Magnetostriction in the magneto-sensitive elastomers with inhomogeneously magnetized particles: pairwise interaction approximation

We analyze the magnetostriction effect occurring in the magneto-sensitive elastomers (MSEs) containing inhomogeneously magnetized particles. As it was shown before, the expression for the interaction potential between two magnetic spheres, that accounts for their mutual inhomogeneous magnetization, can be obtained from the Laplace equation. We use this potential in the approximation formula form to construct magnetic energy of the sample in terms of the pairwise interactions of the particles. We show that this form of magnetic energy leads to the same demagnetizing factor as predicted by the continuum mechanics, confirming that only dipole-dipole magnetic interactions are important on a large scale. As the next step, we examine the role played by the particles arrangement on the magnetostriction effect. We consider different spatial distributions of the magnetic particles: a uniform one, as well as several lattice-type distributions (SC, BCC, HCP and FCC arrangements). We show that the particles arrangement affects significantly the magnetostriction effect if the separation between them became comparable with the particles' dimensions. We also show that, typically, this contribution to the magnetostriction effect is of the opposite sign to the one related with the initial elastomer shape. Finally, we calculate the magnetostriction effect using the same interaction potential but expressed in a form of a series expansion, qualitatively confirming the above findings

Intrinsic modulus and strain coefficients in dilute composites with a Neo-Hookean elastic matrix

A finite element modelling of dilute elastomer composites based on a Neo-Hookean elastic matrix and rigid spherical particles embedded within the matrix was performed. In particular, the deformation field in vicinity of a sphere was simulated and numerical homogenization has been used to obtain the effective modulus of the composite μeff for different applied extension and compression ratios. At small deformations the well-known Smallwood result for the composite is reproduced: μeff=(1+[μ]φ)μ0 with the intrinsic modulus [μ]=2.500. Here φ is the volume fraction of particles and μ0 is the modulus of the matrix solid. However at larger deformations higher values of the intrinsic modulus [μ] are obtained, which increase quadratically with the applied true strain. The homogenization procedure allowed to extract the intrinsic strain coefficients which are mirrored around the undeformed state for principle extension and compression axes. Utilizing the simulation results, stress and strain modifications of the Neo-Hookean strain energy function for dilute composites are proposed

Mechanical properties of magneto-sensitive elastomers: unification of the continuummechanics and microscopic theoretical approaches

A new theoretical formalism is developed for the study of the mechanical behaviour of magneto-sensitive elastomers (MSEs) under a uniform external magnetic field. This formalism allows us to combine macroscopic continuum-mechanics and microscopic approaches for complex analysis of MSEs with different shapes and with different particle distributions. It is shown that starting from a model based on an explicit discrete particle distribution one can separate the magnetic field inside the MSE into two contributions: one which depends on the shape of the sample with finite size and the other, which depends on the local spatial particle distribution. The magneto-induced deformation and the change of elastic modulus are found to be either positive or negative, their dependences on the magnetic field being determined by a non-trivial interplay between these two contributions. Mechanical properties are studied for two opposite types of coupling between the particle distribution and the magneto-induced deformation: absence of elastic coupling and presence of strong affine coupling. Predictions of a new formalism are in a qualitative agreement with existing experimental data

Macroscopic Manifestation of Domain-wall Magnetism and Magnetoelectric Effect in a N\'eel-type Skyrmion Host

We report a magnetic state in GaV$_4$Se$_8$ which emerges exclusively in samples with mesoscale polar domains and not in polar mono-domain crystals. Its onset is accompanied with a sharp anomaly in the magnetic susceptibility and the magnetic torque, distinct from other anomalies observed also in polar mono-domain samples upon transitions between the cycloidal, the N\'eel-type skyrmion lattice and the ferromagnetic states. We ascribe this additional transition to the formation of magnetic textures localized at structural domain walls, where the magnetic interactions change stepwise and spin textures with different spiral planes, hosted by neighbouring domains, need to be matched. A clear anomaly in the magneto-current indicates that the domain-wall-confined magnetic states also have strong contributions to the magnetoelectric response. We expect polar domain walls to commonly host such confined magnetic edge states, especially in materials with long wavelength magnetic order