Coexisting Ferroelectric and Ferrovalley Polarizations in Bilayer Stacked Magnetic Semiconductors

Novel mixed topological state in monolayer MnSbO3

An important goal of modern condensed-matter physics involves the search for new states of matter with emergent properties and desirable functionalities. In this study, based on symmetry analysis and first-principles calculations, the ferromagnetic monolayer MnSbO3 was proven to be a quantum anomalous Hall effect (QAH) insulator with a tunable topological state. As the magnetization direction varies in the xy plane, monolayer MnSbO3 transforms between a QAH insulator with a Chern number C = 1, topological trivial half metal and a QAH insulator with the Chern number C = -1 with a period of 60°. As the magnetization direction is located in the xz plane, the Chern number of the monolayer MnSbO3 changes between C = ±3 and C = ±1, thereby realizing the regulation of the topological phase. Interestingly, a mixed QAH effect and trivial half-metal topological state occur at the topological phase transition point between two QAH effects. As a result, a mixed topological state was achieved in monolayer MnSbO3 by regulating the magnetization direction.

Layer-polarization-engineered ferroelectricity and anomalous valley hall effects in a van der Waals bilayer

Layertronics, engineering the electronic properties through the layer degree of freedom, has attracted considerable attention due to its promising applications in next-generation spintronic technologies. Here, by coupling sliding ferroelectricity with A-type antiferromagnetism, we demonstrate a mechanism for layer-polarization-engineered electronic property through symmetry analysis based on the tight-binding (TB) model. It is found that breaking the inversion symmetry and time-inversion symmetry in the model gives rise to ferroelectricity and a layer-polarized anomalous valley Hall effect. Crucially, this valley polarization is ferroelectrically switchable, enabling non-volatile electrical control of the layer-resolved Berry curvature. Using first-principles calculations, this mechanism and phenomenon are verified in the multiferroic bilayer Janus RuClF. Our findings provide a promising platform for 2D bilayer materials, which hold great potential for applications in nanoelectronic and spintronic devices.

Ferrovalley Physics in Stacked Bilayer Altermagnetic Systems

As an emerging magnetic phase, altermagnets with compensated magnetic order and nonrelativistic spin-splitting have attracted widespread attention. Currently, strain engineering is considered to be an effective method for inducing valley polarization in altermagnets; however, achieving controllable switching of valley polarization is extremely challenging. Herein, combined with the tight-binding model and first-principles calculations, we propose that interlayer sliding can be used to successfully induce and effectively manipulate the large valley polarization in altermagnets. Using the Fe2MX4 (M = Mo, W; X = S, Se, or Te) family as examples, we predict that sliding-induced ferrovalley states in such systems can exhibit many unique properties, including the linearly optical dichroism that is independent of spin-orbit coupling and the anomalous valley Hall effect. These findings imply the correlation among spin, valley, layer, and optical degrees of freedom that makes altermagnets attractive in spintronics, valleytronics, and even their crossing areas.

2D Van der Waals Sliding Ferroelectrics Toward Novel Electronic Devices

Ferroelectric materials, celebrated for their switchable polarization, have undergone significant evolution since their early discovery in Rochelle salt. Initial challenges, including water solubility and brittleness, are overcome with the development of perovskite ferroelectrics, which enable the creation of stable, high-quality thin films suitable for semiconductor applications. As the demand for miniaturization in nanoelectronics has increased, research has shifted toward low-dimensional materials. Traditional ferroelectrics often lose their properties at the nanoscale; however, 2D van der Waals (vdW) ferroelectrics, including CuInP2S6 and α-In2Se3, have emerged as promising alternatives. The recent discovery of sliding ferroelectricity, where polarization is linked to the polar stacking configuration of originally non-polar monolayers, has significantly broadened the scope of 2D ferroelectrics. This review offers a comprehensive examination of stacking orders in 2D vdW materials, stacking-order-linked ferroelectric polarization structures, and their manifestations in metallic, insulating and semiconducting 2D vdW materials. Additionally, it explores the applications of 2D vdW sliding ferroelectrics, and discusses the future prospects in nanotechnology.

Enforced Symmetry Breaking for Anomalous Valley Hall Effect in Two-Dimensional Hexagonal Lattices

The anomalous valley Hall effect (AVHE) is a pivotal phenomenon that allows for the exploitation of the valley degree of freedom in materials. A general strategy for its realization and manipulation is crucial for valleytronics. Here, by considering all possible symmetries, we propose general rules for the realization and manipulation of AVHE in two-dimensional hexagonal lattices. The realization of AVHE requires breaking the enforced symmetry that is associated with different valleys or reverses the sign of Berry curvature. Further manipulation of AVHE requires asymmetry operators connecting two states with opposite signs of Berry curvature. These rules for realizing and manipulating AVHE are extendable to generic points in momentum space. Combined with first-principles calculations, we realize the controllable AVHE in four representative systems, i.e., monolayer AgCrP_{2}Se_{6}, CrOBr, FeCl_{2}, and bilayer TcGeSe_{3}. Our work provides symmetry rules for designing valleytronic materials that could facilitate the experimental detection and realistic applications.

Atypical breathing driven two-dimensional valley multiferroicity

Valley multiferroicity, coupled with ferro-valleytricity and primary ferroicities in a single phase, is of fundamental significance in condensed-matter physics and materials science, as it provides a convenient route to reverse the anomalous valley Hall (AVH) effect. Current research in this field focuses mainly on ferromagnetic ferro-valleytricity, whereas ferroelectric ferro-valleytricity is seldom explored. Here, using symmetry arguments and tight-binding model analysis, we report a novel mechanism of coupling ferro-valleytricity with ferroelectricity, i.e., single-phase valley multiferroicity, in a two-dimensional magnetic lattice. This mechanism correlates to the atypical breathing nature of the magnetic lattice. Importantly, the valley physics, associated with Berry curvature, can be reversed under a ferroelectric transition, thereby guaranteeing the ferroelectrically reversible AVH effect. The underlying physics are discussed in detail. Based on first-principles calculations, we further confirm valley multiferroicity in a real 2D magnetic material of single-layer Gd2CO2. The explored phenomena and mechanism are not only useful for fundamental research in valley multiferroics but also enable a wide range of applications in nanodevices.

In Situ Formation of SnSe2/SnSe Vertical Heterostructures toward Polarization Selectable Band Alignments

2D van der Waals (vdW) layered semiconductor vertical heterostructures with controllable band alignment are highly desired for nanodevice applications including photodetection and photovoltaics. However, current 2D vdW heterostructures are mainly obtained via mechanical exfoliation and stacking process, intrinsically limiting the yield and reproducibility, hardly achieving large-area with specific orientation. Here, large-area vdW-epitaxial SnSe2/SnSe heterostructures are obtained by annealing layered SnSe. These in situ Raman analyses reveal the optimized annealing conditions for the phase transition of SnSe to SnSe2. The spherical aberration-corrected transmission electron microscopy investigations demonstrate that layered SnSe2 epitaxially forms on SnSe surface with atomically sharp interface and specific orientation. Optical characterizations and theoretical calculations reveal valley polarization of the heterostructures that originate from SnSe, suggesting a naturally adjustable band alignment between type-II and type-III, only relying on the polarization angle of incident lights. This work not only offers a unique and accessible approach to obtaining large-area SnSe2/SnSe heterostructures with new insight into the formation mechanism of vdW heterostructures, but also opens the intriguing optical applications based on valleytronic nanoheterostructures.

Prediction of the two-dimensional ferromagnetic semiconductor Janus 2H-ZrTeI monolayer with large valley and piezoelectric polarizations

Two-dimensional room-temperature Janus ferrovalley semiconductors with valley polarization and piezoelectric polarization offer new perspectives for designing multifunctional nanodevices. Herein, using first-principles calculations, we predict that the Janus 2H-ZrTeI monolayer is an intrinsic ferromagnetic semiconductor with in-plane magnetic anisotropy and a Curie temperature of 111 K. The Janus ZrTeI monolayer possesses a significant valley polarization of 141 meV due to time-reversal and inversion symmetry breaking. Based on the valley-contrasting Berry curvature, the anomalous valley Hall effect can be observed under an in-plane electric field. Meanwhile, the breaking of the inversion symmetry and mirror symmetry results in large longitudinal and transverse piezoelectric coefficients. By applying biaxial strain, the Janus 2H-ZrTeI monolayer can also be transformed into a Weyl nodal line semimetal. Furthermore, bilayers of ZrTeI with AB and BA stacking configurations allow the coexistence of valley polarization and ferroelectricity, enabling the manipulation of magnetism, ferroelectric polarization, and valley polarization through interlayer sliding. Our work provides a platform for studying valley polarization, piezoelectricity, and multiferroic coupling, which is significant for the application of multifunctional devices.

Electrical Control of the Valley-Layer Hall Effect in Ferromagnetic Bilayer Lattices

The layertronics based on the layer degree of freedom are of essential significance for the construction and application of new-generation electronic devices. Although the Hall layer effect has been realized theoretically and experimentally, it is mainly based on topological and antiferromagnetic lattices. On the basis of the low-energy effective k·p model, the mechanism of the controllable valley-layer Hall effect (V-LHE) in a bilayer ferromagnetic lattice through interlayer sliding has been proposed. Due to the broken time-reversal and inversion symmetries, the V-LHE based on the valley, layer degree of freedom, ferromagnetism, and ferroelectricity can be predicted. In addition, valley and layer indexes can be controlled by magnetization orientation and slipping, respectively. The mechanism can be demonstrated in the real bilayer CrSI lattice through first-principles calculations. Moreover, V-LHE can be effectively tuned by the perpendicular external electric field in configurations without out-of-plane polarization. These findings provide a new platform for the research of valleytronics and layertronics.

Valley-Related Multipiezo Effect and Noncollinear Spin Current in an Altermagnet Fe2Se2O Monolayer

An altermagnet exhibits many novel physical phenomena because of its intrinsic antiferromagnetic coupling and natural band spin splitting, which are expected to give rise to new types of magnetic electronic components. In this study, an Fe2Se2O monolayer is proven to be an altermagnet with out-of-plane magnetic anisotropy, and its Néel temperature is determined to be 319 K. The spin splitting of the Fe2Se2O monolayer reaches 860 meV. Moreover, an Fe2Se2O monolayer presents a pair of energy valleys, which can be polarized and reversed by applying uniaxial strains along different directions, resulting in a piezovalley effect. Under the strain, the net magnetization can be induced in the Fe2Se2O monolayer by doping with holes, thereby realizing a piezomagnetic property. Interestingly, noncollinear spin current can be generated by applying an in-plane electric field on an unstrained Fe2Se2O monolayer doped with 0.2 hole/formula unit. These excellent physical properties make the Fe2Se2O monolayer a promising candidate for multifunctional spintronic and valleytronic devices.

Layer-Dependent Quantum Anomalous Hall and Quantum Spin Hall Effects in Two-Dimensional LiFeTe

The emergence of an intrinsic quantum anomalous Hall (QAH) insulator with long-range magnetic order triggers unprecedented prosperity for combining topology and magnetism in low dimensions. Here, based on stacked two-dimensional LiFeTe, we confirm that magnetic coupling and topological electronic states can be simultaneously manipulated by just changing the layer numbers. Monolayer LiFeTe shows intralayer ferrimagnetic coupling, behaving as a QAH insulator with Chern number C = 2. Beyond the monolayer, the odd and even layers of LiFeTe correspond to uncompensated and compensated interlayer antiferromagnets, resulting in unexpected QAH and quantum spin Hall (QSH) states, respectively. Moreover, the spin Chern number is proportional to the stacking layer numbers in even-layer LiFeTe, proving that the spin Hall conductivity can be continuously enhanced by increasing layer numbers. Therefore, the odd-even-layer-dependent QAH and QSH effects found in LiFeTe topological insulators offer new insight into regulating quantum states in two-dimensional topological materials.

Ferrovalley and Quantum Anomalous Hall Effect in Janus TiTeCl Monolayer

Ferrovalley materials are garnering significant interest for their potential roles in advancing information processing and enhancing data storage capabilities. This study utilizes first-principles calculations to determine that the Janus monolayer TiTeCl exhibits the properties of a ferrovalley semiconductor. This material demonstrates valley polarization with a notable valley splitting of 80 meV. Additionally, the Berry curvature has been computed across the first Brillouin zone of the monolayer TiTeCl. The research also highlights that topological phase transitions ranging from ferrovalley and half-valley metals to quantum anomalous Hall effect states can occur in monolayer TiTeCl under compressive strains ranging from -1% to 0%. Throughout these strain changes, monolayer TiTeCl maintains its ferromagnetic coupling. These characteristics make monolayer TiTeCl a promising candidate for the development of new valleytronic and topological devices.

Defect effects on the electronic, valley, and magnetic properties of the two-dimensional ferrovalley material VSi2N4

Due to their novel spin and valley properties, two-dimensional (2D) ferrovalley materials are expected to be promising candidates for next-generation spintronic and valleytronic devices. However, they are subject to various defects in practical applications. Therefore, the electronic, valley, and magnetic properties may be modified in the presence of the defects. In this work, utilizing first-principles calculations, we systematically studied the effects of defects on the electronic, valley, and magnetic properties of the 2D ferrovalley material VSi2N4. It has been found that C doping, O doping, and N vacancies result in the half-metallic feature, Si vacancies result in the metallic feature, and V vacancies result in a bipolar gapless semiconductor. These defect-induced electronic properties can be effectively tuned by changing defect concentration and layer thickness. Since the impurity bands do not affect the K and K' valleys, valley polarization is well maintained in O-doped and N-defective systems. Importantly, these defects play a crucial role in modifying the magnetic properties of the pristine VSi2N4, especially the magnitude of local magnetic moments and the magnetic anisotropy energy. Detailed analysis of the density of states demonstrates that the variations of the total magnetic moment and magnetic anisotropy energy with biaxial strain are determined by the electronic states near the Fermi level rather than the type of defect, which provides a new understanding of the effects of defects on the magnetic properties of 2D materials. Moreover, the layer thickness can affect the magnetic coupling between defects and surrounding V atoms. Our results offer insight into the electronic, valley, and magnetic properties of VSi2N4 in the presence of various point defects.

Layer Control of Magneto-Optical Effects and Their Quantization in Spin-Valley Splitting Antiferromagnets

Magneto-optical effects (MOE), interfacing the fundamental interplay between magnetism and light, have served as a powerful probe for magnetic order, band topology, and valley index. Here, based on multiferroic and topological bilayer antiferromagnets (AFMs), we propose a layer control of MOE (L-MOE), which is created and annihilated by layer-stacking or an electric field effect. The key character of L-MOE is the sign-reversible response controlled by ferroelectric polarization, the Néel vector, or the electric field direction. Moreover, the sign-reversible L-MOE can be quantized in topologically insulating AFMs. We reveal that the switchable L-MOE originates from the combined contributions of spin-conserving and spin-flip interband transitions in spin-valley splitting AFMs, a phenomenon not observed in conventional AFMs. Our findings bridge the ancient MOE to the emergent realms of layertronics, valleytronics, and multiferroics and may hold immense potential in these fields.

Coexisting Magnetism, Ferroelectric, and Ferrovalley Multiferroic in Stacking-Dependent Two-Dimensional Materials

Two-dimensional (2D) multiferroic materials have widespread application prospects in facilitating the integration and miniaturization of nanodevices. However, the magnetic, ferroelectric, and ferrovalley properties in one 2D material are rarely coupled. Here, we propose a mechanism for manipulating magnetism, ferroelectric, and valley polarization by interlayer sliding in a 2D bilayer material. Monolayer GdI2 is a ferromagnetic semiconductor with a valley polarization of up to 155.5 meV. More interestingly, the magnetism and valley polarization of bilayer GdI2 can be strongly coupled by sliding ferroelectricity, making these tunable and reversible. In addition, we uncover the microscopic mechanism of the magnetic phase transition by a spin Hamiltonian and electron hopping between layers. Our findings offer a new direction for investigating 2D multiferroic devices with implications for next-generation electronic, valleytronic, and spintronic devices.

High Curie temperature ferromagnetic monolayer T-CrSH and valley physics of T-CrSH/WS2 heterostructure

Two-dimensional magnetic materials are attracting widespread attention not only for their excellent applications in spintronic devices but also for their potential to regulate valley splitting, which is crucial for valleytronics. Herein, we design a monolayer Janus ferromagnetic semiconductor T-CrSH by using first-principles calculations. We reveal that monolayer T-CrSH has a magnetic moment of 3μB per unit cell, which is primarily contributed by the 3d orbitals of the Cr atom. Monte Carlo simulations suggest that the Curie temperature of T-CrSH is 193 K, and it can rise to 402 K when a 5% tensile strain is applied. Furthermore, the valley degeneracy of WS2 can be lifted when monolayer T-CrSH is used as a substrate. The obtained valley splitting in the conduction band is 13.7 meV and that in the valence band is 157.5 meV. In addition, the large valley polarization of 12.8 meV in the conduction band makes it easy to achieve an electron-doped valley Hall current and spin Hall current when performing in an in-plane electric field.

Tunable polarization properties of charge, spin, and valley in Janus VSiGeZ4 (Z = N, P, As) monolayers

Polarization, as an important characterization of the symmetry breaking systems, has attracted tremendous attention in two-dimensional (2D) materials. Due to their significant symmetry breaking, Janus 2D ferrovalley materials provide a desirable platform to investigate the charge, spin, and valley polarization, as well as their coupling effects. Herein, using first-principles calculations, the polarization properties of charge, spin, and valley in Janus VSiGeZ4 (Z = N, P, and As) monolayers are systematically studied. The mirror symmetry breaking leads to a non-zero dipole moment and surface work function difference, indicating the presence of out-of-plane charge polarization. Magnetic properties calculations demonstrate that VSiGeN4 is a 2D-XY magnet with a Berezinskii-Kosterlitz-Thouless temperature of 342 K, while VSiGeP4 and VSiGeAs4 have an out-of-plane magnetization with a Curie temperature below room temperature. The magnetization can be rotated by applying biaxial strain, allowing manipulation of the spin polarization via nonmagnetic means. The spontaneous valley polarization is predicted to be 46, 49, and 70 meV for VSiGeN4, VSiGeP4, and VSiGeAs4, respectively, whose physical origin can be elucidated by employing the model analysis. In particular, the biaxial strain can induce the valley polarization switching from the valence (conduction) band to conduction (valence) band, but it hardly changes the valley polarization strength. Meanwhile, the valley extremum is transformed from the K' (K) to K (K') points. The present work not only provides an underlying insight into the polarization properties of Janus VSiGeZ4 but also offers a class of promising materials for spintronic and valleytronic devices.

Magnetic and Ferroelectric Manipulation of Valley Physics in Janus Piezoelectric Materials

The realization of multiferroic materials offers the possibility of multifunctional electronic device design. However, the coupling between the multiferroicity and piezoelectricity in Janus materials is rarely reported. In this study, we propose a mechanism for manipulating valley physics by magnetization reversing and ferroelectric switching in multiferroic and piezoelectric material. The ferromagnetic VSiGeP4 monolayer exhibits a large valley polarization up to 100 meV, which can be effectively operated by reversing magnetization. Interestingly, the antiferromagnetic VSiGeP4 bilayers with AB and BA stacking configurations allow the coexistence of valley polarization and ferroelectricity, supporting the proposed strategy for manipulating valley physics via ferroelectric switching and interlayer sliding. In addition, the VSiGeP4 monolayer contains remarkable tunable piezoelectricity regulated by electron correlation U. This study proposes a feasible idea for regulating valley polarization and a general design idea for multifunctional devices with multiferroic and piezoelectric properties, facilitating the miniaturization and integration of nanodevices.