Magnetoimpedance spectroscopy of epitaxial multiferroic thin films

Rainer Schmidt, Jofre Ventura, Eric Langenberg, Norbert M. Nemes, Carmen Munuera, Manuel Varela, Mar Garcia-Hernandez, Carlos Leon, and Jacobo Santamaria

Phys. Rev. B 86, 035113 – Published 10 July 2012

Abstract

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 $ɛ^{'}$ 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 $ɛ^{'}$ vs $f$ and $ɛ^{'}$ vs $T$ by a circuit model consisting in a series of two ideal 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 ( $T_{C} \approx 100$ K) and perceptible intrinsic MEC up to −1.5 $%$ near $T_{C}$ were identified unambiguously.

Received 8 May 2012

DOI:https://doi.org/10.1103/PhysRevB.86.035113

Authors & Affiliations

Rainer Schmidt^1,*, Jofre Ventura², Eric Langenberg^2,3, Norbert M. Nemes¹, Carmen Munuera⁴, Manuel Varela², Mar Garcia-Hernandez⁴, Carlos Leon¹, and Jacobo Santamaria¹

¹Universidad Complutense de Madrid, GFMC, Dpto. Física Aplicada III, Facultad de Ciencias Físicas, 28040 Madrid, Spain
²Universitat de Barcelona, Dpto. Física Aplicada i Óptica, Diagonal Sud, Facultats de Física i Química, Martí i Franquès 1, 08028 Barcelona, Spain
³Universidad de Zaragoza, Instituto de Nanociencia de Aragón, Mariano Esquillor, 50018 Zaragoza, Spain
⁴Instituto de Ciencia de Materiales de Madrid–Consejo Superior de Investigaciones Científicas (ICMM-CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain

^*Corresponding author. rainerxschmidt@googlemail.com

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 86, Iss. 3 — 15 July 2012

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Simulated $ɛ^{'}$ vs $T$ data for a series of two RC elements (see inset). The $ɛ^{'}$ vs $T$ curves were calculated at selected frequencies (as indicated) from the analytical expression for $ɛ^{'}$ ( $f$ , $R_{1}$ , $R_{2}$ , $C_{1}$ , $C_{2}$ ) for a series of two RC elements, where the resistance ( $R_{n}$ $=$ $R_{1}$ , $R_{2}$ ) and capacitance ( $C_{1}$ , $C_{2}$ ) values were substituted into $ɛ^{'}$ ( $f$ , $R_{1}$ , $R_{2}$ , $C_{1}$ , $C_{2}$ ) according to the expressions shown in the figure inset. (b) Simulated $ɛ^{'}$ vs $f$ data. The $ɛ^{'}$ vs $f$ curves were calculated at selected temperatures (as indicated) from the analytical expression for $ɛ^{'}$ ( $f$ , $R_{1}$ , $R_{2}$ , $C_{1}$ , $C_{2}$ ) for a series of two RC elements. The exact values of the high and low $ɛ^{'}$ plateaus ( $ɛ^{'}$ $_{high}$ and $ɛ^{'}$ $_{low}$ ) are given, which are equivalent here in both notations: $ɛ^{'}$ vs $T$ and $ɛ^{'}$ vs $f$ .Reuse & Permissions
Figure 2
(a) Dielectric permittivity $ɛ^{'}$ vs $f$ for 50-nm BMO thin film at various selected temperatures as indicated. Open symbols ( $⋄$ ) represent experimental data; full squares (▪) and solid lines represent fits to the data using the equivalent circuit depicted below the curves. The occurrence of two $ɛ^{'}$ plateaus $ɛ^{'}$ $_{high}$ and $ɛ^{'}$ $_{low}$ is consistent with two series dielectric relaxations, represented by a series of two nonideal RC elements, R1-CPE1-C1 and R2-CPE2. R0 and L0 are parasitic contributions. (b) Identical data and fits as in Fig. 2a, transposed into the $ɛ^{'}$ vs $T$ notation at selected frequencies as indicated. The inset shows a magnification of the data at low $T$ on identical axes.Reuse & Permissions
Figure 3
(a) $ɛ^{'}$ vs $f$ for 100-nm BFO thin film at selected temperatures as indicated. Open symbols ( $⋄$ ) represent experimental data; full squares (▪) and solid lines represent fits to the data using the equivalent circuit depicted in the inset of Fig. 3b. Only one dielectric relaxation is indicated and is represented by one nonideal RC element R1-CPE1. R0 and L0 are parasitic contributions. Inset: Dielectric loss $ɛ^{''}$ vs $f$ . An approximately constant loss is indicated at low $T$ . (b) Identical data and fits as in Fig. 3a, transposed into the $ɛ^{'}$ vs $T$ notation at selected frequencies as indicated. The equivalent circuit model is depicted above the curves.Reuse & Permissions
Figure 4
(a) BMO and BFO intrinsic and extrinsic dielectric permittivity $ɛ_{1}$ and $ɛ_{2}$ vs $T$ , obtained from C1/CPE1 and CPE2 in the respective equivalent circuit fits. (b) Magnification of the intrinsic BMO permittivity $ɛ_{1}$ displaying signs of MEC near $T_{C}$ . (c) CPE exponents $n$ , indicative of more ideal ( $n$ ≈ 1) or less ideal ( $n$ < 1) character of the respective dielectric relaxation.Reuse & Permissions
Figure 5
BMO intrinsic and extrinsic resistivity $ρ_{1}$ and $ρ_{2}$ vs $T$ , obtained from R1 and R2 in the BMO equivalent circuit. $ρ_{1}$ shows correlation with $T_{C}$ . The activation energies $E_{A}$ are given in electron volts. Solid lines are linear Arrhenius fits. Inset: Magnification of the $ρ_{1}$ vs $T$ data below $T_{C}$ showing signs of VRH. The solid line represents the VRH fit with the fitted parameters given.Reuse & Permissions
Figure 6
(a) BMO imaginary part of the impedance $- Z$ $^{''}$ vs real part $Z$ $^{'}$ at 95 K for selected applied magnetic fields $H$ (Oersted) as indicated. Open symbols ( $⋄$ ) represent experimental data; full squares (▪) and solid lines represent fits to the data using the equivalent circuit depicted at the top of the curves. The decreasing size of the semicircle indicates MR of the intrinsic BMO film relaxation. The inset displays MR ( $%$ ) vs $H$ (Oersted) at 95 and 100 K, where MR=[R( $H$ =0)–R( $H$ )]/R(0). (b) $ɛ^{'}$ vs $f$ for 50-nm BMO thin film at 95 K for selected applied magnetic fields $H$ (Oersted) as indicated. Open symbols ( $⋄$ ) represent experimental data; full squares (▪), and solid lines represent fits to the data using the equivalent circuit depicted in Fig. 6a. The inset displays MC ( $%$ ) vs $H$ (Oersted) at 50, 95, and 100 K, where MC=[C( $H$ =0)–C( $H$ )]/C(0).Reuse & Permissions

Physical Review B

covering condensed matter and materials physics