Frustrated magnetism in the double perovskite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="normal">L</mml:mi><mml:msub><mml:mi mathvariant="normal">a</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi>LiOs</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>: A comparison with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="normal">L</mml:mi><mml:msub><mml:mi mathvariant="normal">a</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi>LiRu</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>

The frustrated double perovskite $\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiOs}{\mathrm{O}}_{6}$, based on $\mathrm{O}{\mathrm{s}}^{5+}\phantom{\rule{0.16em}{0ex}}(5{d}^{3},\phantom{\rule{0.16em}{0ex}}{\mathrm{t}}_{2}^{3})$ is studied using magnetization, elastic neutron scattering, heat capacity, and muon spin relaxation (\ensuremath{\mu}SR) techniques and compared with isostructural $(P{2}_{1}/n)\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiRu}{\mathrm{O}}_{6},\phantom{\rule{0.16em}{0ex}}\mathrm{R}{\mathrm{u}}^{5+}(4{d}^{3},\phantom{\rule{0.16em}{0ex}}{\mathrm{t}}_{2}^{3})$. While previous studies of $\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiOs}{\mathrm{O}}_{6}$ showed a broad susceptibility maximum $({\ensuremath{\chi}}_{\mathrm{max}})$ near 40 K, heat capacity data indicate a sharp peak at 30 K, similar to $\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiRu}{\mathrm{O}}_{6}$ with ${\ensuremath{\chi}}_{\mathrm{max}}\ensuremath{\sim}30\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and a heat capacity peak at 24 K. Significant differences between the two materials are seen in powder neutron diffraction where the magnetic structure is described by $\mathbit{k}=(1/2\phantom{\rule{0.16em}{0ex}}1/2\phantom{\rule{4pt}{0ex}}0)$ for $\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiOs}{\mathrm{O}}_{6}$, while $\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiRu}{\mathrm{O}}_{6}$ has been reported with $\mathbit{k}=(000)$, structure for face centered lattices. For the $\mathbit{k}=(1/2\phantom{\rule{0.16em}{0ex}}1/2\phantom{\rule{4pt}{0ex}}0)$ structure, one has antiferromagnetic layers stacked antiferromagnetically, while for $\mathbit{k}=(0\phantom{\rule{0.16em}{0ex}}0\phantom{\rule{0.16em}{0ex}}0)$ structure, ferromagnetic layers are stacked antiferromagnetically. In spite of these differences, both can be considered as type I fcc antiferromagnetic structures. For $\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiOs}{\mathrm{O}}_{6}$, the magnetic structure is best described in terms of linear combinations of basis vectors belonging to irreducible representations ${\mathrm{\ensuremath{\Gamma}}}_{2}$ and ${\mathrm{\ensuremath{\Gamma}}}_{4}$. The combinations ${\mathrm{\ensuremath{\Gamma}}}_{2}--{\mathrm{\ensuremath{\Gamma}}}_{4}$ and ${\mathrm{\ensuremath{\Gamma}}}_{2}+{\mathrm{\ensuremath{\Gamma}}}_{4}$ could not be distinguished from refinement of the data. In all cases, the $\mathrm{O}{\mathrm{s}}^{5+}$ moments lie in the $yz$ plane with the largest component along $y$. The total moment is 1.81(4) ${\ensuremath{\mu}}_{\mathrm{B}}$. For $\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiRu}{\mathrm{O}}_{6}$, the $\mathrm{R}{\mathrm{u}}^{5+}$ moments are reported to lie in the $xz$ plane. In addition, while neutron diffraction, \ensuremath{\mu}SR and NMR data indicate a unique ${T}_{\mathrm{N}}=24\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for $\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiRu}{\mathrm{O}}_{6}$, the situation for $\mathrm{L}{\mathrm{a}}_{2}\mathrm{LiOs}{\mathrm{O}}_{6}$ is more complex, with heat capacity, neutron diffraction, and \ensuremath{\mu}SR indicating two ordering events at 30 and 37 K, similar to the cases of cubic $\mathrm{B}{\mathrm{a}}_{2}\mathrm{YRu}{\mathrm{O}}_{6}$ and monoclinic $\mathrm{S}{\mathrm{r}}_{2}\mathrm{YRu}{\mathrm{O}}_{6}$.

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