Magnetic exchange interactions in SrMnO3

We calculate Heisenberg-type magnetic exchange interactions for ${\mathrm{SrMnO}}_{3}$ under isotropic volume expansion by using an approach that is based on total-energy variations due to infinitesimal spin rotations around a given reference state. Our total-energy calculations using density-functional theory (DFT) indicate a transition from antiferromagnetic to ferromagnetic coupling for increasing interatomic distances, corresponding to a sign change of the nearest-neighbor exchange interaction. This sign change cannot easily be understood from a standard superexchange mechanism. Furthermore, the exchange interaction strongly depends on the corresponding reference state. This ``non-Heisenberg'' behavior increases with increasing volume and is also confirmed through noncollinear DFT calculations. An orbital- and energy-resolved decomposition of the exchange coupling suggests that an increased partial occupancy of ${e}_{g}$ orbitals near the Fermi level is crucial both for the sign change and the non-Heisenberg behavior of the nearest-neighbor interaction. Furthermore, even though both ${e}_{g}$ and ${t}_{2g}$ contributions to the exchange interactions decay exponentially for large interatomic distances, the ${e}_{g}$ contribution remains surprisingly strong over relatively large distances along the crystal axes.