Two-Dimensional Fractionally Magnetized Quantum Ferromagnet

We present a theory to realize fractionally magnetized quantum ferromagnet in a
$\mathbf{spin}-S \geqq 2$
bilinear-biquadratic spin systems. The origin of the fractionally magnetized state is spin-liquefaction of ferromagnetism which means partly emergent antiferromagnetism. The realization of the spin-liquefaction of ferromagnetism is guaranteed due to a rigorous eigenstate correspondence between the
$\mathbf{Spin}-S$
model and
$\mathbf{spin} - \frac{1}{2}$
model, i. e., “eigensystem embedding”. This spin-liquefaction theory of ferromagnets can be generalized to any-dimensional lattices. As a typical case, we discuss the two-dimensional models on a square lattice with a numerical exact-diagonalization.