Spin Wave Theory of the Two-Dimensional Heisenberg Antiferromagnet Coupled with Localized Holes

Abstract

The spin wave theory of the two-dimensional Heisenberg antiferromagnet on a square lattice coupled with localized holes, i.e., extra spins, is investigated. This model is a limiting case of the coupled spin-fermion model presented recently to investigate the magnetic mechanism of high- T _c superconductivity. Two schemes of the spin wave theory are proposed according to the relative magnitude of J _K (coupling between the extra and the substrate spins) to J _S (coupling between the substrate spins). The following conclusions are obtained. (1) Small antiferromagnetic (AF) J _K as well as ferromagnetic (F) J _K enhances the AF long-range order suppressing the quantum fluctuations. Large AF J _K , however, reduces the AF long-range order and enhances the quantum fluctuations. We obtain the large attractive interaction only in the latter case. (2) The susceptibility χ _⊥ perpendicular to the staggered magnetization is logarithmically divergent with respect to the external frequency ω when one extra spin is introduced.