Effect of atomic disorder and temperature on incommensurate helical spin waves in the Anderson–Hubbard model

Based on the single-band $t$–$t'$ Anderson–Hubbard model, the effect of disorder on the parameters and ranges of existence of incommensurate helical spin waves is studied. The problem is solved within the functional integration theory in static approximation, taking into account longitudinal fluctuations of the magnetic moment. Magnetic phase diagrams and parameters of incommensurate helical spin waves are obtained as functions of temperatures and electron and impurity concentrations. It is shown that disorder can lead to the first-order transition from the antiferromagnetic phase to the $(Q,\pi)$ phase and the metal–dielectric transition from antiferromagnetic metal to antiferromagnetic dielectric far from the half-filled band. The results obtained are used to explain the incommensurate magnetic order observed in cuprates in the overdoped mode.