Measuring the magnetoelectric effect across scales

Abstract

Magnetoelectric coupling is the material based coupling between electric and magnetic fields without recurrence to electrodynamics. It can arise in intrinsic multiferroics as well as in composites. Intrinsic multiferroics rely on atomistic coupling mechanisms, or coupled crystallographic order parameters, and even more complex mechanisms. They typically require operating temperatures much below T = 0°C in order to exhibit their coupling effects. Room temperature applications are thus excluded. Consequently, composites have been designed to circumvent this limitation. They rely on field coupling between magnetostrictive and piezoelectric materials or in more advanced scenarios on quantum coupling in between both phases.This overview will describe experimental techniques and their particular limitations in accessing these coupling phenomena at different scales. Strain coupling is the dominant coupling mechanism at the macroscale as well as down to the micrometer. At the nanoscale more subtle effects can arise and some care has to be taken when investigating local coupling at interfaces using scanning probe techniques, e. g. due to semiconductor effects, field screening, or gradient and surface effects. At the smallest length scale atomic or molecular coupling can be tested using X‐ray dichroism or probe atoms like 57Fe in Mössbauer spectroscopy. We display a selection of measuring techniques at the different scales and outline possible pitfalls for experimentalists as well as theoreticians when using material parameters extracted from such experimental work. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A new (Ba, Ca) (Ti, Zr)O3 based multiferroic composite with large magnetoelectric effect

“…The shape of the M ME ( H ) curve is typical for bulk multiferroic composites containing CFO4445. Indeed, since the ME effect in such composites is due to strain coupling at the interface, the magnetoelectric coefficient can be written as , where q imn is the piezomagnetic coefficient, is an effective stiffness of the microstructure, and d jkl is the piezoelectric coefficient43. For our experimental conditions, the magnetic field and measured magnetic moment are perpendicular to the electroded sample faces, the shape of the M ME ( H ) curve should follow the magnetic field dependence of the longitudinal piezomagnetic coefficient, q l , that in turn is determined by the field dependence of magnetostriction λ , q l  =  dλ / dH (here the effective uniaxial value of a sample).…”

The Direct and the Converse Magnetoelectric Effect in Multiferroic Cobalt Ferrite–Barium Titanate Ceramic Composites

“…12 In Voigt notation, 30 expression (A1.1) can be written as: 12 In Voigt notation, 30 expression (A1.1) can be written as:…”

“…One factor that is fundamentally critical is the demagnetizing factor. 12,27,29 In our microstructure for low CFO content we naturally obtain isolated more or less spherical CFO inclusions. For them the external field is reduced within the magnetic particle.…”

Sequential piezoresponse force microscopy and the ‘small-data’ problem

“…[29][30][31] The ME effect in such composites takes place via stress mediation, where the field induced strain in one phase leads to a stress on the adjacent phase, which ultimately varies the order parameter (polarization/magnetization) of the other phase. [32][33][34][35][36] Interestingly, the performance of such composites, gauged by the ME coupling coefficient α, is found to be highly sensitive to microstructure. [37][38][39][40] On the other hand, modeling predicts complex domain evolution in composites.…”

“…In the variable-field PFM experiment one effectively measures Δd eff (x, y) = f (x, y, H 0 , E 0 , ΔH), 32 and hence an exact observation of equation 3 is not trivial. Despite this limitation, PFM can reveal the intensity of the ME effect at a local scale, which could be useful information to relate the ME coupling to the material properties, as well as microstructure.…”