We present a detection scheme to search for QCD axion dark matter, that is based on a direct interaction between axions and electrons explicitly predicted by DFSZ axion models. The local axion dark matter field shall drive transitions between Zeeman-split atomic levels separated by the axion rest mass energy m a c 2. Axion-related excitations are then detected with an upconversion scheme involving a pump laser that converts the absorbed axion energy (~hundreds of μeV) to visible or infrared photons, where single photon detection is an established technique. The proposed scheme involves rare-earth ions doped into solid-state crystalline materials, and the optical transitions take place between energy levels of 4f N electron configuration. Beyond discussing theoretical aspects and requirements to achieve a cosmologically relevant sensitivity, especially in terms of spectroscopic material properties, we experimentally investigate backgrounds due to the pump laser at temperatures in the range 1.9 - 4.2 K. Our results rule out excitation of the upper Zeeman component of the ground state by laser-related heating effects, and are of some help in optimizing activated material parameters to suppress the multiphonon-assisted Stokes fluorescence.