Multiferroic Coupling of Ferromagnetic and Ferroelectric Particles through Elastic Polymers

Abstract

Multiferroics are materials that electrically polarize when subjected to a magnetic field and magnetize under the action of an electric field. In composites, the multiferroic effect is achieved by mixing of ferromagnetic (FM) and ferroelectric (FE) particles. The FM particles are prone to magnetostriction (field-induced deformation), whereas the FE particles display piezoelectricity (electrically polarize under mechanical stress). In solid composites, where the FM and FE grains are in tight contact, the combination of these effects directly leads to multiferroic behavior. In the present work, we considered the FM/FE composites with soft polymer bases, where the particles of alternative kinds are remote from one another. In these systems, the multiferroic coupling is different and more complicated in comparison with the solid ones as it is essentially mediated by an electromagnetically neutral matrix. When either of the fields, magnetic or electric, acts on the ‘akin’ particles (FM or FE) it causes their displacement and by that perturbs the particle elastic environments. The induced mechanical stresses spread over the matrix and inevitably affect the particles of an alternative kind. Therefore, magnetization causes an electric response (due to the piezoeffect in FE) whereas electric polarization might entail a magnetic response (due to the magnetostriction effect in FM). A numerical model accounting for the multiferroic behavior of a polymer composite of the above-described type is proposed and confirmed experimentally on a polymer-based dispersion of iron and lead zirconate micron-size particles.

Modelling the effect of particle arrangement on the magnetoelectric response of a polymer multiferroic film

“…To be closer to real systems, we take the orders of magnitude of the material parameters from the estimations and evidence given in the experiments on the synthesis of 003-MF films. 13,15 Namely, the piezoelectric (PE) particles are assumed to be made of barium titanate (BTO) ceramics of approximately round shape and diameters 2-5 mm. The prototype for the ferrimagnetic (FM) filler is cobalt ferrite (CFO) particles which are substantially smaller than the PE ones.…”

“…In these MFs, the particles are entirely surrounded by the polymer in order to make the latter experience in full the mechanical stress generated by the magnetostriction. The most popular matrices are either PVDF (polyvinylidene fluoride) or its copolymer with TrFE (trifluoroethylene) [8][9][10][11][12][13][14][15][16][17] whose piezolelectric ability is higher the greater the content of the so-called b-phase whose amount is intentionally augmented by mechanical pre-processing, for example. 18 The magnetoelectric transducers of the abovedescribed kind are usually designed as oscillatory systems, like cantilevers, membranes, etc.…”

Theoretical Modeling of Magnetoactive Elastomers on Different Scales: A State-of-the-Art Review

“…Magnetic particles are usually modeled as beads bearing point magnetic dipoles located in their centers and either freely rotating [ 30 ] or firmly connected with the particle body so that the particle rotates as a whole to orient its magnetic moment [ 31 , 32 , 33 ]. Additionally, it is assumed that the modulus of the magnetic moment is fixed; this approximation works well for either magnetically isotropic monodomain nanoparticles or magnetically hard ones.…”

“…In recent papers [ 30 , 46 ], the MD model of a multiferroic material, namely an elastomer matrix filled with both ferromagnetic (FM) and ferroelectric (FE) microparticles was proposed. In comparison with previous approaches, the polydispersity of FM and FE particles was taken into account with lognormal distribution of sizes, and the magnetic and electric moments prescribed to the corresponding particles were scaled according to their size.…”

“… ( a ) Snapshot of the system of ferromagnetic and ferroelectric particles in the simulation box demonstrating an MD model of a multiferroic material: blue spheres are FM particles, orange ones are FE particles, white arrows show their magnetic/electric polarizations, green spheres are polymeric beads, green lines denote elastic links; the snapshot region is 10 × 50 × 50 μm along Ox, Oy, and Oz axes, respectively. ( b ) Magnetization increment , where and are magnetizations in normalized units measured without electric bias and under an electric bias of 5 MV/m; experimental data (black) and simulation data (red) with error bars (grey) [ 30 ]. H denotes the magnetic field strength.…”