  Equation of states (EOS) of the spin-polarized nuclear matter (NM) is studied
within the Hartree-Fock (HF) formalism using the realistic density dependent
nucleon-nucleon interaction. With a nonzero fraction $\Delta$ of spin-polarized
baryons in NM, the spin- and spin-isospin dependent parts of the HF energy
density give rise to the \emph{spin symmetry} energy that behaves in about the
same manner as the \emph{isospin symmetry} energy, widely discussed in
literature as the nuclear symmetry energy. The present HF study shows a strong
correlation between the spin symmetry energy and nuclear symmetry energy over
the whole range of baryon densities. The important contribution of the spin
symmetry energy to the EOS of the spin-polarized NM is found to be comparable
with that of the nuclear symmetry energy to the EOS of the isospin-polarized or
asymmetric (neutron-rich) NM. Based on the HF energy density, the EOS of the
spin-polarized ($\beta$-stable) np$e\mu$ matter is obtained for the
determination of the macroscopic properties of neutron star (NS). A realistic
density dependence of the spin-polarized fraction $\Delta$ have been suggested
to explore the impact of the spin symmetry energy to the gravitational mass $M$
and radius $R$, as well as the tidal deformability of NS. Given the empirical
constrains inferred from a coherent Bayesian analysis of gravitational wave
signals of the NS merger GW170817 and the observed masses of the heaviest
pulsars, the strong impacts of the spin symmetry energy $W$, nuclear symmetry
energy $S$, and nuclear incompressibility $K$ to the EOS of nucleonic matter in
magnetar were revealed.
