Evidence of Two Dimensionality in Quasi-One-Dimensional Cobalt Oxides

The quasi-one-dimensional (Q1D) cobalt oxides ${A}_{n+2}{\mathrm{Co}}_{n+1}{\mathrm{O}}_{3n+3}$ ($A=\mathrm{Ca}$, Sr, and Ba, $n=1\ensuremath{-}\ensuremath{\infty}$) were investigated by muon-spin spectroscopy under applied pressures of up to 1.1 GPa. The relationship between the onset N\'eel temperature ${T}_{\mathrm{N}}^{\mathrm{on}}$ and the interchain distance (${d}_{\mathrm{ic}}$), which increases monotonically with $n$, is well fitted by the formula ${T}_{\mathrm{N}}/{T}_{\mathrm{N},0}=(1\ensuremath{-}{d}_{\mathrm{ic}}/{d}_{\mathrm{ic},0}{)}^{\ensuremath{\beta}}$; here ${T}_{\mathrm{N}}^{\mathrm{on}}\ensuremath{\sim}100\text{ }\text{ }\mathrm{K}$ for ${\mathrm{Ca}}_{3}{\mathrm{Co}}_{2}{\mathrm{O}}_{6}$ ($n=1$) and $\ensuremath{\sim}15\text{ }\text{ }\mathrm{K}$ for ${\mathrm{BaCoO}}_{3}$ ($n=\ensuremath{\infty}$) at ambient $P$. The ${T}_{\mathrm{N}}^{\mathrm{on}}\ensuremath{-}{d}_{\mathrm{ic}}$ curve also predicts a large $P$ dependence of ${T}_{\mathrm{N}}$ for the compounds with $n\ensuremath{\ge}5$, i.e., in the vicinity of ${d}_{\mathrm{ic},0}$, while the $n=1--4$ compounds show only a very small effect. Indeed, our high-pressure ${\ensuremath{\mu}}^{+}\mathrm{SR}$ results show that ${T}_{\mathrm{N}}$ of ${\mathrm{BaCoO}}_{3}$ is enhanced by $P$ with a slope of $2.2\text{ }\text{ }\mathrm{K}/\mathrm{GPa}$, whereas no detectable changes by $P$ for both ${\mathrm{Ca}}_{3}{\mathrm{Co}}_{2}{\mathrm{O}}_{6}$ and ${\mathrm{Sr}}_{4}{\mathrm{Co}}_{3}{\mathrm{O}}_{9}$ ($n=2$). This clearly confirms the role of the 2D-antiferromagnetic interaction on ${T}_{\mathrm{N}}^{\mathrm{on}}$ in the Q1D cobalt oxides.

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