  We report on the use of the polarized $^3$He gas filter and neutron resonant
enhancement techniques for the measurement of spin-polarized diffuse neutron
scattering due to ferromagnetic domains. A CoO/Co exchange biased bilayer was
grown on a Ti/Cu/$Al_2O_3$ neutron resonator template. The system is cooled in
an applied magnetic field of $H_a=2000$ Oe through the N\'{e}el temperature of
the antiferromagnet to 10 K where the applied magnetic field is swept as to
measure the magnetic hysteresis loop. After the second magnetization reversal
at the coercive field $H_{c2}=+ 230$ Oe, the system is supposed to approach the
original magnetic configuration. In order to prove that this is not the case
for our exchange biased bilayer, we have measured four off-specular maps I++,
I+-, I-+, I-- at $H_a \approx + 370$ Oe, where the Co magnetic spins were
mostly reversed. They show a striking behavior in the total reflection region:
while the nonspin-flip scattering exhibits no diffuse reflectivity, the
spin-flip scattering shows strong diffuse scattering at incident angles which
satisfy the resonance conditions. Moreover the spin-flip off-specular part of
the reflectivity is asymmetric. The I-+ intensity occurs at higher exit angles
than the specularly reflected neutrons, and the I+- intensity is shifted to
lower angles. Their intensities are noticeably different and there is a
splitting of the resonance positions for the up and down neutron spins
($\alpha_{n} ^{+} \ne \alpha_{n} ^{-}$) . Additionally, a strong influence of
the stray fields from magnetic domains to the resonance splitting is observed.
