To investigate relations between long-range antiferromagnetic (AF) order, superconductivity and two-particle triplet collective excitations we consider a modified two dimensional $t-J$ model at doping close to half filling. The model includes additional hopping $J^{″}$ and nearest sites Coulomb repulsion V. The additional parameters allow us to control closeness of the system to the AF instability. We demonstrate the possibility of coexistence of long-range AF order and $d-g$-wave superconductivity. In the phase with long-range AF order we find, analytically, superconducting gaps and spin-wave renormalization. We demonstrate that at approaching the point of the AF instability the spin-triplet collective excitation arises with energy below the superconducting gap.

• Received 30 April 1998

DOI:https://doi.org/10.1103/PhysRevB.58.14934