Field dependence of the magnetic spectrum in anisotropic and Dzyaloshinskii-Moriya antiferromagnets. I. Theory

We consider theoretically the effects of an applied uniform magnetic field on the magnetic spectrum of anisotropic two-dimensional and Dzyaloshinskii-Moriya layered quantum Heisenberg antiferromagnets. The former case is relevant for systems such as the two-dimensional square lattice antiferromagnet Sr2CuO2Cl2, while the latter is known to be relevant to the physics of the layered orthorhombic antiferromagnet La2CuO4. We first establish the correspondence between the low-energy spectrum obtained within the anisotropic nonlinear sigma model and by means of the spin-wave approximation for a standard easy-axis antiferromagnet. Then, we focus on the field-theory approach to calculate the magnetic-field dependence of the magnon gaps and spectral intensities for magnetic fields applied along the three possible crystallographic directions. We discuss the various possible ground states and their evolution with temperature for the different field orientations, and the occurrence of spin-flop transitions for fields perpendicular to the layers (transverse fields) as well as for fields along the easy axis (longitudinal fields). Measurements of the one-magnon Raman spectrum in Sr2CuO2Cl2 and La2CuO4 and a comparison between the experimental results and the predictions of the present theory will be reported in paper II of this research work [ L. Benfatto et al. Phys. Rev. B 74 024416 (2006)].