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We report on a comprehensive study of the magnetic coupling between soft magnetic Fe layers and hard magnetic Dysprosium (Dy) layers at low temperatures (4.2 - 120K). For our experiments we prepared thin films of Fe and Dy and multilayers of Fe/Dy by ultra-high vacuum sputtering. The magnetic properties of each material were determined with a superconducting quantum interference device. Furthermore, we performed magnetoresistance measurements with similarly grown, microstructured devices, where the anisotropic magnetoresistance (AMR) effect was used to identify the magnetization state of the samples. By analyzing and comparing the corresponding data of Fe and Dy, we show that the presence of a Dy layer on top of the Fe layer significantly influences its magnetic properties and makes it magnetically harder. We perform a systematic evaluation of this effect and its dependence on temperature and on the thickness of the soft magnetic layer. All experimental results can consistently be explained with exchange coupling at the interface between the Fe and the Dy layer. Our experiments also yield a negative sign of the AMR effect of thin Dy films, and an increase of the Dy films' Curie temperature, which is due to growth conditions.