Impedance spectroscopy of multiferroic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Pb</mml:mi><mml:msub><mml:mi mathvariant="normal">Zr</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">Ti</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>∕</mml:mo><mml:mi mathvariant="normal">Co</mml:mi><mml:msub><mml:mi mathvariant="normal">Fe</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>layered thin films

The electrical properties of ferroelectric $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_{3}$ (PZT) and ferromagnetic $\mathrm{Co}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ (CFO) thin film multilayers (MLs) fabricated by pulsed laser deposition technique has been studied by impedance and modulus spectroscopy. The effect of various PZT/CFO configurations having three, five, and nine layers has been systematically investigated. The transmission electron microscopy images revealed that the ML structures were at least partially diffused near the interface. Diffraction patterns indicate clear PZT and CFO crystal structures in the interior and at the interface of the ML structure. Room temperature micro-Raman spectra indicate separate PZT and CFO phases in ML structure without any impurity phase. We studied frequency and temperature dependencies of impedance, electric modulus, and ac conductivity of ML thin films in the ranges of $100\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}--1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ and $200--650\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, respectively. We observed two distinct electrical responses in all the investigated ML films at low temperature $(&lt;400\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ and at elevated temperature $(&gt;400\phantom{\rule{0.3em}{0ex}}\mathrm{K})$. We attributed these contributions to the grain effects at low temperature and grain boundary effects at high temperature. We explained this electrical behavior by Maxwell-Wagner-type contributions arising from the interfacial charge at the interface of the ML structure. Master modulus spectra indicate that the magnitude of grain boundary compared to grain becomes more prominent with the increase in the number of layer. The frequency dependent conductivity results well fitted with the double power law, $\ensuremath{\sigma}(\ensuremath{\omega})=\ensuremath{\sigma}(0)+{A}_{1}{\ensuremath{\omega}}^{{n}_{1}}+{A}_{2}{\ensuremath{\omega}}^{{n}_{2}}$, and the results showed evidence of three types of conduction process at elevated temperature: (i) low frequency $(&lt;1\phantom{\rule{0.3em}{0ex}}\mathrm{kHz})$ conductivity is due to long-range ordering (frequency independent), (ii) midfrequency conductivity $(&lt;10\phantom{\rule{0.3em}{0ex}}\mathrm{kHz})$ may be due to the short-range hopping, and (iii) high frequency $(&lt;1\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})$ conduction is due to the localized relaxation hopping mechanism.