  We introduce the spin entanglement entropy (EE) to characterize spin
excitations. The scalings of EEs are elaborated as $\ln N$, $\ln N+D_k$ and
$2\ln N+D$ for the single-magnon states, two-magnon bound states and two-magnon
continuum, respectively, based on the Bethe ansatz solutions of the
ferromagnetic spin chain with $N$ sites. The $\ln N$ divergence for the bound
states reveals the two magnons emerge as a new quasiparticle. More importantly,
the nonzero intercepts ($D_k,D$) embody the many-body effects of two-magnon
states. In particular, an exact relation between the intercept of EEs and an
observable quantity, the two-magnon distance, is established for the bound
states. In such a case, we quantify the two-magnon confinement in a spin system
by the increasing entanglement with the distance as a particle physics
analogue. Moreover, the EEs can also be used to study the evolution of the
excitations. When the bound states are immersed in the continuum in the
alternating chain, they undergo an oscillating confinement-deconfinement
crossover, shown by the oscillations of the EEs and two-magnon distance with
the chain length.
