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First-principles evidence of Mn moment canting in hole-doped Ba$_{1-2x}$K$_{2x}$Mn$_{2}$As$_{2}$

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 $3.9 μ_{B}$ 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.