muSR study on quasi-one-dimensional cobalt/rhodium oxides

Thanks to the unique power of muon-spin spectroscopy, we found that the quasi-one-dimensional Co-Rh oxides $A_{n+2}$CoRh$_{n}$O$_{3n+3}$ ($A$ = Ca, Sr; $n$=1, 2, and 3) exhibit a two-dimensional antiferromagnetic transition that ranges from $T_{\rm N}^{\rm on}$=185~K for $n$=1 to 125~K for $n$=3 with a transition width ($\Delta T$) of about 80~K. The variation of $T_{\rm N}^{\rm on}$ with $n$ is explained by the increase in the distance between the neighboring CoRh$_n$O$_{3n+3}$ chains. Static magnetic order is observed below the endpoint of $T_{\rm N}$ (=$T_{\rm N}^{\rm on}$-$\Delta T$) for each of the three samples. The existence of the two-frequency components in the ZF-spectrum indicates the appearance of ferrimagnetic order for Ca$_3$CoRhO$_6$ below 20~K.