We investigate the oscillation spectrum of rotating Newtonian neutron stars endowed with purely toroidal magnetic fields, using a time-evolution code to evolve linear perturbations in the Cowling approximation. The background star is generated by numerically solving the magnetohydrodynamics equilibrium equations and may be non-spherical by virtue of both rotation and magnetic effects; hence, our perturbations and background are fully consistent. Whilst the background field is purely toroidal, the perturbed field is mixed poloidal–toroidal. From Fourier analysis of the perturbations, we are able to identify a number of magnetically restored Alfvén (or a) modes. We show that in a rotating star pure inertial and a-modes are replaced by hybrid magneto-inertial modes, which reduce to a-modes in the non-rotating limit and inertial modes in the non-magnetic limit. We show that the r-mode instability is suppressed by magnetic fields in sufficiently slowly rotating stars. In addition, we determine magnetic frequency shifts in the f-mode. We discuss the astrophysical relevance of our results, in particular for magnetar oscillations
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