Theory of magnon-hole interaction for the anisotropic t-J model

The general Holstein-Primakoff transformation is used to get a theory of the magnon-hole interaction for the anisotropic t-J model in a three-dimensional tetragonal lattice. The sublattice magnetization, internal energy, and specific heat are calculated by taking into account the contributions of magnon-magnon, magnon-hole, and hole-hole as well as antiferromagnetic spin polaron interactions. We obtain a uniform expression for these quantities, which is governed by the concentration of doping and the anisotropic degree. The results show that the effect of the small interlayer coupling in a layered realistic copper-oxide superconductors turns indeed the temperature dependence of the physical quantities from two-dimensional to quasi-two-dimensional behavior at low temperature.