Nonlinear transport associated with spin-density-wave dynamics in Ca$_3$Co$_{4}$O$_9$

We have carried out the transient nonlinear transport measurements on the layered cobalt oxide Ca$_3$Co$_{4}$O$_9$, in which a spin density wave (SDW) transition is proposed at $T_{\rm SDW} \simeq 30$ K. We find that, below $T_{\rm SDW}$, the electrical conductivity systematically varies with both the applied current and the time, indicating a close relationship between the observed nonlinear conduction and the SDW order in this material. The time dependence of the conductivity is well analyzed by considering the dynamics of SDW which involves a low-field deformation and a sliding motion above a threshold field. We also measure the transport properties of the isovalent Sr-substituted systems to examine an impurity effect on the nonlinear response, and discuss the obtained threshold fields in terms of thermal fluctuations of the SDW order parameter.