  We investigate how a phase transition from neutron-star matter to
spin-polarized neutron matter affects the equation of state and mass-radius
relation of neutron stars. While general extension schemes for the equation of
state allow for high pressures inside neutron stars, we find that a phase
transition to spin-polarized neutron matter excludes extreme regimes. Hence,
such a transition limits the maximum mass of neutron stars to lie below
2.6$-$$2.9 \, M_{\odot}$, depending on the microscopic nuclear forces used,
while significantly larger masses could be reached without these constraints.
These limits are in good agreement with recent constraints extracted from the
neutron-star merger GW170817 and its electromagnetic counterpart. Assuming the
description in terms of spin-polarized neutron matter to be valid in the center
of neutron stars, we find that stars with a large spin-polarized domain in
their core are ruled out by GW170817.
