  The random substitutional solid solution between the antiferromagnetic (AFM)
full-Heusler alloy Ru$_2$MnSn and the ferromagnetic (FM) full-Heusler alloy
Ru$_2$FeSn provides a rare opportunity to study FM-AFM phase competition in a
near-lattice-matched, cubic system, with full solubility. At intermediate $x$
in Ru$_2$Mn$_{1-x}$Fe$_x$Sn this system displays suppressed magnetic ordering
temperatures, spatially coexisting FM and AFM order, and strong coercivity
enhancement, despite rigorous chemical homogeneity. Here, we construct the most
detailed temperature- and $x$-dependent understanding of the magnetic phase
competition and coexistence in this system to date, combining
wide-temperature-range neutron diffraction and small-angle neutron scattering
with magnetometry and specific heat measurements on thoroughly characterized
polycrystals. A complete magnetic phase diagram is generated, showing FM-AFM
coexistence between $x \approx 0.30$ and $x \approx 0.70$. Important new
insight is gained from the extracted length scales for magnetic phase
coexistence (25-100 nm), the relative magnetic volume fractions and ordering
temperatures, in addition to remarkable $x$-dependent trends in magnetic and
electronic contributions to specific heat. An unusual feature in the magnetic
phase diagram (an intermediate FM phase) is also shown to arise from an
extrinsic effect related to a minor Ru-rich secondary phase. The established
magnetic phase diagram is then discussed with the aid of phenomenological
modeling, clarifying the nature of the mesoscale phase coexistence with respect
to the understanding of disordered Heisenberg models.
