Magnetoimpedance spectroscopy of epitaxial multiferroic thin films

The detection of true magnetocapacitance (MC) as a manifestation of magnetoelectric coupling (MEC) in multiferroic materials is a nontrivial task, because pure magnetoresistance (MR) of an extrinsic Maxwell-Wagner-type dielectric relaxation can lead to changes in capacitance [G. Catalan, Appl. Phys. Lett. 88, 102902 (2006)]. In order to clarify such difficulties involved with dielectric spectroscopy on multiferroic materials, we have simulated the dielectric permittivity ${\ensuremath{\varepsilon}}^{\ensuremath{'}}$ of two dielectric relaxations in terms of a series of one intrinsic film-type and one extrinsic Maxwell-Wagner-type relaxation. Such a series of two relaxations was represented in the frequency- ($f--$) and temperature- ($T--$) dependent notations ${\ensuremath{\varepsilon}}^{\ensuremath{'}}$ vs $f$ and ${\ensuremath{\varepsilon}}^{\ensuremath{'}}$ vs $T$ by a circuit model consisting in a series of twoideal resistor-capacitor (RC) elements. Such simulations enabled rationalizing experimental $f--$, T-, and magnetic field- ($H--$) dependent dielectric spectroscopy data from multiferroic epitaxial thin films of BiMnO${}_{3}$ (BMO) and BiFeO${}_{3}$ (BFO) grown on Nb-doped SrTiO${}_{3}$. Concomitantly, the deconvolution of intrinsic film and extrinsic Maxwell-Wagner relaxations in BMO and BFO films was achieved by fitting $f$-dependent dielectric data to an adequate equivalent circuit model. Analysis of the $H$-dependent data in the form of determining the $H$-dependent values of the equivalent circuit resistors and capacitors then yielded the deconvoluted MC and MR values for the separated intrinsic dielectric relaxations in BMO and BFO thin films. Substantial intrinsic MR effects up to 65$%$ in BMO films below the magnetic transition (${T}_{C}\ensuremath{\approx}100$ K) and perceptible intrinsic MEC up to \ensuremath{-}1.5$%$ near ${T}_{\mathrm{C}}$ were identified unambiguously.