The exchange interactions and magnetic structure in layered system CuMnO${}_2$ (mineral crednerite) and in nonstoichiometric system Cu${}_{1.04}$Mn${}_{0.96}$O${}_2$, with triangular layers distorted due to orbital ordering of the Mn${}^{3+}$ ions, are studied by ab initio band-structure calculations, which were performed within the GGA + $U$ approximation. The exchange interaction parameters for the Heisenberg model within the Mn planes and between the Mn planes are estimated. We explain the observed in-plane magnetic structure by the dominant mechanism of the direct $d\text{−}d$ exchange between neighboring Mn ions. The superexchange via O ions, with 90${}^{\circ }$ Mn–O–Mn bonds, plays a less important role for the in-plane exchange. The interlayer coupling is largely dominated by one exchange path between the half-filled $3z^2-r^2$ orbitals of Mn${}^{3+}$. The change of interlayer coupling from antiferromagnetic in pure CuMnO${}_2$ to ferromagnetic in doped material is also explained by our calculations.

• Received 3 October 2013
• Revised 23 December 2013

DOI:https://doi.org/10.1103/PhysRevB.89.024406