  The effects of the application of a magnetic field on the diagonal stripe
spin-glass phase is studied in lightly doped La_{2-x}Sr_xCuO_4 (x=0.014 and
0.024). With increasing magnetic field, the magnetic elastic intensity at the
diagonal incommensurate (DIC) positions (1,\pm\epsilon,0) decreases as opposed
to the increase seen in superconducting samples. This diminution in intensity
with increasing magnetic field originates from a spin reorientation transition,
which is driven by the antisymmetric exchange term in the spin Hamiltonian. On
the other hand, the transition temperature, the incommensurability, and the
peak width of the diagonal incommensurate correlations are not changed with
magnetic field. This result suggests that the magnetic correlations are
determined primarily by the charge disproportionation and that the geometry of
the diagonal incommensurate magnetism is also determined by effects, that is,
stripe formation which are not purely magnetic in origin. The
Dzyaloshinskii-Moriya antisymmetric exchange is nevertheless important in
determining the local spin structure in the DIC stripe phase.
