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The random substitutional solid solution between the antiferromagnetic (AFM)full-Heusler alloy Ru$_2$MnSn and the ferromagnetic (FM) full-Heusler alloyRu$_2$FeSn provides a rare opportunity to study FM-AFM phase competition in anear-lattice-matched, cubic system, with full solubility. At intermediate $x$in Ru$_2$Mn$_{1-x}$Fe$_x$Sn this system displays suppressed magnetic orderingtemperatures, spatially coexisting FM and AFM order, and strong coercivityenhancement, despite rigorous chemical homogeneity. Here, we construct the mostdetailed temperature- and $x$-dependent understanding of the magnetic phasecompetition and coexistence in this system to date, combiningwide-temperature-range neutron diffraction and small-angle neutron scatteringwith magnetometry and specific heat measurements on thoroughly characterizedpolycrystals. A complete magnetic phase diagram is generated, showing FM-AFMcoexistence between $x \approx 0.30$ and $x \approx 0.70$. Important newinsight is gained from the extracted length scales for magnetic phasecoexistence (25-100 nm), the relative magnetic volume fractions and orderingtemperatures, in addition to remarkable $x$-dependent trends in magnetic andelectronic contributions to specific heat. An unusual feature in the magneticphase diagram (an intermediate FM phase) is also shown to arise from anextrinsic effect related to a minor Ru-rich secondary phase. The establishedmagnetic phase diagram is then discussed with the aid of phenomenologicalmodeling, clarifying the nature of the mesoscale phase coexistence with respectto the understanding of disordered Heisenberg models.

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Understanding Magnetic Phase Coexistence in Ru$_2$Mn$_{1-x}$Fe$_x$Sn  Heusler Alloys: A Neutron Scattering, Thermodynamic, and Phenomenological  Analysis