Mechanisms of the magnetic incommensurability in p-type cuprate perovskites

We use the t-J model and Mori projection operator formalism for calculating the magnetic susceptibility of p-type cuprates in the superconducting and pseudogap phases. The lack of extended tails in the peaks of the hole spectral function was shown to provide an incommensurate low-frequency response with hole dispersions derived from photoemission. The theory reproduces the hourglass dispersion of the susceptibility maxima with the upper branch reflecting the dispersion of localized spin excitations and the lower branch being due to incommensurate maxima of their damping. The intensive resonance peak appears when the hourglass waist falls below the bottom of the electron-hole continuum. In the pseudogap phase, the Fermi arcs lead to a quasi-elastic incommensurate response for low temperatures. This result explains the lack of the superconducting gap in the susceptibility of phase-separated underdoped lanthanum cuprates. It may also explain the strengthening of the quasi-elastic response by magnetic fields and impurities. The theory accounts for the magnetic stripe reorientation from the axial to diagonal direction at low hole concentrations.