  The quantum size effect on the in-plane paramagnetic critical field in Pb
nanofilms is investigated with the use of the spin-generalized Bogolubov-de
Gennes equations. It is shown that the critical field oscillates as a function
of the nanofilm thickness with the period of $\sim2$ ML (even-odd oscillations)
modulated by the beating effect. This phenomena is studied in terms of the
quantization of the electron energy spectra caused by the confinement of the
electron motion in the direction perpendicular to the sample. The calculated
values of critical fields for different nanofilm thicknesses are analyzed in
the context of Clogston-Chandrasekhar limit. The influence of the thermal
effect on the magnetic field induced superconductor to normal metal transition
is also discussed. Furthermore, the thickness-dependence of the electron-phonon
coupling and its influence on the value of the critical magnetic field are
studied.
