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-$S$ ($\geqq 1$) 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 $M=1-1/\left(2S\right)$ 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.

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• Fractionalization
• Magnetic order
• Magnetism
• Quantum entanglement
• Quantum phase transitions
• Spin liquid
• 1-dimensional spin chains
• Exact diagonalization
• Exact solutions for many-body systems