Role of next-nearest-neighbor hopping in thet-t’-Jmodel

A next-nearest-neighbor hopping t’ in the t-t’-J model has a different sign between the hole- and electron-doped systems of high-${\mathit{T}}_{\mathit{c}}$ cuprates: t’<0 for the hole-doped system and t’>0 for the electron-doped system. We show that the sign is responsible for the remarkable difference of antiferromagnetic (AF) phases between the two systems. To reveal this and clarify the role of t’, we examine magnetic excitations of the t-t’-J model by employing exact diagonalization techniques for 4×4 and √18 × √18 lattices. In the low-doping region (two-hole case of the √18 × √18 lattice), AF spin correlations are stabilized for the case of t’>0, i.e., electron-doping case, but not for the case of t’<0. In the high-doping region (four-hole case of the 4×4 lattice and more) magnetic excitations are mainly controlled by the geometry of the Fermi surface of the noninteracting system.