  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.
