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Electric Field Control of Three-Dimensional Vortex States in Core-Shell Ferroelectric Nanoparticles

45 Pages Posted: 30 Apr 2020 Publication Status: Accepted

See all articles by Anna N. Morozovska

Anna N. Morozovska

National Academy of Sciences of Ukraine - Institute of Physics

Eugene A. Eliseev

National Academy of Sciences of Ukraine - Institute for Problems of Materials Science

Riccardo Hertel

Institute of Physics and Chemistry of Materials of Strasbourg (IPCMS)

Yevhen M. Fomichov

Charles University in Prague - Faculty of Mathematics and Physics

Victoria Tulaidan

Taras Shevchenko National University of Kyiv

Victor Yu Reshetnyak

Taras Shevchenko National University of Kyiv

Dean R. Evans

Wright Patterson Air Force Base - Materials and Manufacturing Directorate

Abstract

The fundamental question whether the structure of curled topological states, such as ferroelectric vortices, can be controlled by the application of an irrotational electric field is open. In this work, we studied the influence of irrotational external electric fields on the formation, evolution, and relaxation of ferroelectric vortices in spherical nanoparticles. In the framework of the Landau-Ginzburg-Devonshire approach coupled with electrostatic equations, we performed finite element modeling of the polarization behavior in a ferroelectric barium titanate core covered with a "tunable" paraelectric strontium titanate shell placed in a polymer or liquid medium. A stable two-dimensional vortex is formed in the core after a zero-field relaxation of an initial random or poly-domain distribution of the polarization, where the vortex axis is directed along one of the core crystallographic axes. Subsequently, sinusoidal pulses of a homogeneous electric field with variable period, strength, and direction are applied. The field-induced changes of the vortex structure consist in the appearance of an axial kernel in the form of a prolate nanodomain, the kernel growth, an increasing orientation of the polarization along the field, and the onset of a single-domain state. We introduced the term "kernel" to name the prolate nanodomain developed near the vortex axis and polarized perpendicular to the vortex plane. In ferromagnetism, this region is generally known as the vortex core. Unexpectedly, the in-field evolution of the polarization includes the formation of Bloch point structures, located at two diametrically opposite positions near the core surface. After removal of the electric field, the vortex recovers spontaneously; but its structure, axis orientation, and vorticity can be different from the initial state. As a rule, the final state is a stable three-dimensional polarization vortex with an axial dipolar kernel, which has a lower energy compared to the initial purely azimuthal vortex. The nature of this counterintuitive result is that the gradient energy of the axial vortex without a kernel is significantly higher, while the formation of a vortex kernel only leads to a smaller increase of the depolarization energy.The analysis of the torque and electrostatic forces acting on the core-shell nanoparticle in an irrotational electric field showed that the torque acting on the vortex with a kernel tends to rotate the nanoparticle in such way that the vortex axis becomes parallel to the field direction. The vortex (with or without a kernel) is electrostatically neutral, and therefore the force acting on the nanoparticle is absent for a homogeneous electric field, and nonzero for the field with a strong spatial gradient.The vortex states with a kernel possess a manifold degeneracy, appearing from three equiprobable directions of vortex axis, clockwise and counterclockwise directions of polarization rotation along the vortex axis, and two polarization directions in the kernel. This multitude of the vortex states in a single core are promising for applications of core-shell nanoparticles and their ensembles as multi-bit memory and related logic units. The rotation of a vortex kernel over a sphere, possible for the core-shell nanoparticles in a soft matter medium with controllable viscosity, may be used to imitate qubit features.

Keywords: core-shell nanoparticles, ferroelectric vortices, vortex kernel, irrotational electric field

Suggested Citation

Morozovska, Anna N. and Eliseev, Eugene A. and Hertel, Riccardo and Fomichov, Yevhen M. and Tulaidan, Victoria and Reshetnyak, Victor Yu and Evans, Dean R., Electric Field Control of Three-Dimensional Vortex States in Core-Shell Ferroelectric Nanoparticles. Available at SSRN: https://ssrn.com/abstract=3581341 or http://dx.doi.org/10.2139/ssrn.3581341

Anna N. Morozovska (Contact Author)

National Academy of Sciences of Ukraine - Institute of Physics ( email )

Kyiv
Ukraine

Eugene A. Eliseev

National Academy of Sciences of Ukraine - Institute for Problems of Materials Science

Kyiv
Ukraine

Riccardo Hertel

Institute of Physics and Chemistry of Materials of Strasbourg (IPCMS) ( email )

Bâtiment 69, 23 Rue du Loess
Strasbourg, 67200
France

Yevhen M. Fomichov

Charles University in Prague - Faculty of Mathematics and Physics

Sokolovska 83
Prague, 186 75
Czech Republic

Victoria Tulaidan

Taras Shevchenko National University of Kyiv

вул. Володимирська, 60
Kyiv, 01601
Ukraine

Victor Yu Reshetnyak

Taras Shevchenko National University of Kyiv ( email )

вул. Володимирська, 60
Kyiv, 01601
Ukraine

Dean R. Evans

Wright Patterson Air Force Base - Materials and Manufacturing Directorate ( email )

United States

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