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The spontaneous spin polarization of strongly interacting matter due toaxial-vector and tensor type interactions is studied at zero temperature andhigh baryon-number densities. We start with the mean-field Lagrangian for theaxial-vector and tensor interaction channels, and find in the chiral limit thatthe spin polarization due to the tensor mean field ($U$) takes place first asthe density increases for sufficiently strong coupling constants, and then thatdue to the axial-vector mean field ($A$) emerges in the region of finite tensormean field. This can be understood that making the axial-vector mean fieldfinite requires a broken chiral symmetry somehow, which is achieved by thefinite tensor mean field in the present case. It is also found from symmetryargument that there appear the type I (II) Nambu-Goldstone modes with a linear(quadratic) dispersion in the spin polarized phase with $U\neq0$ and $A=0$($U\neq0$ and $A\neq0$), although these two phases exhibit the same symmetrybreaking pattern.

Spin polarized phases in strongly interacting matter: interplay between axial-vector and tensor mean fields