*3.5. Temperature Dependent Conductance*

The temperature dependence of the conductance in the Au/Cr/LNO/Pt stack is given in Figure 5. We observe three current regimes. In -1 , for temperatures above 300 K, an activation energy of 0.63 eV was obtained; in -<sup>2</sup> , between 300 K and about 100 K, we obtain an activation energy of 0.18 eV. For temperatures below 100 K -3 , we obtain an activation energy of only 0.03 eV. Very similar regimes have been proposed very recently for the lifetime of bound polaron in lightly-doped Fe:LNO via Monte-Carlo simulations [35].

**Figure 5.** Temperature dependence of the current for thin-film LNO. Measured current at different voltages from 360 K to 77 K. We can observe different regimes of thermal activation -1 above 300 K with Ea = 0.63 eV, at -2 between 300 K and 100 K with Ea = 0.18 eV and -3 below 100 K with a thermal activation of Ea = 0.03 eV. These are overlaid with the inverse bound polaron lifetime, as calculated by Monte Carlo (MC) simulations.

The processes which are assigned to these three regimes are given as:


The simulated bound polaron lifetime by Mhaouech and Guilbert is overlaid on the aforementioned temperature-dependent I–V curves given in Figure 5.

Thus, we can conclude that the current through the exfoliated LNO thin film is mainly governed by an interplay of bound and free small polaron transport, depending on the given temperature. As iron impurities act as deep traps, they will inhibit any further conduction. The hopping activation energy of Fe2<sup>+</sup> is given to be 0.35 eV [36], hence, only a little larger than Li for bound and free polarons, but as the hopping rate follows w <sup>∼</sup> e−r/<sup>a</sup> <sup>≈</sup> e−r[Å], hopping transport is very unlikely for the given concentrations and even for lightly doped Fe:LNO not relevant. A conversion to bound and small polarons is unlikely due to the high binding energy of 1.22 eV.
