Labyrinthine domains in ferroelectric nanoparticles: Manifestation of a gradient-induced morphological transition

Abstract

In the framework of the Landau-Ginzburg-Devonshire (LGD) approach we studied finite size effects of the phase diagram and domain structure evolution in spherical nanoparticles of uniaxial ferroelectric. The particle surface is covered by a layer of screening charge characterized by finite screening length. The phase diagram, calculated in coordinates "particle radius -screening length" has a wide region of versatile poly-domain structures separating single-domain ferroelectric and nonpolar paraelectric phases. Unexpectedly, we revealed a region of stable irregular labyrinthine domains in the nanoparticles of uniaxial ferroelectric CuInP2S6 with the first order paraelectric-ferroelectric phase transition. We established that the origin of labyrinthine domains is the mutual balance of LGD, polarization gradient and electrostatic energies. The branching of the domain walls appears and increases rapidly when the polarization gradient energy decreases below the critical value.Allowing for the generality of LGD approach, we expect that the gradient-induced morphological transition can be the source of labyrinthine domains appearance in many spatially-confined ferroics with long-range order parameter, including relaxors, ferromagnetics, antiferrodistortive materials and materials with incommensurate ferroic phases.

Inverse transition of labyrinthine domain patterns in ferroelectric thin films

“…1 show the evolution of the parallel stripes ground-state upon slowly increasing temperature. In the references 47,48 , authors study the morphology of equilibrium domain patterns depending on the magnitude of gradient terms within the classical Landau-Ginzburg-Devonshire theory, and find that the labyrinthine-like ground state can be stabilized if the gradient energy is sufficiently reduced. Therefore, we can conclude that in our case the effective gradient energy is above the critical value of the gradient which grants parallel stripes ground state upon slowly annealing the system.…”

Domains and domain walls in multiferroics

“…The number and size of the ferroelectric domains that form will depend on the details of the boundary conditions (Figure 1(d)), such as crystal size, shape, orientation, local defect structure and, critically, the energy costs associated with the insertion of domain walls. Thus, depending on the boundary conditions, a thin ferroelectric film can either form a single-domain state or break into multiple nanodomains [2,6], which has been used to engineer ferroelectric domains [7][8][9][10]. This can easily be observed by half covering a large single crystal with electrodes and cooling the sample through its Curie temperature: the area under the electrodes will form larger domains than the uncovered area due to the presence of screening charges from the electrodes, while the area in air will have a finer domain structure due to the depolarizing fields (see, e.g.…”

Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics

“…Understanding the intricate formation processes at play in the formation of modulated phases is thus pivotal for the development of future technologies, e.g., domain wall nanoelectronics [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]21,22 , a field of research that has recently seen fiery surge of interest. So far, modulated phases of ferroelectric domains such as the dipolar maze or labyrinthine phase 23 , and the nano-bubble or skyrmionic phase 21,22,24 have been somewhat regarded as conceptually disparate [24][25][26][27][28][29][30] . We here numerically predict and experimentally evidence that, depending on the magnitude of the external field, temperature and the kinetics of the phase separation, topologically non-trivial phases emerge upon sub-critically quenching tetragonal Pb(Zr x Ti 1 − x )O 3 through either spinodal decomposition or nucleation processes.…”