Heisenberg antiferromagnet with a low concentration of static defects

Effect of broken symmetry on resonant inelastic x-ray scattering from undoped cuprates

We study the magnetic excitation spectra of resonant inelastic x-ray scattering (RIXS) at the L-edge from undoped cuprates beyond the fast collision approximation. We analyse the effect of the symmetry breaking ground state on the RIXS process of the Heisenberg model by using a projection procedure. We derive the expressions of the scattering amplitude in both one-magnon and two-magnon excitation channels. Each of them consists of the isotropic and anisotropic contributions. The latter is a new finding and attributed to the long range order of the ground state. The presence of anisotropic terms is supported by numerical calculations on a two-dimensional spin cluster. We express the RIXS spectra in the form of spin-correlation functions with the coefficients evaluated on the cluster, and calculate the function in a two dimensional system within the 1/S expansion. Due to the anisotropic terms, the spectral intensities are considerably enhanced around momentum transfer q = 0 in both one-magnon and two-magnon excitation channels. This finding may be experimentally confirmed by examining carefully the q-dependence of the spectra.

Long-range order and low-energy spectrum of diluted 2D quantum antiferromagnet

The problem of a diluted two-dimensional quantum antiferromagnet on a square lattice is studied using spin-wave theory. The influence of impurities on static and dynamic properties is investigated and a good agreement with experiments and Monte Carlo data is found. The hydrodynamic description of spin waves breaks down at characteristic wavelengths Lambda greater than exp(const/x), x being an impurity concentration, while the order parameter is free from anomalies. We argue that this dichotomy originates from strong scattering of the low-energy excitations in two dimensions.