  The influence of a uniform external magnetic field on the dynamical spin
response of cuprate superconductors in the superconducting state is studied
based on the kinetic energy driven superconducting mechanism. It is shown that
the magnetic scattering around low and intermediate energies is dramatically
changed with a modest external magnetic field. With increasing the external
magnetic field, although the incommensurate magnetic scattering from both low
and high energies is rather robust, the commensurate magnetic resonance
scattering peak is broadened. The part of the spin excitation dispersion seems
to be an hourglass-like dispersion, which breaks down at the heavily low energy
regime. The theory also predicts that the commensurate resonance scattering at
zero external magnetic field is induced into the incommensurate resonance
scattering by applying an external magnetic field large enough.
