Low-temperature electrical transport in bilayer manganite La 1.2 Sr 1.8 Mn 2 O 7

The temperature T and magnetic-field H dependences of anisotropic in-plane ${\ensuremath{\rho}}_{\mathrm{ab}}$ and out-of-plane ${\ensuremath{\rho}}_{c}$ resistivities are investigated in single crystals of the bilayer manganite ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}.$ Below the Curie transition temperature ${T}_{c}$=125 K, ${\ensuremath{\rho}}_{\mathrm{ab}}$ and ${\ensuremath{\rho}}_{c}$ display almost the same temperature dependence with an up-turn around 50 K. In the metallic regime (50 K $l~Tl~$ 110 K), both ${\ensuremath{\rho}}_{\mathrm{ab}}(T)$ and ${\ensuremath{\rho}}_{c}(T)$ follow a ${T}^{9/2}$ dependence, consistent with the two-magnon scattering. We found that the value of the proportionality coefficient ${B}_{\mathrm{ab}}^{\mathrm{fit}}$ and the ratio of the exchange interaction ${J}_{\mathrm{ab}}{/J}_{c},$ obtained by fitting the data, are in excellent agreement with the calculated ${B}_{\mathrm{ab}}$ based on the two-magnon model and ${J}_{\mathrm{ab}}{/J}_{c}$ deduced from neutron scattering, respectively. This provides further support for this scattering mechanism. At even lower T, in the nonmetallic regime $(Tl50 \mathrm{K}),$ both the in-plane ${\ensuremath{\sigma}}_{\mathrm{ab}}$ and out-of-plane ${\ensuremath{\sigma}}_{c}$ conductivities obey a ${T}^{1/2}$ dependence, consistent with weak-localization effects. Hence this demonstrates the three-dimensional metallic nature of the bilayer manganite ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ at $Tl{T}_{c}.$