Spontaneous flexoelectric/flexomagnetic effect in nanoferroics

Abstract

Within the Landau-Ginsburg-Devonshire phenomenological approach we study the ferroic nanosystems properties changes caused by the flexo-effect (flexoelectric, flexomagnetic, flexoelastic) existing spontaneously due to the inhomogeneity of order parameters. Exact solution for the spatially inhomogeneous mechanical displacement vector allowing for flexocoupling contribution was found for nanowires and thin pills. Strong influence of flexo-effect in nanorods and thin pills leads to the displacements of the atoms resulting into the unit cell symmetry changes, which lead to the phase transition temperature shift, as well as the flat geometry in radial direction transforms into the saucer-like one. The new phenomena can be considered as true manifestation of the spontaneous flexo-effect existence. It was shown that flexo-effect leads to (a) the appearance of new linear and nonlinear contribution and renormalization of coefficients before the order parameter gradient, (b) essentially influences the transition temperature, piezoelectric response and the spatial distribution of the order parameter, (c) results in renormalization of extrapolation length in the boundary conditions. These effects cannot be neglected for ferroelectrics, the renormalization being important for nanoparticles of arbitrary shape, while the linear and nonlinear terms is essential for the thin pills only. They are absent for nanowires with the order parameter directed along the wire axis. We demonstrated that the flexoelectric coupling decreases the polarization gradient self-consistently and so makes polarization more homogeneous. The divergences of dielectric permittivity and correlation radius at some critical value of flexoelectric coefficient originate from the critical radius dependence on the coefficient. This peculiar behavior shows a new way to govern material properties. The effect of the correlation radius renormalization by the flexoelectric effect leads to the renormalization of the intrinsic width of ferroelectric domain walls.

Atomic-scale evolution of modulated phases at the ferroelectric–antiferroelectric morphotropic phase boundary controlled by flexoelectric interaction

“…Specifically, we note that the gradient term is renormalized by the flexoelectric effects as  g g f s = − 2 , 36,52 where s is the elastic compliance, and can potentially become negative. This suggests mechanisms for domain wall instability.…”

Fundamentals of flexoelectricity in solids

“…The conventional phenomenological approach was bridged [51] to Bursian's theory [21] and the importance of the surface effects in the flexoelectric behavior of ferroelectrics was identified by Tagantsev and Yurkov [51]. It was shown by Indenbom et al [23], Eliseev et al [52], and Yurkov [53] that taking flexoelectricity into account will lead to a modification of the electrical and mechanical boundary conditions.…”

“…However, a more quantitative comparison with the theory is not currently possible. The phonon data cannot be compared with theoretical results since such a comparison requires theoretical values for the tensor M ij (see equation (52)) controlling the dynamic contribution to the flexoelectricity, which are not currently available. The quantitative interpretation of the data obtained from macroscopic measurements is also problematic in view of a possible contribution of the surface piezoelectricity, the quantitative theory of which is not yet developed.…”

Piezoelectricity above the Curie temperature? Combining flexoelectricity and functional grading to enable high-temperature electromechanical coupling

“…Flexoelectricity has recently received much attention, e.g., it suggests tantalizing possibilities such as creating effectively piezoelectric materials without using piezoelectrics. [5][6][7][8][9][10] In a recent work, Chandratre and Sharma showed, using quantum calculations, that merely by creating triangular holes in graphene nano ribbons, flexoelectricity enabled the ensuing structure to behave like a piezoelectric. 11 Their central idea is simple and the present work takes advantage of the following observation.…”