“…In Table I, we report the total energies ͑calculated per formula unit containing one Mn atom͒ with respect to the FM phase. If we restrict to the FM and AFM-A, C, and G orderings ͑i.e., we neglect possible next-nearest-neighbors AFM coupling͒, the situation for HoMnO 3 , TbMnO 3 , and YMnO 3 is common to the well studied LaMnO 3 , where the most stable magnetic configuration, as experimentally observed 16 and theoretically confirmed, 17,18 is the AFM-A type. 19 However, the inclusion of the AFM-E in the subset of considered magnetic configurations largely changes the scenario: interestingly, among the collinear magnetic orderings, ͑i͒ HoMnO 3 show AFM-E as a magnetic ground state, in excellent agreement with experiments, ͑ii͒ both YMnO 3 and TbMnO 3 show the AFM-E type TABLE I.…”