In the folder "calcHP_and_vcrelax" there are -- for each of the two investigated materials -- the final iteration of the self-consistent DFT+U+V (or DFT+U) procedure, consisting in an alternate evaluation of Hubbard parameters and structural optimization, as described in the main text. For each material, there are different investigated magnetic orderings: antiferromagnetic (B-, S- and T-types) and ferromagnetic (ferro). For the DFT+U+V method there are, for each of the S- and T-types orderings, two additional states: lowest energy ones and a metastable ones. Note for the nomenclature: the "*-true" stands for "_(a)" as reported in the paper: e.g. s-type-true = S_(a). Conversely, "*-meta" refers to the metastable states "_(b)" and "_(c)" as in the main paper. For each magnetic order, there is an initial DFT(+U[+V]) calculation for the ground state total energy ("1run" folders); this calculation is however carried out with the metallic code, even if the system is insulating, in order to initialize the starting magnetization. To have magnetic state as output the insulating code (this is needed for technical reasons of the HP code), a second scf calculation is run, where we read the charge density and the wavefunctions from the first calculation, and it very quickly converges after few interations ("2run" folders). Then, we calculate the Hubbard parameters (in the folders "calc_HP") and finally, with the new parameters, we perform variable-cell structural relaxation ("relax" folders). In the folder "polarization", the organisation follows the same logic. Here, since DFT+U gives semi-metallic states (see the main paper), there are the calculations of the electric polarization in the DFT+U+V formalism only.