We explore ferroelectric properties of cleaved 2-D flakes of copper indium thiophosphate, CuInP2S6 (CITP), and probe size effects along with limits of ferroelectric phase stability, by ambient and ultra high vacuum scanning probe microscopy. CITP belongs to the only material family known to display ferroelectric polarization in a van der Waals, layered crystal at room temperature and above. Our measurements directly reveal stable, ferroelectric polarization as evidenced by domain structures, switchable polarization, and hysteresis loops. We found that at room temperature the domain structure of flakes thicker than 100 nm is similar to the cleaved bulk surfaces, whereas below 50 nm polarization disappears. We ascribe this behavior to a well-known instability of polarization due to depolarization field. Furthermore, polarization switching at high bias is also associated with ionic mobility, as evidenced both by macroscopic measurements and by formation of surface damage under the tip at a bias of 4 V-likely due to copper reduction. Mobile Cu ions may therefore also contribute to internal screening mechanisms. The existence of stable polarization in a van-der-Waals crystal naturally points toward new strategies for ultimate scaling of polar materials, quasi-2D, and single-layer materials with advanced and nonlinear dielectric properties that are presently not found in any members of the growing "graphene family".

An ab initio-based model of the temperature-induced ferroelectric phase transition in Sn2P2S6 (SPS) as a prototype of an unconventional ferroelectric is developed. The order parameter in SPS is found as the valley line on a total-energy surface of the zone-center fully symmetrical Ag and polar Bu distortions. Significant nonlinear coupling between order parameter and strain is observed. Monte Carlo simulations describe the additional low-temperature rearrangement in polar structure, which appears in domain boundaries, and describe the relaxation phenomena near the ferroelectric phase transition.

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Polar van der Waals chalcogenophosphates exhibit unique properties, such as negative electrostriction and multi-well ferrielectricity, and enable combining dielectric and 2D electronic materials. Using low temperature piezoresponse force microscopy, we revealed coexistence of piezoelectric and non-piezoelectric phases in CuInP 2 Se 6 , forming unusual domain walls with enhanced piezoelectric response. From systematic imaging experiments we have inferred the formation of a partially polarized antiferroelectric state, with inclusions of structurally distinct ferrielectric domains enclosed by the corresponding phase boundaries. The assignment is strongly supported by optical spectroscopies and density-functionaltheory calculations. Enhanced piezoresponse at the ferrielectric/antiferroelectric phase boundary and the ability to manipulate this entity with electric field on the nanoscale expand the existing phenomenology of functional domain walls. At the same time, phase-coexistence in chalcogenophosphates may lead to rational strategies for incorporation of ferroic functionality into van der Waals heterostructures, with stronger resilience toward detrimental size-effects.

Within the framework of Landau-Ginzburg-Devonshire (LGD) theory we studied the role of the flexocoupling between the order parameter and elastic strain gradients in the stability of a spatially-modulated phase (SMP) in ferroics with commensurate and incommensurate long-range ordered phases under the presence of squired elastic strain gradient. The squired elastic strain gradient is required for the free energy stability to arbitrary strain gradients.Obtained analytical expressions showed that the fundamental upper limit for the magnitude of the static bulk flexoelectric effect strength, established by Yudin and Tagantsev under the absence of squired elastic strain gradient and higher order gradients terms, should be substituted by the temperature-dependent condition on the flexoelectric coupling strength under the presence of the gradient terms. Moreover, we established that the SMP appears and becomes stable in commensurate ferroics if the flexocoupling constant exceeds the critical value, defined by the reduced temperature, strain and order parameter gradients constants, striction and expansion coefficients in the LGD functional.We calculated the soft phonon dispersion in ferroics with commensurate and incommensurate longrange ordered phases allowing for the squired elastic strain gradient, as well as static and dynamic flexocoupling.Appeared that the dispersion for the optic mode is slightly sensitive to the flexocoupling, while the dispersion of acoustic mode strongly depends on the coupling strength. Obtained results demonstrate that the non-trivial differences in the dispersion of optic and acoustic modes appear under the change of flexocoupling constant.Hence the experimental determination of soft phonon dispersion can give the important information about the influence of the strain gradient and flexocoupling on the SMP in ferroics with commensurate and incommensurate long-range order. These theoretical predictions require experimental verification.

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.

An analysis of the P2S6 cluster electronic structure and its comparison with the crystal valence band in the paraelectric and ferroelectric phases has been done by first-principles calculations for Sn2P2S6 ferroelectrics. The origin of ferroelectricity has been outlined. It was established that the spontaneous polarization follows from the stereochemical activity of the electron lone pair of tin cations, which is determined by hybridization with P2S6 molecular orbitals. The chemical bonds covalence increase and rearrangement are related to the valence band changes at transition from the paraelectric phase to the ferroelectric phase.

Flexoelectric effect impact on the generalized susceptibility and soft phonons dispersion was not studied in the long-range ordered phases of ferroics. Within Landau-Ginzburg-Devonshire approach we obtained analytical expressions for the generalized susceptibility and phonon dispersion relations in the ferroelectric phase. The joint action of static and dynamic flexoelectric effect induces non-diagonal components of generalized susceptibility, which amplitude is proportional to the convolution of the spontaneous polarization with flexocoupling constants.The flexocoupling essentially broadens the k-spectrum of generalized susceptibility and leads to the additional "pushing away" of the optical and acoustic soft mode phonon branches. The degeneration of the transverse optic and acoustic modes disappears in the ferroelectric phase in comparison with the paraelectric phase due to the joint action of flexoelectric coupling and ferroelectric nonlinearity. Obtained results can be principally important for the theoretical analyses of the experimental data broad spectrum including neutron and Brillouin scattering.