  We present a theory to realize entangled quantum spin states with fractional
magnetization. The origin of magnetization reduction is partly emergent
antiferromagnetism, that is, spin-liquefaction of ferromagnetism. We study a
ferromagnetic bilinear coupling region of the spin-$S$ $({\geqq} 1)$
bilinear-biquadratic spin chain based on (i) a rigorous eigenstate
correspondence between the spin-$S$ model and spin-$\frac12$ model and (ii) a
numerical exact-diagonalization calculation up to $S=3$. As a result, we obtain
a fractional magnetized $M=1-1/(2S)$ phase, where ground states have quantum
entanglement-reflecting corresponding spin-$\frac12$ antiferromagnetic ground
states in a ferromagnetic background. This spin-liquefaction theory of
ferromagnets can be generalized to any-dimensional lattices even under a
magnetic field. This fractional ferromagnetism opens the new research field of
quantum ferromagnets.
