Noise spectroscopy: a sensitive probe to explore hot electron effect in highly correlated systems*

Non-linear electrical conductance in ferromagnetic insulating (FMI) state of manganites can give rise to reversible colossal electro-resistance and current induced resistance change due to heating of the electrons in the system. In FMI state ($<$120K), the temperature of the lattices or phonon ($T_{ph})$ and electrons ($T_{e})$ in the sample can decouple by high input power density giving rise to heating of the electronic bath. We investigated whether white noise like Nyquist noise can be used to measure $T_{e}$ (which is expected to be larger than $T_{ph})$ when the two baths get decoupled. The use of the Nyquist noise to measure $T_{e}$ assumes that the electron bath forms a proper temperature bath in equilibrium. A dc stressing current was used to heat the electron bath while a small ac signal was used to measure the noise. With enhanced power input to the electron system, the white noise enhances and there is a large deviation from the simple estimate of Nyquist relation (4$k_{B}T_{e}R_{sample})$ indicating that the electron system is not in thermal equilibrium and is a non-ergodic system where Fluctuation Dissipation Theorem has broken down.