnetars produced in binary neutron stars mergers. We explore the role of temperature, baryon number density, trapped neutrinos, droplet size, and magnetic fields within the multiple reflection expansion formalism. Quark matter is described within the MIT bag model and is assumed to be in chemical equilibrium under weak interactions. We discuss some astrophysical consequences of our results.
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