Marie Kratochvilova, Fei-Ting Huang, Maria-Teresa Fernandez Diaz, Milan Klicpera, Sarah J. Day, Stephen P. Thompson, Yoon-Seok Oh, Bin Gao, Sang-Wook Cheong, Je-Geun Park
We present the results of the high-temperature neutron and x-ray diffraction experiments on the Ca3-xSrxTi2O7 (x = 0.5, 0.8, 0.85, 0.9) compounds. The ferro- to paraelectric transition in these hybrid improper ferroelectric materials arises from the so-called trilinear coupling. Depending on the Strontium content, various structures and phase transitions, different from theoretical predictions, emerge. The in-situ x-ray powder diffraction indicates a direct ferro- to paraelectric transition between the orthorhombic A21am and tetragonal undistorted I4/mmm phase for x < 0.6. We identified a reduction in the trilinear coupling robustness by increasing the Sr-doping level to lead to the emergence of the intermediate tetragonal P42/mnm phase and the gradual suppression of the orthorhombic phase. The observed character of the structure transitions and the Ca3-xSrxTi2O7 phase diagram are discussed in the framework of theoretical models of other related hybrid improper ferroelectric systems.
Xianghan Xu, Fei-Ting Huang, Yubo Qi, Sobhit Singh, Karin M. Rabe, Dimuthu Obeysekera, Junjie Yang, Ming-Wen Chu, Sang-Wook Cheong
HfO2, a simple binary oxide, holds ultra-scalable ferroelectricity integrable into silicon technology. Polar orthorhombic (Pbc21) form in ultra-thin-films ascribes as the plausible root-cause of the astonishing ferroelectricity, which has thought not attainable in bulk crystals. Though, perplexities remain primarily due to the polymorphic nature and the characterization challenges at small-length scales. Herein, utilizing a state-of-the-art Laser-Diode-heated Floating Zone technique, we report ferroelectricity in bulk single-crystalline HfO2:Y as well as the presence of anti-polar Pbca phase at different Y concentrations. Neutron diffraction and atomic imaging demonstrate (anti-)polar crystallographic signatures and abundant 90o/180o ferroelectric domains in addition to the switchable polarization with little wake-up effects. Density-functional theory calculations suggest that the Yttrium doping and rapid cooling are the key factors for the desired phase. Our observations provide new insights into the polymorphic nature and phase controlling of HfO2, remove the upper size limit for ferroelectricity, and also pave a new road toward the next-generation ferroelectric devices.
Fei-Ting Huang, Yanbin Li, Fei Xue, Jae-Wook Kim, Lunyong Zhang, Ming-Wen Chu, Long-Qing Chen, Sang-Wook Cheong
How topological defects, unavoidable at symmetry-breaking phase transitions in a wide range of systems, evolve through consecutive phase transitions with different broken symmetries remains unexplored. Nd2SrFe2O7, a bilayer ferrite, exhibits two intriguing structural phase transitions and dense networks of the so-called type-II Z8 structural vortices at room temperature, so it is an ideal system to explore the topological defect evolution. From our extensive experimental investigation, we demonstrate that the cooling rate at the second-order transition (1290oC) plays a decisive role in determining the vortex density at room temperature, following the universal Kibble-Zurek mechanism. In addition, we discovered a transformation between topologically-distinct vortices (Z8 to Z4 vortices) at the first-order transition (550oC), which conserves the number of vortex cores. Remarkably, the Z4 vortices consist of two phases with an identical symmetry but two distinct magnitudes of an order parameter. Furthermore, when lattice distortion is enhanced by chemical doping, a new type of topological defects emerges: loop domain walls with orthorhombic distortions in the tetragonal background, resulting in unique pseudo-orthorhombic twins. Our findings open a new avenue to explore the evolution of topological defects through multiple phase transitions.
Seongjoon Lim, Sobhit Singh, Fei-Ting Huang, Shangke Pan, Kefeng Wang, Jaewook Kim, Jinwoong Kim, David Vanderbilt, Sang-Wook Cheong
Electric currents have the intriguing ability to induce magnetization in nonmagnetic crystals with sufficiently low crystallographic symmetry. Some associated phenomena include the non-linear anomalous Hall effect in polar crystals and the nonreciprocal directional dichroism in chiral crystals when magnetic fields are applied. In this work, we demonstrate that the same underlying physics is also manifested in the electronic tunneling process between the surface of a nonmagnetic chiral material and a magnetized scanning probe. In the paramagnetic but chiral metallic compound Co$_{1/3}$NbS$_2$, the magnetization induced by the tunneling current is shown to become detectable by its coupling to the magnetization of the tip itself. This results in a contrast across different chiral domains, achieving atomic-scale spatial resolution of structural chirality. To support the proposed mechanism, we used first-principles theory to compute the chirality-dependent current-induced magnetization and Berry curvature in the bulk of the material. Our demonstration of this magnetochiral tunneling effect opens up a new avenue for investigating atomic-scale variations in the local crystallographic symmetry and electronic structure across the structural domain boundaries of low-symmetry nonmagnetic crystals.
Kai Du, Xiaochen Fang, Choongjae Won, Chandan De, Fei-ting Huang, Fernando J. Gomez-Ruiz, Adolfo Del Campo, Sang-Wook Cheong
The formation of topological defects after a symmetry-breaking phase transition is an overarching phenomenon that encodes rich information about the underlying dynamics. Kibble-Zurek mechanism (KZM), which describes these nonequilibrium dynamics, predicts defect densities of these second-order phase transitions driven by thermal fluctuations. It has been verified as a successful model in a wide variety of physical systems, finding applications from structure formation in the early universe to condensed matter systems. However, whether topologically-trivial Ising domains, one of the most common and fundamental types of domains in condensed matter systems, also obey the KZM has never been investigated in the laboratory. We examined two different kinds of three-dimensional (3D) structural Ising domains: clockwise (CW)/counter-clockwise (CCW) ferro-rotation domains in NiTiO3 and up/down polar domains in BiTeI. While the KZM slope of ferro-rotation domains in NiTiO3 agrees well with the prediction of the 3D Ising model, the KZM slope of polar domains in BiTeI surprisingly far exceeds the theoretical limit, setting an exotic example where possible weak long-range dipolar interactions play a critical role in steepening the KZM slope of non-topological quantities. Our results demonstrate the validity of KZM for Ising domains and reveal an enhancement of the power-law exponent and a possible reduction of the dynamic critical exponent z for transitions with long-range interactions.
Sang-Wook Cheong, Fei-Ting Huang
The flow of time moves in one direction in any spatial position and orientation in this universe. Chiral objects, which lack mirror symmetry, retain their chirality regardless of their position or orientation. Despite being seemingly independent, time and chirality share common features such as universality -- applying to 'any position and orientation' -- and a binary nature, such as forward/backward time flow versus left/right chirality. We introduce the concept of Time Chirality and discuss the conjugate relationship between time chirality and traditional chirality. We explore how time chirality can manifest in certain magnetic states, and examine the novel physical phenomena associated with time-chiral magnetic states. This discussion offers a fresh perspective on true time reversal symmetry breaking and temporal nonreciprocity.
Sang-Wook Cheong, Fei-Ting Huang
Ferromagnetism can be characterized by various unique phenomena such as non-zero magnetization (inducing magnetic attraction/repulsion), diagonal piezomagnetism, nonreciprocal circular dichroism (such as Faraday effect), odd-order (including linear) anomalous Hall effect, and magneto-optical Kerr effect. We identify all broken symmetries requiring each of the above phenomena, and also the relevant magnetic point groups (MPGs) with those broken symmetries. All of ferromagnetic point groups, relevant for ferromagnets, ferri-magnets and weak ferromagnets, can certainly exhibit all of these phenomena, including non-zero magnetization. Some of true antiferromagnets, which are defined as magnets with MPGs that do not belong to ferromagnetic point groups, can display these phenomena through magnetization induced by external perturbations such as applied current, electric fields, light illumination, and strain. Such MPGs are identified for each external perturbation. Since high-density and ultrafast spintronic technologies can be enabled by antiferromagnets, our findings will be an essential guidance for the future magnetism-related science as well as technology.
Yubo Qi, Sobhit Singh, Claudia Lau, Fei-Ting Huang, Xianghan Xu, Frederick J. Walker, Charles H. Ahn, Sang-Wook Cheong, Karin M. Rabe
Hafnia (HfO$_2$)-based thin films have promising applications in nanoscale electronic devices due to their robust ferroelectricity and integration with silicon. However, HfO$_2$ has various stable and metastable polymorphs with quite similar structures and energies. Identifying and stabilizing the ferroelectric functional phases of HfO$_2$ have attracted intensive research interest in recent years. In this work, first-principles calculations on (111)-oriented HfO$_2$ are used to discover that imposing an in-plane shear strain on the tetragonal phase induces a nonpolar to polar phase transition. This in-plane shear-induced polar phase is shown to be an epitaxial distortion of a known metastable ferroelectric $Pnm2_1$ phase of HfO$_2$. It is proposed that this ferroelectric $Pnm2_1$ phase can account for the recently observed ferroelectricity in the (111)-oriented HfO$_2$-based thin film [Nature Materials 17, 1095-1100 (2018)]. Further investigation of this second functional ferroelectric phase in HfO$_2$ could potentially improve the performances of HfO$_2$-based films in logic and memory devices.
Sang-Wook Cheong, Fei-Ting Huang
Kinetomagnetism refers to magnetization induced by (electric) current, encompassing longitudinal or transverse effects and even- or odd-order phenomena. The essential prerequisite for kinetomagnetism is the breaking of PT (=Parity times Time reversal) symmetry. Altermagnets, characterized by full spin compensation and broken PT symmetry, are associated with spin-split electronic bands. Altermagnets with non-zero net magnetizations (M-type) fall within the ferromagnetic point group and are classified as orbital ferrimagnets. In contrast, S- and A-type altermagnets only exhibit non-zero net magnetizations under external perturbations, such as (electric) current or mechanical stress, which preserve PT symmetry. This study delves into the intriguing interplay between altermagnetism and kinetomagnetism, emphasizing magnetic point group classifications, called as the SAM classification. Various orders of the anomalous Hall effect are analyzed alongside kinetomagnetism, extending the discussion to certain non-magnetic materials with low symmetry. The MPG analysis for kinetomagnetism and altermagnetism highlights significant scientific and technological opportunities, particularly in materials explorations.
Sang-Wook Cheong, Fei-Ting Huang
Altermagnetism is introduced as a category of magnetic states with vanishing net magnetic moment, and consists of collinear alternating (i.e., antiferromagnetic-like) spins and alternating variations of local structures around spins in such a way that the symmetry allows ferromagnetic behaviors such as anomalous Hall effect and magneto-optical Kerr effects. Altermagnets exhibiting ferromagnetic behaviors without any external perturbations (called type-I) turn out to belong to the ferromagnetic point group, and represent a form of weak ferromagnetic states. Other altermagnets (called type-II and type-III) can have ferromagnetic behaviors only with external perturbations, which conserve parity-time reversal (PT) symmetry. All types of altermagnets themselves have broken PT symmetry. The concept of altermagnetism can be extended to accommodate multiple spin and local-structure variations (thus, include non-collinear spins), and this extended form of altermagnetism offers an intriguing opportunity to leverage complementary advantages of both ferromagnetism and antiferromagnetism, and thus holds great promise for, for example, various spintronic applications.
Sang-Wook Cheong, Fei-Ting Huang
Symmetry often governs the laws of nature, and breaking symmetry accompanies a new order parameter and emergent observable phenomena. Herein, we focus on broken Parity (P)-Time (T) symmetry, which lifts the Kramers' degeneracy, and thus, guarantees non-trivial spin textures in excitation spectra. To attain non-zero measurables, we use the concept of symmetry operational similarity (SOS), which consider the symmetry relationship between a specimen and an experimental setup, rather than the symmetry of specific coupling terms. Even without specific coupling terms, this SOS approach can tell if the relevant phenomenon is a zero, non-zero odd-order or non-zero even-order effect. We discuss systematically numerous steady-state physical phenomena, in which breaking P-T symmetry is a necessary condition. These phenomena include Odd-order or Even-order Anomalous Hall Effect, Optical activities, Directional nonreciprocity in transverse magnetic field, Diagonal or Off-diagonal current-induced magnetization (current can be associated with electrons, phonons, or light), Diagonal or Off-diagonal piezomagnetism and piezoelectricity. Some of these phenomena turn out to be conjugate to each other through P to T. Our findings unveil numerous new non-traditional candidate materials for various exotic physical phenomena, many of which have never been realized in the standard coupling term/tensorial approaches, and are a transformative and unconventional avenue for symmetry-guided materials designs and discoveries.
Sang-Wook Cheong, Seongjoon Lim, Kai Du, Fei-Ting Huang
Based on symmetry consideration, quasi-one-dimensional (1D) objects, relevant to numerous observables or phenomena, can be classified into eight different types. We provide various examples of each 1D type, and discuss their Symmetry Operational Similarity (SOS) relationships, which are often permutable. A number of recent experimental observations, including current-induced magnetization in polar or chiral conductors, non-linear Hall effect in polar conductors, spin-polarization of tunneling current to chiral conductors, and ferro-rotational domain imaging with linear gyration are discussed in terms of (permutable) SOS. In addition, based on (permutable) SOS, we predict a large number of new phenomena in low symmetry materials that can be experimentally verified in the future.
Yoon Seok Oh, Xuan Luo, Fei-Ting Huang, Yazhong Wang, Sang-Wook Cheong
Standing on successful first principles predictions for new functional ferroelectric materials, a number of new ferroelectrics have been experimentally discovered. Utilizing trilinear coupling of two types of octahedron rotations, hybrid improper ferroelectricity has been theoretically predicted in ordered perovskites and the Ruddlesden-Popper compounds (Ca$_{3}$Ti$_{2}$O$_{7}$, Ca$_{3}$Mn$_{2}$O$_{7}$, and (Ca/Sr/Ba)$_{3}$(Sn/Zr/Ge)$_{2}$O$_{7}$). However, the ferroelectricity of these compounds has never been experimentally confirmed and even their polar nature has been under debate. Here we provide the first experimental demonstration of room-temperature switchable polarization in the bulk crystals of Ca$_{3}$Ti$_{2}$O$_{7}$ as well as Sr-doped Ca$_{3}$Ti$_{2}$O$_{7}$. In addition, (Ca,Sr)$_{3}$Ti$_{2}$O$_{7}$ is found to exhibit an intriguing ferroelectric domain structure resulting from orthorhombic twins and (switchable) planar polarization. The planar domain structure accompanies abundant charged domain walls with conducting head-to-head and insulating tail-to-tail configurations, which exhibit two-order-of-magnitude conduction difference. These discoveries provide new research opportunities not only on new stable ferroelectrics of Ruddlesden-Popper compounds, but also on meandering conducting domain walls formed by planar polarization.
Shangfei Wu, Xianghan Xu, Fei-Ting Huang, Turan Birol, Sang-Wook Cheong, Girsh Blumberg
We employ polarization-resolved Raman spectroscopy to study the lattice dynamics of the polar charge density wave phase of the superconductor Mo$_3$Al$_2$C with structural chirality. We show the phononic signatures of the charge density wave transition at $T^*$ = 155\,K in Mo$_3$Al$_2$C. The detailed temperature dependence of these phonon modes' frequency, half width at half maximum, and integrated area below $T^*$ reveal anomalies at an intermediate temperature $T' \sim$ 100\,K, especially for the low-energy modes at 130 and 180\,\cm-1. We discuss the origin of these phonon anomalies within the polar charge density wave phase of Mo$_3$Al$_2$C.
Kai Du, Daegeun Jo, Xianghan Xu, Fei-Ting Huang, Ming-Hao Lee, Ming-Wen Chu, Kefeng Wang, David Vanderbilt, Hyun-Woo Lee, Sang-Wook Cheong
The exploration of transverse electromagnetic responses in solids with broken spatial-inversion (I) and/or time-reversal (T) symmetries has unveiled numerous captivating phenomena, including the (anomalous) Hall effect, Faraday rotations, non-reciprocal directional dichroism, and off-diagonal linear magnetoelectricity, all within the framework of magnetotoroidicity. Here, we introduce a novel class of transverse electromagnetic responses originating from electrotoroidicity in ferro-rotational (FR) systems with preserved I and T symmetries, distinct from magnetotoroidicity. We discover a high-order off-diagonal magnetic susceptibility of FR domains and a reduced linear diagonal magnetic susceptibility at FR domain walls in doped ilmenite FeTiO3. The non-trivial "Hall-like" effect of the former corresponds to an anomalous transverse susceptibility in the presence of spontaneous electrotoroidal moments in FR materials. Our findings unveil an emergent type of transverse electromagnetic responses even in I and T symmetry-conserved conditions and illustrate new functionalities of abundant FR materials.
Xianghan Xu, Yazhong Wang, Fei-Ting Huang, Kai Du, Elizabeth A. Nowadnick, Sang-Wook Cheong
The successful theoretical prediction and experimental demonstration of hybrid improper ferroelectricity (HIF) provides a new pathway to couple octahedral rotations, ferroelectricity, and magnetism in complex materials. To enable technological applications, a HIF with a small coercive field is desirable. We successfully grow Sr3Sn2O7 single crystals, and discover that they exhibit the smallest electric coercive field at room temperature among all known HIFs. Furthermore, we demonstate that a small external stress can repeatedly erase and re-generate ferroelastic domains. In addition, using in-plane piezo-response force microscopy, we characterize abundant charged and neutral domain walls. The observed small electrical and mechanical coercive field values are in accordance with the results of our first-principles calculations on Sr3Sn2O7, which show low energy barriers for both 90° and 180° polarization switching compared to those in other experimentally demonstrated HIFs. Our findings represent an advance towards the possible technological implemetation of functional HIFs.
Sang-Wook Cheong, Fei-Ting Huang, Minhyong Kim
The symmetry of the whole experimental setups, including specific sample environments and measurables, can be compared with that of specimens for observable physical phenomena. We, first, focus on one-dimensional (1D) experimental setups, independent from any spatial rotation around one direction, and show that eight kinds of 1D objects (four; vectorlike, the other four; director-like), defined in terms of symmetry, and their dot and cross products are an effective way for the symmetry consideration. The dot products form a Z2xZ2xZ2 group with Abelian additive operation, and the cross products form a Z2xZ2 group with Abelian additive operation or Q8, a non-abelian group of order eight, depending on their signs. Those 1D objects are associated with characteristic physical phenomena. When a 3D specimen has Symmetry Operational Similarity (SOS) with (identical or lower, but not higher, symmetries than) an 1D object with a particular phenomenon, the 3D specimen can exhibit the phenomenon. This SOS approach can be a transformative and unconventional avenue for symmetry-guided materials designs and discoveries.
Kai Du, Bin Gao, Yazhong Wang, Xianghan Xu, Jaewook Kim, Rongwei Hu, Fei-Ting Huang, Sang-Wook Cheong
The direct domain coupling of spontaneous ferroelectric polarization and net magnetic moment can result in giant magnetoelectric (ME) coupling, which is essential to achieve mutual control and practical applications of multiferroics. Recently, the possible bulk domain coupling, the mutual control of ferroelectricity (FE) and weak ferromagnetism (WFM) have been theoretically predicted in hexagonal LuFeO3. Here, we report the first successful growth of highly-cleavable Sc-stabilized hexagonal Lu0.6Sc0.4FeO3 (h-LSFO) single crystals, as well as the first visualization of their intrinsic cloverleaf pattern of vortex FE domains and large-loop WFM domains. The vortex FE domains are on the order of 0.1-1 μm in size. On the other hand, the loop WFM domains are ~100 μm in size, and there exists no interlocking of FE and WFM domain walls. These strongly manifest the decoupling between FE and WFM in h-LSFO. The domain decoupling can be explained as the consequence of the structure-mediated coupling between polarization and dominant in-plane antiferromagnetic spins according to the theoretical prediction, which reveals intriguing interplays between FE, WFM, and antiferromagnetic orders in h-LSFO. Our results also indicate that the magnetic topological charge tends to be identical to the structural topological charge. This could provide new insights into the induction of direct coupling between magnetism and ferroelectricity mediated by structural distortions, which will be useful for the future applications of multiferroics.
Sabine N. Neal, Sobhit Singh, Xiaochen Fang, Choongjae Won, Fei-ting Huang, Sang-Wook Cheong, Karin M. Rabe, David Vanderbilt, Janice L. Musfeldt
In order to explore the properties of a two-sublattice ferroelectric, we measured the infrared and Raman scattering response of CuInP2S6 across the ferroelectric and glassy transitions and compared our findings to a symmetry analysis, calculations of phase stability, and lattice dynamics. In addition to uncovering displacive character and a large hysteresis region surrounding the ferroelectric transition temperature T_C, we identify the vibrational modes that stabilize the polar phase and confirm the presence of two ferroelectric variants with opposite polarizations. Below TC, a poorly understood relaxational or glassy transition at Tg is characterized by local structure changes in the form of subtle peak shifting and activation of low frequency out-of-plane Cu- and In-containing modes. The latter are due to changes in the Cu/In coordination environments and associated order-disorder processes. Moreover, Tg takes place in two steps with another large hysteresis region and significant underlying scattering. Combined with imaging of the room temperature phase separation, this effort lays the groundwork for studying CuInP2S6 under external stimuli and in the ultra-thin limit.
Fei-Ting Huang, Seong Joon Lim, Sobhit Singh, Jinwoong Kim, Lunyong Zhang, Jae-Wook Kim, Ming-Wen Chu, Karin M. Rabe, David Vanderbilt, Sang-Wook Cheong
Much of the dramatic growth in research on topological materials has focused on topologically protected surface states. While the domain walls of topological materials such as Weyl semimetals with broken inversion or time-reversal symmetry can provide a hunting ground for exploring topological interfacial states, such investigations have received little attention to date. Here, utilizing in-situ cryogenic transmission electron microscopy combined with first-principles calculations, we discover intriguing domain-wall structures in MoTe2, both between polar variants of the low-temperature(T) Weyl phase, and between this and the high-T high-order topological phase. We demonstrate how polar domain walls can be manipulated with electron beams and show that phase domain walls tend to form superlattice-like structures along the c axis. Scanning tunneling microscopy indicates a possible signature of a conducting hinge state at phase domain walls. Our results open avenues for investigating topological interfacial states and unveiling multifunctional aspects of domain walls in topological materials.