Ferroelectric domain walls are boundaries between regions with different polarization orientations in a ferroelectric material. Using first principles calculations, we characterize all different types of domain walls forming on ($11\bar{1}$), ($111$) and ($1\bar{1}0$) crystallographic planes in thermoelectric GeTe. We find large structural distortions in the vicinity of most of these domain walls, which are driven by polarization variations. We show that such strong strain-order parameter coupling will considerably reduce the lattice thermal conductivity of GeTe samples containing domain walls with respect to single crystal. Our results thus suggest that domain engineering is a promising path for enhancing the thermoelectric figure of merit of GeTe.
GeTe has been proposed as the father compound of a new class of functional materials displaying bulk Rashba effects coupled to ferroelectricity: ferroelectric Rashba semiconductors. In nice agreement with first principle calculations, we show by angular resolved photoemission and piezo-force microscopy that GeTe displays surface and bulk Rashba bands arising from the intrinsic inversion symmetry breaking provided by the remanent ferroelectric polarization. This work points to the possibility to control the spin chirality of bands in GeTe by acting on its ferroelectric polarization.
GeTe is a well-known ferroelectric and thermoelectric material that undergoes a structural phase transition from a rhombohedral to the rocksalt structure at $\sim 600-700$ K. We present a first principles approach to calculate the thermal expansion of GeTe in the rhombohedral phase up to the Curie temperature. We find the minimum of the Helmholtz free energy with respect to each structural parameter in a manner similar to the traditional Gr{ü}neisen theory, and account for the temperature dependence of elastic constants. We obtain the temperature variation of the structural parameters of rhomb…
A comprehensive mapping of the spin polarization of the electronic bands in ferroelectric a-GeTe(111) films has been performed using a time-of-flight momentum microscope equipped with an imaging spin filter that enables a simultaneous measurement of more than 10.000 data points (voxels). A Rashba type splitting of both surface and bulk bands with opposite spin helicity of the inner and outer Rashba bands is found revealing a complex spin texture at the Fermi energy. The switchable inner electric field of GeTe implies new functionalities for spintronic devices.
By performing density functional theory (DFT) and Green's functions calculations, complemented by X-ray Photoemission Spectroscopy, we investigate the electronic structure of Fe/GeTe(111), a prototypical ferromagnetic/Rashba-ferroelectric interface. We reveal that such system exhibits several intriguing properties resulting from the complex interplay of exchange interaction, electric polarization and spin-orbit coupling. Despite a rather strong interfacial hybridization between Fe and GeTe bands, resulting in a complete suppression of the surface states of the latter, the bulk Rashba bands are…
Controlling charge-spin current conversion by electric fields is crucial in spintronic devices, which can be realized in diatom ferroelectric semiconductor GeTe where it is established that ferroelectricity can change the spin texture. We demonstrated that the spin Hall conductivity (SHC) can be further tuned by ferroelectricity based on the density functional theory calculations. The spin texture variation driven by the electric fields was elucidated from the symmetry point of view, highlighting the interlocked spin and orbital degrees of freedom. We observed that the origin of SHC can be att…
Experimental investigations of the phase transition in GeTe provide contradictory conclusions regarding the nature of the phase transition. Considering growing interest in technological applications of GeTe, settling these disputes is of great importance. To that end, we present a molecular dynamics study of the structural phase transition in GeTe using a machine-learned interatomic potential with ab-initio accuracy. First, we calculate the asymmetric shape of the radial distribution function of the nearest-neighbor bonds above the critical temperature, in agreement with previous studies. Howe…
Since its birth in the 1990s, semiconductor spintronics has suffered from poor compatibility with ferromagnets as sources of spin. While the broken inversion symmetry of some semiconductors may alternatively allow for spin-charge interconversion, its control by electric fields is volatile. Ferroelectric Rashba semiconductors stand as appealing materials unifying semiconductivity, large spin-orbit coupling, and non-volatility endowed by ferroelectricity. However, their potential for spintronics has been little explored. Here, we demonstrate the non-volatile, ferroelectric control of spin-to-cha…
Rashba materials have appeared as an ideal playground for spin-to-charge conversion in prototype spintronics devices. Among them, $α$-GeTe(111) is a non-centrosymmetric ferroelectric (FE) semiconductor for which a strong spin-orbit interaction gives rise to giant Rashba coupling. Its room temperature ferroelectricity was recently demonstrated as a route towards a new type of highly energy-efficient non-volatile memory device based on switchable polarization. Currently based on the application of an electric field, the writing and reading processes could be outperformed by the use of femtosecon…
Calculations of the optical properties of GeTe in the cubic NaCl and rhombohedral ferroelectric structures are reported. The rhombohedral ferroelectric distortion increases the band gap from 0.11 eV to 0.38 eV. Remarkably, substantial changes in optical properties are found even at high energies up to 5 eV. The results are discussed in relation to the bonding of GeTe and to phase change materials based on it.
Based on the first-principles calculations, we investigated the ferroelectric properties of two-dimensional (2D) Group-IV tellurides XTe (X=Si, Ge and Sn), with a focus on GeTe. 2D Group-IV tellurides energetically prefer an orthorhombic phase with a hinge-like structure and an in-plane spontaneous polarization. The intrinsic Curie temperature Tc of monolayer GeTe is as high as 570 K and can be raised quickly by applying a tensile strain. An out-of-plane electric field can effectively decrease the coercive field for the reversal of polarization, extending its potential for regulating the polar…
GeTe wins the renewed research interest due to its giant bulk Rashba spin orbit coupling (SOC), and becomes the father of a new multifunctional material, i.e., ferroelectric Rashba semiconductor. In the present work, we investigate Rashba SOC at the interface of the ferroelectric semiconductor superlattice GeTe(111)/InP(111) by using the first principles calculation. Contribution of the interface electric field and the ferroelectric field to Rashba SOC is revealed. A large modulation to Rashba SOC and a reversal of the spin polarization is obtained by switching the ferroelectric polarization. …
Germanium telluride features special spin-electric effects originating from spin-orbit coupling and symmetry breaking by the ferroelectric lattice polarization, which opens up many prospectives for electrically tunable and switchable spin electronic devices. By Mn doping of the α-GeTe host lattice, the system becomes a multiferroic semiconductor possessing magnetoelectric properties in which the electric polarization, magnetization and spin texture are coupled to each other. Employing spin- and angle-resolved photoemission spectroscopy in bulk- and surface-sensitive energy ranges and by varyin…
Ferroelectric Rashba semiconductors (FERSC) have recently emerged as a promising class of spintronics materials. The peculiar coupling between spin and polar degrees of freedom responsible for several exceptional properties, including ferroelectric switching of Rashba spin texture, suggests that the electron's spin could be controlled by using only electric fields. In this regard, recent experimental studies revealing charge-to-spin interconversion phenomena in two prototypical FERSC, GeTe and SnTe, appear extremely relevant. Here, by employing density functional theory calculations, we invest…
$α$-GeTe(111) is a non-centrosymmetric ferroelectric material, for which a strong spin-orbit interaction gives rise to giant Rashba split states in the bulk and at the surface. The detailed dispersions of the surface states inside the bulk band gap remains an open question because they are located in the unoccupied part of the electronic structure, making them inaccessible to static angle-resolved photoemission spectroscopy. We show that this difficulty can be overcome via in-situ potassium doping of the surface, leading to a rigid shift of 80 meV of the surface states into the occupied states…
In systems with broken inversion symmetry spin-orbit coupling (SOC) yields a Rashba-type spin splitting of electronic states, manifested in a k-dependent splitting of the bands. While most research had previously focused on 2D electron systems, recently a three-dimensional (3D) form of such Rashba-effect was found in a series of bismuth tellurohalides. Whereas these materials exhibit a very large spin-splitting, they lack an important property concerning functionalization, namely the possibility to switch or tune the spin texture. This limitation can be overcome in a new class of functional ma…
The proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity $κ$. However, the $κ$ of GeTe increases at the ferroelectric phase transition near $700$ K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in $κ$ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Negative thermal expansion increases phonon grou…
The electrical manipulation of spins in semiconductors, without magnetic fields or auxiliary ferromagnetic materials, represents the holy grail for spintronics. The use of Rashba effect is very attractive because the k-dependent spin-splitting is originated by an electric field. So far only tiny effects in two-dimensional electron gases (2DEG) have been exploited. Recently, GeTe has been predicted to have bulk bands with giant Rashba-like splitting, originated by the inversion symmetry breaking due to ferroelectric polarization. In this work, we show that GeTe(111) surfaces with inwards or out…
Ferroelectric GeTe is unveiled to exhibit an intriguing multiple non-trivial topology of the electronic band structure due to the existence of triple-point and type-II Weyl fermions, which goes well beyond the giant Rashba spin splitting controlled by external fields as previously reported. Using spin- and angle-resolved photoemission spectroscopy combined with ab initio density functional theory, the unique spin texture around the triple point caused by the crossing of one spin degenerate and two spin-split bands along the ferroelectric crystal axis is derived. This consistently reveals spin …
The dynamical, dielectric and elastic properties of GeTe, a ferroelectric material in its low temperature rhombohedral phase, have been investigated using first-principles density functional theory. We report the electronic energy bands, phonon dispersion curves, electronic and low frequency dielectric tensors, infra-red reflectivity, Born effective charges, elastic and piezoelectric tensors and compare them with the existing theoretical and experimental results, as well as with similar quantities available for other ferroelectric materials, when appropriate.
Magnetic skyrmions are chiral nanoscale spin textures which are usually induced by Dzyaloshinskii-Moriya interaction (DMI). Recently, magnetic skyrmions have been observed in two-dimensional (2D) van der Waals (vdW) ferromagnetic materials, such as Fe$_{3}$GeTe$_{2}$. The electric control of skyrmions is important for their potential application in low-power memory technologies. Here, we predict that DMI and magnetic skyrmions in a Fe$_{3}$GeTe$_{2}$ monolayer can be controlled by ferroelectric polarization of an adjacent 2D vdW ferroelectric In$_{2}$Se$_{3}$. Based on density functional theor…
Among two-dimensional materials, Fe$_3$GeTe$_2$ has come to occupy a very important place owing to its ferromagnetic nature with one of the highest Curie temperatures among known van der Waals materials and the potential for hosting skyrmions. In this combined experimental and theoretical work, we investigate the magnetic bubble domains as well as the microscopic domain wall profile using spin-polarized scanning tunneling microscopy in combination with atomistic spin-dynamics simulations performed with parameters from density functional theory calculations. We find a weak magneto-electric effe…
Peierls-Boltzmann transport equation, coupled with third-order anharmonic lattice dynamics calculations, has been widely used to model lattice thermal conductivity ($κ_{l}$) in bulk crystals. However, its application to materials with structural phase transition at relatively high temperature is fundamentally challenged by the presence of lattice instabilities (imaginary phonon modes). Additionally, its accuracy suffers from the absence of higher-than-third-order phonon scattering processes, which are important near/above the Debye temperature. In this letter, we present an effective scheme th…
The recent surge of interest in phase change materials GeTe, Ge$_2$Sb$_2$Te$_5$, and related compounds motivated us to revisit the structural phase transition in GeTe in more details than was done before. Rhombohedral-to-cubic ferroelectric phase transition in GeTe has been studied by high resolution neutron powder diffraction on a spallation neutron source. We determined the temperature dependence of the structural parameters in a wide temperature range extending from 309 to 973 K. Results of our studies clearly show an anomalous volume contraction of 0.6\% at the phase transition from the rh…
Recently large Rashba-like spin splitting has been observed in certain bulk ferroelectrics. In contrast with the relativistic Rashba effect, the chiral spin texture and large spin-splitting of the electronic bands depend strongly on the character of the band and atomic spin-orbit coupling. We establish that this can be traced back to the so-called orbital Rashba effect, also in the bulk. This leads to an additional dependence on the orbital composition of the bands, which is crucial for a complete picture of the effect. Results from first-principles calculations on ferroelectic GeTe verify the…
The control of spin-dependent properties by voltage, not involving magnetization switching, has significant advantages for low-power spintronics. Here, we predict that the interfacial crystal Hall effect (ICHE) can serve for this purpose. We show that the ICHE can occur in heterostructures composed of compensated antiferromagnetic metals and non-magnetic insulators due to reduced symmetry at the interface, and it can be made reversible if the antiferromagnet is layered symmetrically between two identical ferroelectric layers. We explicitly demonstrate this phenomenon using density functional t…
While an ideal antiparallel ferroelectric wall is considered a unit cell in width (~0.5nm), we show using phase field modeling that the threshold field for moving this wall dramatically drops by 2-3 orders of magnitude if the wall were diffuse by only ~2-3nm. Since antiparallel domain walls are symmetry allowed in all ferroelectrics, and since domain wall broadening on nanometer scale is widely reported in literature, this mechanism is generally applicable to all ferroelectrics.
The motion of ferroelectric domain walls (DW) is critical for various technological applications of ferroelectric materials. One important question that is of interest both scientifically and technologically is whether the ferroelectric DW has momentum. To address this problem, we performed canonical ensemble molecular dynamics simulations of 180$^\circ$ and 90$^\circ$ DWs under applied electric field. Examination of the evolution of the polarization and local structure of DWs reveals that they stop moving after the removal of electric field. Thus, our computational study shows that ferroelect…
We report on the evolution of ferromagnetic domain walls during magnetization reversal in elastically coupled ferromagnetic-ferroelectric heterostructures. Using optical polarization microscopy and micromagnetic simulations, we demonstrate that the spin rotation and width of ferromagnetic domain walls can be accurately controlled by the strength of the applied magnetic field if the ferromagnetic walls are pinned onto 90 degrees ferroelectric domain boundaries. Moreover, reversible switching between magnetically charged and uncharged domain walls is initiated by magnetic field rotation. Switchi…
We investigate oscillation dynamics of a periodic structure of the $180^\circ$ domain walls in nanometricaly thin substrate-deposited ferroelectric films and superlattices. We calculate dynamic permittivity of such structures and reveal a collective resonance mode, which in the typical ferroelectric compounds, PbTiO3/SrTiO3, lies in the sub- and low THz frequency range of 0.3-3THz. We propose the reflection-absorbtion spectroscopy experiments to observe this mode.
High-resolution X-ray photoemission electron microscopy (X-PEEM) is a well-established method for imaging ferroelectric domain structures. Here, we expand the scope of application of X-PEEM and demonstrate its capability for imaging and investigating domain walls in ferroelectrics with high-spatial resolution. Using ErMnO3 as test system, we show that ferroelectric domain walls can be visualized based on photo-induced charging effects and local variations in their electronic conductance can be mapped by analyzing the energy distribution of photoelectrons. Our results open the door for non-dest…
Deterministic polarization reversal in ferroelectric and multiferroic films is critical for their exploitation in nanoelectronic devices. While ferroelectricity has been studied for nearly a century, major discrepancies in the reported values of coercive fields and saturation polarization persist in literature for many materials. This raises questions about the atomic-scale mechanisms behind polarization reversal. Unconventional ferroelectric switching in $ε$-Fe2O3 films, a material that combines ferrimagnetism and ferroelectricity at room temperature, is reported here. High-resolution in-situ…
Although enhanced conductivity at ferroelectric domain boundaries has been found in BiFeO$_3$ films, Pb(Zr,Ti)O$_3$ films, and hexagonal rare-earth manganite single crystals, the mechanism of the domain wall conductivity is still under debate. Using conductive atomic force microscopy, we observe enhanced conductance at the electrically-neutral domain walls in semiconducting hexagonal ferroelectric TbMnO$_3$ thin films where the structure and polarization direction are strongly constrained along the c-axis. This result indicates that domain wall conductivity in ferroelectric rare-earth manganit…
Flexoelectric effect is the coupling between strain, polarization and their gradients, which are prominent at the nanoscale. Although this effect is important to understand nanostructures, such as domain walls in ferroelectrics, its electronic mechanism is not clear. In this work, we combined phase-field simulations and first-principles calculations to study the 180° domain walls in tetragonal ferroelectric PbTiO3, and found that the ultimate source of Néel components is the gradient of the square of spontaneous polarizations. Electronic structural analysis reveals that there is a redistributi…
We investigated the ferroelectric domain wall propagation in epitaxial Pb(Zr,Ti)O3 thin films over a wide temperature range (3 - 300 K). We measured the domain wall velocity under various electric fields and found that the velocity data is strongly nonlinear with electric fields, especially at low temperature. We found that, as one of surface growth problems, our domain wall velocity data from ferroelectric epitaxial film could be classified into the creep, depinning, and flow regimes due to competition between disorder and elasticity. The measured values of velocity and dynamical exponents in…
Ferroelectric domain walls are attracting broad attention as atomic-scale switches, diodes and mobile wires for next-generation nanoelectronics. Charged domain walls in improper ferroelectrics are particularly interesting as they offer multifunctional properties and an inherent stability not found in proper ferroelectrics. Here we study the energetics and structure of charged walls in improper ferroelectric YMnO$_3$, InMnO$_3$ and YGaO$_3$ by first principles calculations and phenomenological modeling. Positively and negatively charged walls are asymmetric in terms of local structure and width…
The conductive domain wall (CDW) is extensively investigated in ferroelectrics, which can be considered as a quasi-two-dimensional reconfigurable conducting channel embedded into an insulating material. Therefore, it is highly important for the application of ferroelectric nanoelectronics. Hitherto, most CDW investigations are restricted in oxides, and limited work has been reported in non-oxides to the contrary. Here, by successfully synthesizing the non-oxide ferroelectric Sn2P2S6 single crystal, we observed and confirmed the domain wall conductivity by using different scanning probe techniq…
The interaction of ferroelectric 180 degree domain wall with a strongly inhomogeneous electric field of biased Scanning Probe Microscope tip is analyzed within continuous Landau-Ginzburg-Devonshire theory. Equilibrium shape of the initially flat domain wall boundary bends, attracts or repulses from the probe apex, depending on the sign and value of the applied bias. For large tip-wall separations, the probe-induced domain nucleation is possible. The approximate analytical expressions for the polarization distribution are derived using direct variational method. The expressions provide insight …
Domain walls are the topological defects that mediate polarization reversal in ferroelectrics, and they may exhibit quite different geometric and electronic structures compared to the bulk. Therefore, a detailed atomic-scale understanding of the static and dynamic properties of domain walls is of pressing interest. In this work, we use first-principles methods to study the structures of $180^{\circ}$ domain walls, both in their relaxed state and along the ferroelectric reversal pathway, in ferroelectrics belonging to the family of corundum derivatives. Our calculations predict their orientatio…
We present a first-principles study of model domain walls (DWs) in prototypic ferroelectric PbTiO3. At high temperature the DW structure is somewhat trivial, with atoms occupying high- symmetry positions. However, upon cooling the DW undergoes a symmetry-breaking transition characterized by a giant dielectric anomaly and the onset of a large and switchable polarization. Our results thus corroborate previous arguments for the occurrence of ferroic orders at structural DWs, providing a detailed atomistic picture of a temperature-driven DW-confined transformation. Beyond its relevance to the fiel…
The behavior of antiferromagnetic domain wall (ADW) against the background of a periodic ferroelectric domain structure has been investigated. It has been shown that the structure and the energy of ADW change due to the interaction with a ferroelectric domain structure. The ferroelectric domain boundaries play the role of pins for magnetic spins, the spin density changes in the vicinity of ferroelectric walls. The ADW energy becomes a periodical function on a coordinate which is the position of ADW relative to the ferroelectric domain structure. It has been shown that the energy of the magneti…
The impact of free charges on the local pressure on a charged ferroelectric domain wall produced by an electric field has been analyzed. A general formula for the local pressure on a charged domain wall is derived considering full or partial compensation of bound polarization charges by free charges. It is shown that the compensation can lead to a very strong reduction of the pressure imposed on the wall from the electric field. In some cases this pressure can be governed by small nonlinear effects. It is concluded that the free charge compensation of bound polarization charges can lead to sub…
We report two series of structures representing two types of $180^\circ$ ferroelectric domain walls in $\mathrm{HfO_2}$ and $\mathrm{ZrO_2}$. We model the domain structures with different width by density functional theory calculations. The results reveal the dependency of domain wall energy and polarization on domain width. We show how the directions of polarization of ferroelectric domains can be determined from experimentally observed Hf atoms, despite the fact that the knowledge about the positions of O atoms is missing. The two series of structures thus provide more thorough interpretatio…
First-principles calculations for pristine neutral ferroelectric domain walls in BiFeO$_3$ reveal that excess electrons are selectively trapped by the domain walls, while holes are only weakly attracted. Such trapped excess electrons may be responsible for the thermally activated electrical conductivity at domain walls observed in experiments. In the case of a periodic array of domain walls, the trapped excess electrons create a zigzag potential, whose amplitude depends on the electron concentration in the material and the domain-wall distance. The potential is asymmetric for 71° and 109° doma…
Ferroelectrics usually adopt a multi-domain state with domain walls separating domains with polarization axes oriented differently. It has long been recognized that domain walls can dramatically impact the properties of ferroelectric materials. The enhancement of low-field susceptibility/permittivity under subswitching conditions is usually attributed to the reversible domain wall vibration. Recent experiments highlight the stationary domain wall contribution to the dielectric susceptibility irrespective of any lateral displacements or deformations of the wall. We study the effects of domain w…
We report the first investigation of the piezoelectric response on a nanoscale in the poled ferroelectric crystals with engineered configuration of domains. Piezoresponse force microscopy of tetragonal 0.63PMN-0.37PT relaxor-based ferroelectric crystals reviled that the d33 piezoelectric coefficient is significantly reduced within the distance of about 1 um from the uncharged engineered domain wall. This finding is essential for understanding the mechanisms of the giant piezoresponse in relaxor-based crystals and for designing new piezoelectric materials.
Using the classic ferroelectric BaTiO$_3$ as an example, we show that the 180 degree ferroelectric domain wall, long considered to be of Ising-type and charge neural, contains both Bloch and Neel type polarization components, and is thus charged. The bound charge density at the wall may reach as high as 10$^6$~10$^7$ Cm$^{-3}$. It is demonstrated that the flexoelectric effect arising from stress inhomogeneity is responsible for the additional Bloch and Neel polarization components. The magnitudes of these additional components are determined by the competing depolarization and flexoelectric fi…
The symmetry of boundaries between ferroelectric, ferroelastic and antiphase domains is a key element for a theoretical understanding of their properties. Here, we derive this symmetry from their organic relation to the symmetry of the primary transition order parameters. The domain wall symmetries are shown to coincide with directions of the order-parameter n-dimensional vector space, corresponding to sum of the vectors associated with adjacent domain states. This property is illustrated by the determination of the domain wall maximal symmetries in BaTiO3, LaAlO3, SrTiO3 and Gd2(MoO4)3. Besid…
Ferroelectric domain walls exhibit a range of interesting electrical properties and are now widely recognized as functional two-dimensional systems for the development of next-generation nanoelectronics. A major achievement in the field was the development of a fundamental framework that explains the emergence of enhanced electronic direct-current (DC) conduction at the domain walls. In this Review, we discuss the much less explored behavior of ferroelectric domain walls under applied alternating-current (AC) voltages. We provide an overview of the recent advances in the nanoscale characteriza…
The role of elastic defects on the kinetics of 180-degree uncharged ferroelectric domain wall motion is explored using continuum time-dependent LGD equation with elastic dipole coupling. In one dimensional case, ripples, steps and oscillations of the domain wall velocity appear due to the wall-defect interactions. While the defects do not affect the limiting-wall velocity vs. field dependence, they result in the minimal threshold field required to activate the wall motions. The analytical expressions for the threshold field are derived and the latter is shown to be much smaller than the thermo…
Ferroelectric domain walls represent multifunctional 2D-elements with great potential for novel device paradigms at the nanoscale. Improper ferroelectrics display particularly promising types of domain walls, which, due to their unique robustness, are the ideal template for imposing specific electronic behavior. Chemical doping, for instance, induces p- or n-type characteristics and electric fields reversibly switch between resistive and conductive domain-wall states. Here, we demonstrate diode-like conversion of alternating-current (AC) into direct-current (DC) output based on neutral 180$^{\…
Modulating the polarization of a beam of quantum particles is a powerful method to tailor the macroscopic properties of the ensuing energy flux as it directly influences the way in which its quantum constituents interact with other particles, waves or continuum media. Practical polarizers, being well developed for electric and electromagnetic energy, have not been proposed to date for heat fluxes carried by phonons. Here we report on atomistic phonon transport calculations demonstrating that ferroelectric domain walls can operate as phonon polarizers when a heat flux pierces them. Our simulati…
