  We use neutron scattering to study the influence of a magnetic field on spin
structures of Nd$_2$CuO$_4$. On cooling from room temperature, Nd$_2$CuO$_4$
goes through a series of antiferromagnetic (AF) phase transitions with
different noncollinear spin structures. While a c-axis aligned magnetic field
does not alter the basic zero-field noncollinear spin structures, a field
parallel to the CuO$_2$ plane can transform the noncollinear structure to a
collinear one ("spin-flop" transition), induce magnetic disorder along the
c-axis, and cause hysteresis in the AF phase transitions. By comparing these
results directly to the magnetoresistance (MR) measurements of
Nd$_{1.975}$Ce$_{0.025}$CuO$_4$, which has essentially the same AF structures
as Nd$_2$CuO$_4$, we find that a magnetic-field-induced spin-flop transition,
AF phase hysteresis, and spin c-axis disorder all affect the transport
properties of the material. Our results thus provide direct evidence for the
existence of a strong spin-charge coupling in electron-doped copper oxides.
