Presently we report spin-polarized state transport in semiconductor-dielectric-iron-semiconductor (SDIS) four-nanolayer sandwich devices. The exchange-resonance spectra in such devices are quite specific, differing also from spectra observed earlier in other three-nanolayer devices. The theoretical model developed earlier is extended and used to interpret the available experimental results. A detailed ab initio analysis of the magnetic-field dependence of the output magnetic moment is also performed. The model predicts an exchange spectrum comprising a series of peaks, with the spectral structure determined by several factors, discussed in the paper. Published by Elsevier Ltd.