  Motivated by recent inelastic neutron scattering experiments up to a
high-energy region for La-based cuprates, we compute (q,omega) maps of the
imaginary part of the dynamical magnetic susceptibility chi(q,omega) in the
slave-boson mean-field approximation to the two-dimensional t-J model. While
the strong spectral weight appears at incommensurate positions, namely at q neq
Q =(pi,pi), for low energy, the incommensurate signals disperse with increasing
omega and finally merge into a commensurate signal at a particular energy
omega=omega_Q. These features are seen in both the d-wave pairing state and the
normal state. In particular, the incommensurate signals below omega_Q in the
normal state are due to the Fermi surface geometry, which we expect for
La-based cuprates because of a tendency to d-wave type Fermi surface
deformations. Above omega_Q, strong signals appear to trace an upward
dispersion especially for a low doping rate in the d-wave pairing state while
typically broad spectral weight is obtained around q=Q in the normal state.
Salient features of magnetic excitations in La-based cuprates are thus
naturally captured in terms of particle-hole excitations. Global understanding
of magnetic excitations in high-Tc cuprates is discussed through a comparison
with magnetic excitations in YBa_2Cu_3O_y.
