Effects of Reduced Dimensionality on Spin Dynamics in the Layered Perovskite ${\mathrm{La}}_{1.4}{\mathrm{Sr}}_{1.6}{\mathrm{Mn}}_2{\mathrm{O}}_7$

We report zero-field muon spin rotation data in single crystals of ${\mathrm{La}}_{1.4}{\mathrm{Sr}}_{1.6}{\mathrm{Mn}}_2{\mathrm{O}}_7$ for $T=5\mathrm{}–325\mathrm{K}$. The spin-lattice relaxation rate is spatially inhomogeneous below the 3D magnetic transition temperature $T_C$ and anisotropic above $T_C$. We find evidence against 2D spin ordering or in-plane correlations above $T_C$. Additionally, the very slow spin fluctuations found below $T_C$ in cubic (3D) perovskites like $(\mathrm{La},\mathrm{Ca}){\mathrm{MnO}}_3$ or $(\mathrm{La},\mathrm{Sr}){\mathrm{MnO}}_3$, and attributed to relatively small magnetoelastic polarons, are absent in ${\mathrm{La}}_{1.4}{\mathrm{Sr}}_{1.6}{\mathrm{Mn}}_2{\mathrm{O}}_7$. This suggests that the polaron size in the layered material is significantly larger than in the 3D perovskites.