Resonance peak and incommensurability in cuprate perovskites

The magnetic susceptibility of yttrium and lanthanum cuprates is interpreted based on the self-consistent solution of the t-J model of Cu-O planes. To take a proper account of strong electron correlations inherent in cuprates, the calculations were carried out in the formalism of the Hubbard operators and Mori’s projection operator technique. The calculations correctly reproduce the frequency and momentum dependences of the resonance peak in YBa₂Cu₃O_{7 ? y} and its variation with doping and temperature in the normal and superconducting states. In lanthanum cuprates, spin excitations near the antiferromagnetic wave vector Q = (π, π) are overdamped and, therefore, a broad maximum is observed in the susceptibility instead of a sharp peak. For low frequencies, temperatures, and hole concentrations x ≥ 0.02, the susceptibility is peaked at incommensurate wave vectors (π ± 2πδ, π), (π, π ± 2πδ). The incommensurability is connected with the minimum in the magnon damping at Q in the crystal with a short-range antiferromagnetic order. Generally, the incommensurate magnetic response is not accompanied by an inhomogeneity of the charge-carrier density.