Impedance spectroscopy of epitaxial multiferroic thin films

Temperature dependent impedance spectroscopy enables the many contributions to the dielectric and resistive properties of condensed matter to be deconvoluted and characterized separately. We have achieved this for multiferroic epitaxial thin films of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ (BFO) and $\mathrm{Bi}\mathrm{Mn}{\mathrm{O}}_3$ (BMO), key examples of materials with strong magnetoelectric coupling. We demonstrate that the true film capacitance of the epitaxial layers is similar to that of the electrode interface, making analysis of capacitance as a function of film thickness necessary to achieve deconvolution. We modeled non-Debye impedance response using Gaussian distributions of relaxation times and reveal that conventional resistivity measurements on multiferroic layers may be dominated by interface effects. Thermally activated charge transport models yielded activation energies of $0.60\pm 0.05\mathrm{eV}$ (BFO) and $0.25\pm 0.03\mathrm{eV}$ (BMO), which is consistent with conduction dominated by oxygen vacancies (BFO) and electron hopping (BMO). The intrinsic film dielectric constants were determined to be $320\pm 75$ (BFO) and $450\pm 100$ (BMO).

Figure 1

(Color online) Impedance response of circuit elements on a phasor diagram: applied voltage $U\left(\omega t\right)$, current response $I_R$ for an ideal resistor in phase with $U\left(\omega t\right)$, $I_C$ for an ideal capacitor with a $-\pi ∕2$ phase shift, $I_{RC}$ for a series resistor-capacitor combination with phase shift $\delta$, $I_L$ for an inductor with phase shift $+\pi ∕2$, and $I_{\mathrm{CPE}}$ for a CPE describing a nonideal capacitor with a frequency independent phase shift $\gamma$ with respect to the ideal capacitor; one phase of the applied voltage corresponds to a $2\pi$ rotation of the $U\left(\omega t\right)$ arrow.

Figure 2

(Color online) (a) Sample geometry for ac impedance measurements of insulating multiferroic layers on a low-resistivity Nb-STO substrate using top-top Pt electrodes. (b) Equivalent circuit model.

Figure 3

(Color online) Capacitance values for C1 (◇,◆) and C2 (◻, ∎) for BFO films normalized to contact area $A$ (◇, ◻) and to the geometrical factor $g$ (◆, ∎) vs film thickness, data taken at $30°\mathrm{C}$.

Figure 4

(Color online) (a)–(c) Impedance complex plane plots of $-Z^{″}-Z^{\prime }$ ($\Omega$ vs $\Omega$) of a $50\mathrm{nm}$ thickness BFO thin-film spectrum at $200°\mathrm{C}$: $◻=\text{data}$, $◻=\text{Voigt}$ model, $∎=\mathrm{CPE}$ model.

Figure 5

(Color online) (a) Plots of capacitance C2 from CPE fits corrected to $\mathrm{F}{\mathrm{cm}}^{-1}$ (◆, ∎) and from Voigt fits (◇,◻) in $\mathrm{F}{\mathrm{cm}}^{-1}$ vs $T$; data taken from $50\mathrm{nm}$ BFO (◻,∎) and $50\mathrm{nm}$ BMO (◇,◆) films. Black solid lines indicate where ${ϵ}_2^{\prime }$ and ${\rho }_{\mathit{dc}}$ values were extracted, whereas dashed lines indicate deviations from approximately constant behavior. (b) Real part of the film dielectric constants ${ϵ}_2^{\prime }$ (dimensionless) for BFO and BMO.

Figure 6

(Color online) Plots of R2 for $50\mathrm{nm}$ BFO (◻,∎) and BMO (◇,◆) films in $\Omega \mathrm{cm}$ vs $1∕T$ from Voigt (◻,◇) and CPE (∎,◆) fits; the activation energies were determined from the slopes of ln(R2) vs $1∕T$ plots.