We obtained a time series of spectra covering the secondary maximum in the I band of the bright Type Ia supernova 2014J in M82 with the TIGRE telescope. Comparing the observations with theoretical models calculated with the time dependent extension of the phoenix code, we identify the feature that causes the secondary maximum in the I-band light curve. Fe ii 3d6(3D)4s–3d6(5D)4p and similar high-excitation transitions produce a blended feature at ∼7500 Å, which causes the rise of the light curve towards the secondary maximum. The series of observed spectra of SN 2014J and archival data of SN 2011fe confirm this conclusion. We further studied the plateau phase of the R-band light curve of SN 2014J and searched for features which contribute to the flux. The theoretical models do not clearly indicate a new feature that may cause the R-band plateau phase. However, Co ii features in the range of 6500–7000 Å and the Fe ii feature of the I band are clearly seen in the theoretical spectra, but do not appear to provide all of the flux necessary for the R-band plateau.