Radiative corrections to spin waves in the interacting hole-spin model

We investigate the quantum fluctuation effect of the two-dimensional Heisenberg antiferromagnet coupled to conduction holes via a Kondo-type exchange interaction. By the use of the large-S expansion, we find that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction around the momentum transfer Q of antiferromagnetic (AFM) fluctuations has the crucial effect of "melting" the AFM long-range order. We obtain a qualitative phase boundary as a function of temperature and hole doping. We examine analytically the effects of the renormalized spin waves on the superconducting phase. We show the effects of quantum spin fluctuations on the superconducting phase boundary and the NMR spin relaxation rate.