The magnetism of the Fe/Cr/Sn/Cr multilayers was studied by the first-principle density functional theory. Possible reasons for an experimentally well-known drop of the hyperfine field (HFF) at Sn with a decrease of the Cr width (at 3 nm) are considered. The calculations by LAPW and SKKR methods showed that two solutions exist in the Fe9/Cr14/Sn/Cr2 system. One of them originates from the antiferromagnetic order in the bulk Cr, and the other is connected to the incommensurate spin density wave (ISDW) in Cr, which is realized in our case in a Cr film thinner than the half-length period of commonly observed ISDW. The ISDW solution is investigated in more detail with respect to its dependence on temperature and the accuracy of the Fermi-surface description. In the Cr layers with width lower than a quarter of the wave (3 nm), the ISDW cannot exist and thus cannot be a cause of the sharp drop of the Sn HFF. It is shown by the calculation of the Fe3/Cr8/Sn/Cr8 system that another possible reason for the HFF drop, connected to imperfections at the Fe/Cr interface, may cause a significant decrease in the HFF at Sn. This is shown for an interfacial Fe/Cr mixing.