  Many Heusler compounds possess magnetic properties well-suited for
applications as spintronic materials. The pseudo-binary
Mn$_{0.5}$Fe$_{0.5}$Ru$_2$Sn, formed as a solid solution of two full Heuslers,
has recently been shown to exhibit exchange hardening suggestive of two
magnetic phases, despite existing as a \textit{single} chemical phase. We have
performed a first-principles study of the chemical and magnetic degrees of
freedom in the Mn$_{1-x}$Fe$_{x}$Ru$_2$Sn pseudo-binary to determine the origin
of the unique magnetic behavior responsible for exchange hardening within a
single phase. We find a transition from antiferromagnetic (AFM) to
ferromagnetic (FM) behavior upon replacement of Mn with Fe, consistent with
experimental results. The lowest energy orderings in Mn$_{1-x}$Fe$_{x}$Ru$_2$Sn
consist of chemically- and magnetically-uniform (111) planes, with Fe-rich
regions preferring FM ordering and Mn-rich regions preferring AFM ordering,
independent of the overall composition. Analysis of the electronic structure
suggests that the magnetic behavior of this alloy arises from a competition
between AFM-favoring Sn-mediated superexchange and FM-favoring RKKY exchange
mediated by spin-polarized conduction electrons. Changes in valency upon
replacement of Mn with Fe shifts the balance from superexchange-dominated
interactions to RKKY-dominated interactions.
