Elementary-spin-excitation spectrum of undoped and doped single-band Hubbard models

We have calculated the elementary-spin-excitation spectrum of undoped and doped Hubbard models in one and two dimensions. We have obtained the gap of the spectrum at Q=({π},{π}) in the doped strong-coupling Hubbard model by a Lanczos diagonalization study of the {}10 ×{} {}10 site cluster. The result is qualitatively in agreement with the experimental observation of the ``spin gap'' by Rossat-Mignod et al. We conclude that the ``spin gap'' can be accounted for with the doped strong-coupling Hubbard model without any symmetry reductions and is one of the intrinsic properties of the Hubbard model.