The compound BaFe${}_2$As${}_2$ is the proptotypical example of the 122 family of high-$T_c$ Fe-based superconductors that crystallize in the ThCr${}_2$Si${}_2$ structure. Isostructural compounds can be formed by replacing Fe with another transition metal; using Mn produces the material BaMn${}_2$As${}_2$, which unlike its Fe-based cousin has an insulating ground state with a large magnetic moment of $3.9{\mu }_B$ and G-type antiferromagnetic order. Despite its lack of superconductivity, the material is interesting in its own right. Recent experimental studies have shown that hole doping the compound by substituting K for Ba leads to metallic behavior and a spontaneous, weak, in-plane magnetization, which was attributed to the holes fully polarizing independent of the Mn moments, producing half-metallic behavior. However, the observed in-plane magnetization can also be understood as a small canting of the Mn moments. Using density functional theory, we demonstrate that a Mn moment canting occurs upon hole doping the compound. We argue that this is due to the competition between the super- and double-exchange interactions, which we support using a simple tight-binding model of the superexchange–double-exchange interaction and the Andersen force theorem. Our calculations also rule out an in-plane polarization of As holes as an explanation for the in-plane magnetization.

• Received 6 November 2013

DOI:https://doi.org/10.1103/PhysRevB.89.060403