Magneto-solid-mechanical model of two-component, core-crust, paramagnetic neutron star responding to quake-induced perturbation by differentially rotational, torsional, oscillations of crustal electron-nuclear solid-state plasma about axis of magnetic field frozen in the immobile paramagnetic core is developed. Particular attention is given to the node-free torsional crust-against-core vibrations under combined action of Lorentz magnetic and Hookes elastic forces; the damping is attributed to Newtonian force of shear viscose stresses in crustal solid-state plasma. The spectral formulae for the frequency and lifetime of this toroidal mode are derived in analytic form and discussed in the context of quasi-periodic oscillations of the X-ray outburst flux from quaking magnetars. The application of obtained theoretical spectra to modal analysis of available data on frequencies of oscillating outburst emission suggests that detected variability is the manifestation of crustal Alfvens seismic vibrations restored by Lorentz force of magnetic field stresses.
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