The ground state for S 0 =1 and the low-lying excited states including localized states for S 0 =1/2 of a linear Heisenberg ferromagnet of spin 1/2 containing an antiferromagnetic impurity spin are calculated, where S 0 is a magnitude of the impurity spin. In these cases they belong to the subspace spanned by the two spin deviation kets. The two magnon states are solved. The method is based on the excitation from the rigorous one magnon localized state. The wave functions and the averages of the Z component of each spin are calculated. Numerical calculations for a ring consisting of twelve spins are performed. The results are in good agreement with analytical results for the ground state energy and localized levels.
We calculate the dynamical structural factor of the
S=1 bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in
0< q< qc and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point,
qc shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in
0< q< qc. As the bond-alternation becomes strong,
qc shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is
93 which is slightly smaller than that in the
S=1 Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.