First-principles stabilization of an unconventional collinear magnetic ordering in distorted manganites

First-principles calculations have been performed for different collinear magnetic orderings in orthorhombic manganites, such as ${\mathrm{HoMnO}}_{3}$, ${\mathrm{TbMnO}}_{3}$, and ${\mathrm{YMnO}}_{3}$, showing large ${\mathrm{GdFeO}}_{3}$-like distortions. Our results suggest that the AFM-$E$ type ordering, experimentally observed in ${\mathrm{HoMnO}}_{3}$ and recently proposed from model Hamiltonian studies, is indeed the magnetic ground state. Its stability is strongly connected with octahedral distortions and points to the relevance of structural more than chemical effects. The calculated exchange constants, extracted from a Heisenberg model used to fit the first-principles total energies, show that the ferromagnetic in-plane nearest-neighbor coupling is reduced compared to less-distorted manganites, such as ${\mathrm{LaMnO}}_{3}$. In parallel, the antiferromagnetic next-nearest-neighbor coupling along planar $\mathrm{Mn}\text{\ensuremath{-}}\mathrm{O}\text{\ensuremath{-}}\mathrm{O}\text{\ensuremath{-}}\mathrm{Mn}$ paths in highly distorted manganites plays a relevant role in the stabilization of the AFM-$E$ spin configuration. In agreement with experiments, the density of states shows that this phase is insulating with an indirect band gap of $\ensuremath{\sim}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.