Quantum nonlinear sigma model and spin-wave theory studies of lamellar quantum Heisenberg antiferromagnets with random nonmagnetic impurities

We have studied the static and dynamic magnetic properties of Heisenberg quantum antiferromagnets (QHAF) diluted by random nonmagnetic impurities, such as La₂Cu_1−xM _xO₄ (M = Mg, Zn), using spin-wave theory and the quantum nonlinear sigma model (QNLσM). To study the interplay of quantum fluctuations and non-magnetic disorder on La₂Cu_{1− x}M_xO₄, we modeled the lamellar QHAF as a lattice with tetragonal symmetry and studied the system using spin-wave theory in the ordered phase and modified spin-wave theory in the paramagnetic phase. The Green's function method was applied to study the magnetic properties of La₂Cu_{1− x}M_xO₄. The nonmagnetic disorder is treated by the single-site averaged t-matrix approximation. We calculated the local magnetic moment, the two-dimensional spin-correlation length, the nuclear relaxation rate, and the 3D Néel temperature, all of which showed good agreement with the available data of quantum MC simulations and experiments. We found that the hydrodynamic description of spin-wave breaks down at a characteristic wave-vector k_c, while the order parameter is free from anomalies. We argue that this dichotomy originates from the strong scattering of the low-energy excitations in two dimensions. We alternatively propose a two-dimensional effective-field theory (the quantum nonlinear sigma model) combined with classical percolation theory to study the enhanced effects of quantum fluctuations on the magnetic properties of La₂Cu_1−xM _xO₄ introduced by the nonmagnetic disorder. The spin stiffness and the spin-wave velocity are renormalized by nonmagnetic dilution according to classical percolation theory. Both theories show that the effect of quantum fluctuations on the suppression of magnetic ordering is enhanced by nonmagnetic doping.