Two-dimensional intrinsic and extrinsic ferromagnetic behavior of layered ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_2{\mathrm{O}}_7$ single crystals

The low-field magnetization $M$ and susceptibility χ are reported for the two-layered Ruddleson-Popper phase ${\mathrm{S}\mathrm{r}\mathrm{O}(\mathrm{L}\mathrm{a}}_{1-x}{\mathrm{Sr}}_x{\mathrm{MnO}}_3{)}_2\mathrm{\hspace{1em}}\mathrm{for}\mathrm{\hspace{0.5em}}x=0.4\mathrm{}$ (denoted ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_2{\mathrm{O}}_7)$ with an in-plane magnetic easy axis. As $T$ approaches the Curie temperature ( $T_C=116\mathrm{}$ K) on cooling, where the metal-insulator transition occurs in zero field, χ diverges as $H^{-1/{\delta }^{\prime }},$ with $\delta =21\mathrm{}\pm 5$. Also, near an extrinsic Curie transition attributed to ∼0.1% volume fraction of intergrowths at $T^{*}=2.47\mathrm{}\hspace{0.5em}{T}_C,$ $M$ scales as $(1\mathrm{}-{T/T)}^{\beta },$ with $\beta =0.25\mathrm{}\pm 0.02$. These results can be understood within the context of two-dimensional $\mathrm{XY}$ models, and provide some perspective of the layered manganites.