  The electronic structure of the rare-earth mononitrides LnN (where
Ln=rare-earth), which are promising materials for future spintronics
applications, is difficult to resolve experimentally due to a strong influence
of defects on their transport and optical properties. At the same time, LnN are
challenging for theory, since wide semiconducting/semimetallic 2p and 5d bands
need to be described simultaneously with strongly correlated 4f states. Here,
we calculate the many-body spectral functions and optical gaps of a series of
LnN (with Ln= Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er) by a density-functional+dynamical
mean-field theory (DFT+DMFT) approach treating the correlated Ln 4f shells
within the quasi-atomic Hubbard-I approximation. The on-site Coulomb
interaction in the 4f shell is evaluated by a constrained DFT+Hubbard-I
approach. Furthermore, to improve the treatment of semiconducting bands in
DFT+DMFT, we employ the modified Becke-Johnson semilocal exchange potential.
Focusing on the paramagnetic high-temperature phase, we find that all
investigated LnN are pd semiconductors with gap values ranging from 1.02 to
2.14 eV along the series. The pd band gap is direct for light Ln= La...Sm and
becomes indirect for heavy rare-earths. Despite a pronounced evolution of the
Ln 4f states along the series, empty 4f states are invariably found above the
bottom of the 5d conduction band. The calculated spectra agree well with those
available from x-ray photoemission, x-ray emission and x-ray absorption
measurements.
