Incommensurate Magnetic Fluctuations in the UnderdopedCopper Oxide Materials

The doping dependence of magnetic fluctuations in the underdopedcopper oxide materials are studied within the t-J model. It isshown that away from the half-filling, the magnetic Bragg peaks from the dynamical spin structure factor spectrum S(k,ω) areincommensurate with the lattice. Although the incommensurabilityδ(x) is almost energy-independent, the dynamical spin susceptibility χ^'(k,ω) at the incommensurate wave vectors is changed dramatically with energies, which is consistent with the experiments.