  Dense neutron matter with recently developed BSk19 and BSk21 Skyrme effective
forces is considered in magnetic fields up to $10^{20}$ G at zero temperature.
The breaking of the rotational symmetry by the magnetic field leads to the
differentiation between the pressures along and perpendicular to the field
direction which becomes significant in the fields $H>H_{th}\sim10^{18}$ G. The
longitudinal pressure vanishes in the critical field
$10^{18}<H_c\lesssim10^{19}$ G, resulting in the longitudinal instability of
neutron matter. For the Skyrme force fitted to the stiffer underlying equation
of state (BSk21 vs. BSk19) the threshold $H_{th}$ and critical $H_c$ magnetic
fields become larger. The longitudinal and transverse pressures as well as the
anisotropic equation of state of neutron matter are determined under the
conditions relevant for the cores of magnetars.
