Deviations from linearity in impedance spectroscopy measurements confirmed by Kramers-Kronig analysis

We investigate the electric response of a kerosene cell containing magnetic nanoparticles. The cell is submitted to an external potential difference and its impedance is measured for increasing values of the potential amplitude. The analysis of the experimental data by means of the Kramers-Kronig relations indicates an unexpected deviation from the linear behaviour situated close to the frequency identifying the minimum of the cell's reactance modulus. We show that this departure from linearity could be related to the imaginary part of the ions’ bulk density when its variation cannot be considered as a small quantity. The analysis is performed in the one-type mobile ions approximation of the Poisson-Nernst-Planck model assuming Ohmic boundary conditions on the electrodes. Fitting the data using linear models gives poor results any time the Kramers-Kronig analysis shows deviations from linearity.