Temperature dependence of magnetization and optical magnon gap in bilayer antiferromagnetic YBa₂Cu₃O₆

Abstract

We study the magnetization and spin excitations of anisotropic bilayer antiferromagnets. We consider a model Hamiltonian which incorporates the inplane, the intrabilayer and the interlayer exchange couplings for a cuprate which has two CuO₂ layers per unit cell. The expression for the sublattice magnetization is obtained by employing the Green's function technique and we have used the Callen decoupling approximation. The numeral results, obtained using the parameters appropriate for YBa₂Cu₃O₆, a bilayer antiferromagnet, show that Callen decoupling procedure gives a value of the Neel temperature which is in reasonable agreement with the measured value of 450 K for YBa₂Cu₃O₆. We have discussed the effects of anisotropy in exchange coupling constants on the Neel temperature of the system and results for the 3D case are also presented. Further, we obtain energy values for the spin excitations (magnons) of the bilayer systems. The excitation spectrum consists of two branches namely the acoustic branch and the optic branch. These branches are separated by an energy gap and the value of this gap at zero wave vector is known as optical magnon gap E_G. This gap is found to be dependent on temperature as well as on the anisotropy in the values of the exchange coupling parameters of the system. We have numerically evaluated the anisotropy and the temperature dependence of E_G for YBa₂Cu₃O₆.