  Spin polarized states in dense neutron matter with recently developed Skyrme
effective interaction (BSk20 parametrization) are considered in the magnetic
fields $H$ up to $10^{20}$ G at finite temperature. In a strong magnetic field,
the total pressure in neutron matter is anisotropic, and the difference between
the pressures parallel and perpendicular to the field direction becomes
significant at $H>H_{th}\sim10^{18}$ G. The longitudinal pressure decreases
with the magnetic field and vanishes in the critical field
$10^{18}<H_c\lesssim10^{19}$ G, resulting in the longitudinal instability of
neutron matter. With increasing the temperature, the threshold $H_{th}$ and
critical $H_c$ magnetic fields also increase. The appearance of the
longitudinal instability prevents the formation of a fully spin polarized state
in neutron matter and only the states with moderate spin polarization are
accessible. The anisotropic equation of state is determined at densities and
temperatures relevant for the interiors of magnetars. The entropy of strongly
magnetized neutron matter turns out to be larger than the entropy of the
nonpolarized matter. This is caused by some specific details in the dependence
of the entropy on the effective masses of neutrons with spin up and spin down
in a polarized state.
