Modest magnetic field gradients in the region of a reflecting sample s
urface (either magnetic or nonmagnetic) are sufficient to significantl
y perturb neutron reflectivity. Polarized neutron experiments on a 850
Angstrom-thick film of deuterated polystyrene on silicon showed a sig
nificant spin dependence of the reflectivity when the material was sur
rounded by magnetic circuitry that provided a transverse gradient (Del
ta B similar or equal to 0.004 MA m(-1) when integrated over the neutr
on path. The main effect of a field gradient is to modify the componen
t of the neutron momentum perpendicular to the surface, k(z0), to k(z)
(+/-) = (k(z0)(2) +/- c)(1/2). The sign indicates the neutron spin ori
entation relative to the applied field and c is proportional to Delta
B. The effect may be of some use: the insertion of a known gradient ar
ound a nonmagnetic sample permits the set of measurements necessary to
obtain the reflectivity of the sample not only in amplitude but also
in phase.