Heat capacity of naturally layered<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">SrO</mml:mi><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">La</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">Sr</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">MnO</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>single crystals

We measured the heat capacity of $\mathrm{SrO}{({\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{MnO}}_{3})}_{2}$ single crystals $(0.32\ensuremath{\leqslant}x\ensuremath{\leqslant}0.64)$ in the temperature range of $3--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and in magnetic fields to $9\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. In order to evaluate the magnetic entropy of the system, we compare data for samples of different composition to decompose the lattice and magnetic contributions. We extract the magnetic contribution by using a sample with no long-range magnetic ordering transition to serve as a reference. We find that the magnetic entropy below room temperature is significantly reduced compared to expectations based on localized moments. But a recent model that invokes a Griffith's singularity indicates that the missing entropy can reside at elevated temperatures due to short-range ordered clusters of effective spin 8.

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