Incommensurate magnetic fluctuations in the underdoped copper oxide materials

The doping dependence of magnetic fluctuations in the underdoped copper oxi de materials are studied within the t-J model. It is shown that away from t he half-filling, the magnetic Bragg peaks from the dynamical spin structure factor spectrum S(k,omega) are incommensurate with the lattice. Although t he incommensurability delta (x) is almost energy-independent, the dynamical spin susceptibility chi " (k,omega) at the incommensurate wave vectors is changed dramatically with energies, which is consistent with the experiment s.