  As additional neutron scattering experiments are performed on a variety of
high temperature superconducting compounds it appears that magnetic
incommensuration is a phenomenon common to all of the samples studied. The
newest experimental results indicate that incommensurate peaks exist at
momentum ${\bf q}=\pi(1,1\pm\delta)$ and $\pi(1\pm\delta,1)$ in
$La_{2-x}Sr_xCuO_4}$ (LSCO) and ${\rm YBa_2Cu_3O_{7-\delta}}$ (YBCO). The
dependence of $\delta$ with hole doping appears to be similar in both
materials. In addition, new ARPES data for LSCO as a function of doping show
that its Fermi surface is qualitatively similar to the one of YBCO, contrary to
what was previously believed. Early theoretical attempts to explain LSCO and
YBCO behavior usually relied on one- or three-band Hubbard models or the t-J
model with electron hopping beyond nearest-neighbor and with different
parameter values for each material. In this paper it is shown that using a one
band Hubbard U-t-$t'$ model with a unique set of parameters, U/t=6 and
$t'$/t=-0.25, good agreement is obtained between computational calculations and
neutron scattering and ARPES experiments for LSCO and YBCO. It is also shown
that using a more negative $t'$/t will induce short-range magnetic
incommensuration along the diagonal direction in the Brillouin zone, in
qualitative disagreement with the experimental results. At the finite
temperatures of the present Monte Carlo simulation it is also observed that in
this model the tendency to incommensuration appears to be more related to the
shape of the two-dimensional Fermi surface and the strength of the interaction,
rather than to charge order.
