| Summary: | <p>Synchrotron X-ray powder diffraction data indicate that La<small><sub>0.5</sub></small>Sr<small><sub>0.5</sub></small>Mn<small><sub>0.5</sub></small>Rh<small><sub>0.5</sub></small>O<small><sub>3</sub></small> and La<small><sub>0.5</sub></small>Sr<small><sub>0.5</sub></small>Fe<small><sub>0.5</sub></small>Rh<small><sub>0.5</sub></small>O<small><sub>3</sub></small> adopt distorted perovskite structures (space group <em>Pnma</em>) with <em>A</em>-site and <em>B</em>-site cation disorder. A combination of XPS and <small><sup>57</sup></small>Fe Mössbauer data indicate the transition metal cations in the two phases adopt Mn<small><sup>3+</sup></small>/Rh<small><sup>4+</sup></small> and Fe<small><sup>3+</sup></small>/Rh<small><sup>4+</sup></small> oxidation state combinations respectively. Transport data indicate both phases are insulating, with <em>ρ vs</em>. <em>T</em> dependences consistent with 3D variable-range hopping. Magnetisation data reveal that La<small><sub>0.5</sub></small>Sr<small><sub>0.5</sub></small>Mn<small><sub>0.5</sub></small>Rh<small><sub>0.5</sub></small>O<small><sub>3</sub></small> adopts a ferromagnetic state below <em>T</em><small><sub>c</sub></small> ∼ 60 K, which is rationalized on the basis of coupling <em>via</em> a dynamic Jahn–Teller distortion mechanism. In contrast, magnetic data reveal La<small><sub>0.5</sub></small>Sr<small><sub>0.5</sub></small>Fe<small><sub>0.5</sub></small>Rh<small><sub>0.5</sub></small>O<small><sub>3</sub></small> undergoes a transition to a spin-glass state at <em>T</em> ∼ 45 K, attributed to frustration between nearest-neighbour Fe–Rh and next-nearest-neighbour Fe–Fe couplings.</p>
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