Theory of fractionally magnetized quantum ferromagnet

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