  The two-component, core-crust, model of a neutron star with homogenous
internal and dipolar external magnetic field is studied responding to
quake-induced perturbation by substantially nodeless differentially rotational
Alfv\'en oscillations of the perfectly conducting crustal matter about axis of
fossil magnetic field frozen in the immobile core. The energy variational
method of the magneto-solid-mechanical theory of a viscoelastic perfectly
conducting medium pervaded by magnetic field is utilized to compute the
frequency and lifetime of nodeless torsional vibrations of crustal solid-state
plasma about the dipole magnetic-moment axis of the star. It is found that
obtained two-parametric spectral formula for the frequency of this toroidal
Alfven mode provides fairly accurate account of rapid oscillations of the X-ray
flux during the flare of SGR 1806-20 and SGR 1900+14, supporting the
investigated conjecture that these quasi-periodic oscillations owe its origin
to axisymmetric torsional oscillations predominately driven by Lorentz force of
magnetic field stresses in the finite-depth crustal region of the above
magnetars.
