Nyquist noise as probe of hot-electron effects in the ferromagnetic insulating state of manganites

Hole-doped rare-earth manganites (like La$_{1-x}$Ca$_{x}$MnO$_{3})$ in the ferromagnetic insulating (FMI) state show large non-linear conductance. Such non-linear conductance can arise due to hot-electron effect which originates from decoupling of the electron and lattice temperatures at high power level. The non-linear conductance manifests as electro-resistance or current induced resistance change. We report here low frequency temperature dependent noise measurement which allows us to estimate the electronic temperature by measuring Nyquist noise (``white noise'' in contrast to 1/f noise) in La$_{0.8}$Ca$_{0.2}$MnO$_{3}$ single crystals which has a distinct FMI state below 100K. The measurement was performed with low ac biasing current which was mixed with a high current density d.c that leads to electron heating. We observed that in the insulating state, above a certain input d.c power, the Nyquist noise increases by a large extent and this is coupled to the onset of non-linear conduction as signalled by the power dependence of the differential conductance. The experiment establishes a direct link between hot-electron effect and non-linear conductance.