  The violent giant flares of magnetars excite QPOs which persist for hundreds
of seconds, as seen in the X-ray tail following the initial burst. Recent
studies, based on single-fluid barotropic magnetar models, have suggested that
the lower-frequency QPOs correspond to magneto-elastic oscillations of the
star. The higher frequencies, however, in particular the strong 625 Hz peak,
have proved harder to explain, except as high mode multipoles. In this work we
study the time evolutions of non-axisymmetric oscillations of two-fluid
Newtonian magnetars with no crust. We consider models with superfluid neutrons
and normal protons, and poloidal and toroidal background field configurations.
We show that multi-fluid physics (composition-gradient stratification,
entrainment) tends to increase Alfven mode frequencies significantly from their
values in a single-fluid barotropic model. The higher-frequency magnetar QPOs
may then be naturally interpreted as Alfven oscillations of the multi-fluid
stellar core. The lower-frequency QPOs are less easily explained within our
purely fluid core model, but we discuss the possibility that these are crustal
modes.
