  The spin effect of electrons/positrons ($e^-$/$e^+$) and polarization effect
of $\gamma$ photons are investigated in the interaction of two
counter-propagating linearly polarized 10-PW-class laser pulses with a thin
foil target. The processes of nonlinear Compton scattering and nonlinear
Breit-Wheeler pair production based on spin- and polarization-resolved
probabilities are implemented into the particle-in-cell (PIC) algorithm by
Monte Carlo methods. It is found from PIC simulations that the average degree
of linear polarization of emitted $\gamma$ photons can exceed $50\%$. This
polarization effect leads to reduced positron yield by about $10\%$. At some
medium positron energies, the reduction can reach $20\%$. Furthermore, we also
observe that the local spin polarization of $e^-$/$e^+$ leads to a slight
decrease of the positron yield about $2\%$ and some anomalous phenomena about
the positron spectrum and photon polarization at the high-energy range, due to
spin-dependent photon emissions. Our results indicate that spin and
polarization effects should be considered in calculating the pair production
and laser-plasma interaction with the laser power of 10-PW class.
