  Spin polarized states in neutron matter at a strong magnetic field are
considered in the model with the Skyrme effective interaction (SLy4, SLy7
parametrizations). Analyzing the self-consistent equations at zero temperature,
it is shown that a thermodynamically stable branch of solutions for the spin
polarization parameter as a function of density corresponds to the negative
spin polarization when the majority of neutron spins are oriented oppositely to
the direction of the magnetic field. Besides, beginning from some threshold
density being dependent on the magnetic field strength the self-consistent
equations have also two other branches (upper and lower) of solutions for the
spin polarization parameter with the positive spin polarization.
  The free energy corresponding to the upper branch turns out to be very close
to the free energy corresponding to the thermodynamically preferable branch
with the negative spin polarization. As a consequence, at a strong magnetic
field, the state with the positive spin polarization can be realized as a
metastable state at the high density region in neutron matter which under
decreasing density at some threshold density changes into a thermodynamically
stable state with the negative spin polarization. The calculations of the
neutron spin polarization parameter and energy per neutron as functions of the
magnetic field strength show that the influence of the magnetic field remains
small at the field strengths up to $10^{17}$ G.
