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Black hole-torus systems from compact binary mergers are possible engines forgamma-ray bursts (GRBs). During the early evolution of the post-merger remnant,the state of the torus is determined by a combination of neutrino cooling andmagnetically-driven heating processes, so realistic models must include botheffects. In this paper, we study the post-merger evolution of a magnetizedblack hole-neutron star binary system using the Spectral Einstein Code (SpEC)from an initial post-merger state provided by previous numerical relativitysimulations. We use a finite-temperature nuclear equation of state andincorporate neutrino effects in a leakage approximation. To achieve the neededaccuracy, we introduce improvements to SpEC's implementation ofgeneral-relativistic magnetohydrodynamics (MHD), including the use ofcubed-sphere multipatch grids and an improved method for dealing withsupersonic accretion flows where primitive variable recovery is difficult. Wefind that a seed magnetic field triggers a sustained source of heating, but itsthermal effects are largely cancelled by the accretion and spreading of thetorus from MHD-related angular momentum transport. The neutrino luminositypeaks at the start of the simulation, and then drops significantly over thefirst 20\,ms but in roughly the same way for magnetized and nonmagnetizeddisks. The heating rate and disk's luminosity decrease much more slowlythereafter. These features of the evolution are insensitive to grid structureand resolution, formulation of the MHD equations, and seed field strength,although turbulent effects are not fully converged

Evolution of the Magnetized, Neutrino-Cooled Accretion Disk in the Aftermath of a Black Hole Neutron Star Binary Merger