Magnetoelectric coupling coefficient in multiferroic capacitors: Fact vs Artifacts

Abstract

Multiferroic materials are characterized by their magnetoelectric coupling coefficient, which can be obtained using a lock-in amplifier by measuring the voltage developed across a multiferroic capacitor in a time-variable magnetic field, Hac cos( ωt), where Hac and ω are the amplitude and frequency of the applied magnetic field. The measurement method, despite its simplicity, is subject to various parasitic effects, such as magnetic induction, which leads to significant over-estimation of the actual magnetoelectric response. This article outlines the measurement theory for a multiferroic capacitor using the lock-in technique. It is demonstrated that the inductive contribution has linear proportionality with Hac, ω, and Hacω. It is shown that the true magnetoelectric coupling response is retrieved from the real component of the lock-in signal. Using a polymer-nanoparticle multiferroic composite, the internal consistency of the proposed measurement method is experimentally demonstrated, and it is shown that the actual multiferroic signal can be retrieved using the lock-in technique by removing the magnetic induction contribution from the signal. It is observed that the magnetoelectric voltage shows only a linear dependence with Hac, a saturating behavior with ω, and Hacω. Furthermore, a measurement protocol for reliable reporting of magnetoelectric coupling coefficient has been provided.