Effective flexoelectric and flexomagnetic response of ferroics

Eliseev, Eugene A.; Morozovska, Anna N.; Khist, Victoria V.; Polinger, V. Z.

doi:10.1016/bs.ssp.2019.09.002

Cited by 11 publications

(4 citation statements)

References 71 publications

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“…The difference is that flexomagnetic is a pervasive effect on all materials with any symmetry, the discovery of which dates back to the current decade. Flexomagneticity is the coupling between the polarization and the strain gradient, but piezomagneticity is the coupling between the polarization and the strain itself [16][17][18][19][20][21][22][23]. The small-scale theme is the main debate in MMPs technology, which shows the more effective role of flexomagneticity.…”

Section: Introductionmentioning

confidence: 99%

On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

Malikan

Wiczenbach

Eremeyev

2021

Continuum Mech. Thermodyn.

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By relying on the Euler–Bernoulli beam model and energy variational formula, we indicate critical temperature causes in the buckling of piezo-flexomagnetic microscale beams. The corresponding size-dependent approach is underlying as a second strain gradient theory. Small deformations of elastic solids are assessed, and the mathematical discussion is linear. Regardless of the pyromagnetic effects, the thermal loading of the thermal environment varies in three states along with the thickness, which is linear, uniform, and parabolic forms. We then establish the results by developing consistent shape functions that independently evaluate boundary conditions. Next, we analytically develop and explore the effective properties of the studied beam concerning vital factors. It was achieved that piezomagnetic-flexomagnetic microbeams are more affected by the thermal environment while the thermal loading is parabolically distributed across the thickness, particularly when the boundaries involve simple supports.

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Section: Introductionmentioning

confidence: 99%

On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

Malikan

Wiczenbach

Eremeyev

2021

Continuum Mech. Thermodyn.

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“…The flexoelectric effect exists in all ferroics [6][7][8][9], in contrast to the flexomagnetic [10] and flexomagnetoelectric [11,12] effects, the existence of which is critically sensitive to the presence of time inversion and its connection with other operations of point symmetry of a particular material [13,14].…”

Section: Introductionmentioning

confidence: 99%

Flexosensitive polarization vortices in thin ferroelectric films

et al. 2021

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We consider theoretically the influence of the flexoelectric coupling on the spatial distribution and temperature behavior of spontaneous polarization for several types of stable domain structure in thin ferroelectric films, such as stripe domains and vortices. Finite element modelling (FEM) for BaTiO3 films and analytical calculations within the Landau-Ginzburg-Devonshire approach reveals that an outof-plane polarization component can be very sensitive to the flexoelectric coupling for periodic quasi-2D stripe domains and 3D vortex-antivortex structures. However, the influence is rather different for these structures. The flexoelectric coupling increases significantly the amplitude of a small out-of-plane polarization component in the stripe domains, and the "up" or "down" direction of the component is defined by the sign of the flexoelectric coefficients. Concerning the vortex-antivortex pairs, their antivortices with in-plane anti-сirculation have smooth wide dipolar cores through the entire film, whose shape and other features are almost insensitive to the coupling. The vortices with in-plane vorticity have spike-like cores with an out-of-plane quadrupolar moment induced by the flexoelectric coupling. The cores are located near the film-dead layer interfaces. FEM results corroborated by analytical calculations prove that a change of the flexoelectric coefficient sign leads to a reorientation of the core axial polarization, making the flexo-sensitive 3D vortices similar to the recently introduced "flexons" in cylindrical nanoparticles. The relatively wide temperature range (from 200 to 400 K) of the flexosensitive vortices' existence gives us the hope that they can be observed experimentally in thin ferroelectric films by scanning probe and nonlinear optical microscopy methods.

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“…These traits have led to a growing interest in and research into the flexomagnetic effect in recent years [ 1 , 2 ]. Currently, the role of the flexomagnetic effect in the physics of dielectrics has been investigated in some studies and has shown promising practical applications [ 3 , 4 , 5 , 6 , 7 ]. On the other hand, the difference between theoretical and experimental results shows a limited understanding in this field.…”

Section: Introductionmentioning

confidence: 99%

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Malikan

Eremeyev

2020

Nanomaterials

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Among various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In this article, we develop a model of a simultaneously coupled piezomagnetic–flexomagnetic nanosized Euler–Bernoulli beam and solve the corresponding problems. In order to evaluate the FM on the nanoscale, the well-known nonlocal model of strain gradient (NSGT) is implemented, by which the nanosize beam can be transferred into a continuum framework. To access the equations of nonlinear bending, we use the variational formulation. Converting the nonlinear system of differential equations into algebraic ones makes the solution simpler. This is performed by the Galerkin weighted residual method (GWRM) for three conditions of ends, that is to say clamp, free, and pinned (simply supported). Then, the system of nonlinear algebraic equations is solved on the basis of the Newton–Raphson iteration technique (NRT) which brings about numerical values of nonlinear deflections. We discovered that the FM effect causes the reduction in deflections in the piezo-flexomagnetic nanobeam.

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Effective flexoelectric and flexomagnetic response of ferroics

Cited by 11 publications

References 71 publications

On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

On thermal stability of piezo-flexomagnetic microbeams considering different temperature distributions

Flexosensitive polarization vortices in thin ferroelectric films

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

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