Large Valley Polarization Research Articles

Multiferroic properties and the layer-stacking quantum anomalous Hall effect in two-dimensional RuOHX (X = F, Cl, Br)

Exploring the physics coupled with layer degrees of freedom in materials has become a hot topic in quantum layertronics. We propose a robust second-order topological insulator monolayer RuOHX (X = F, Cl, and Br), a two-dimensional ferromagnetic semiconductor with large valley polarization, capable of undergoing topological phase transition induced by strain effect. In the bilayer RuOHX, we achieve layer-polarized anomalous Hall effect through interlayer sliding, originating from layer-stacking Berry curvature. Moreover, it can be controlled and reversed by the direction of ferroelectric polarization. Under appropriate biaxial strain, the bilayer RuOHX exhibits quantum layer spin Hall effect in which the helical edge states are manifested as spin-chirality-locking, due to the degeneracy of layer-polarized quantum anomalous Hall effect. Our work explores the potential application via layer-stacking topological properties for future quantum device applications.

Prediction of large spin-valley polarization in the Janus 2H–WSSe monolayer on VN magnetic substrate

Two-dimensional heterostructures based on transition metal dichalcogenides (TMDs) exhibit broad application prospects in valleytronics due to the space-reversal symmetry breaking and strong spin–orbit coupling. In this work, the electronic structure, magnetic anisotropy and valley polarization of 2H–WSSe/VN van der Waals heterostructure under various interlayer spacings, magnetic angle and in-plane strain are investigated in detail by first-principles calculations. The stacked configuration of Se-C2-1 with most stable structure shows the largest valley polarization of 386.5[Formula: see text]meV. By adjusting the interlayer spacing of heterostructure, the largest valley polarization of 702.7[Formula: see text]meV appears in Se-C2-1 stacked configuration with interlayer spacing of 2.24 Å. The magnetic angle [Formula: see text] exhibits significant effects on valley polarization and magnetic anisotropy of 2H–WSSe/VN heterostructures. The stability and valley polarization of 2H–WSSe/VN heterostructure decrease after the in-plane biaxial strain is applied. The large and tunable valley polarization as well as magnetic anisotropy in the 2H–WSSe/VN heterostructures make it potential applications in valleytronic devices.

Strain-driven valley-dependent Berry phase effects and topological transitions in Janus SVGeN2 monolayer

The manipulation of valley-dependent properties in two-dimensional (2D) materials is intriguing for developing valleytronics. Using first-principles calculations, we explore valley-dependent properties of Janus SVGeN2 monolayer and reveal large and tunable valley polarization by tensile strain. The SVGeN2 monolayer possesses excellent stability. Furthermore, strain-driven topological magneto-valley phase transitions are predicted for this monolayer, leading to the valley quantum anomalous Hall (VQAH) phenomenon. The VQAH state, which is featured by the coexistence of complete valley polarization and topological phase, is confirmed by sign reversal of Berry curvature and the nontrivial band topology. The calculated magnetic anisotropy energy indicates that the Janus SVGeN2 monolayer possesses a ferromagnetic ground state and in-plane magnetization. Our investigation provides some physical insights into the strain-driven topological phase transition and manipulation of valley-dependent properties to realize giant valley polarization in the Janus 2D magnet.

Chiral breathing-valley locking in two-dimensional kagome lattice Ta3I8

The exploration of valley-related physics is essential to the development and refinement of valleytronics. Here, a paradigm called chiral breathing-valley locking (CBVL) is proposed, in which two chiral “breathing” phases are completely locked to their valley indexes. Utilizing first-principles calculations, a two-dimensional (2D) kagome lattice with large spontaneous valley polarization (VP), namely, monolayer Ta3I8, is proposed to realize CBVL. There are two breathing phases with chiral symmetry in Ta3I8, and they can change to each other under some conditions. The valley indexes change between “−K” and “K” along the breathing of the two chiral symmetric phases, so CBVL can be obtained. Remarkably, the VP is up to 199.7 meV, so CBVL can cause the obvious switching of the anomalous valley Hall effect (AVHE). Additionally, a 2D Janus Kagome structure TaI4X4 is constructed to confirm experimentally the feasibility of electric field modulation on the CBVL. The built-in electric field and the breathing mode can mutually influence each other in TaI4X4, which provides a synergistic regulation of the AVHE. Our findings broaden the horizon for exploring AVHE materials and provide a platform for future valleytronic applications.

Large valley polarization and the valley-dependent Hall effect in a Janus TiTeBr monolayer.

Ferrovalley materials hold great promise for implementation of logic and memory devices in valleytronics. However, there have so far been limited ferrovalley materials exhibiting significant valley polarization and high Curie temperature (TC). Using first-principles calculations, we predict that the TiTeBr monolayer is a promising ferrovalley candidate. It exhibits intrinsic ferromagnetism with TC as high as 220 K. It is indicated that an out-of-plane alignment of magnetization demonstrates a valley polarization up to 113 meV in the topmost valence band, as further verified by perturbation theory considering both the spin polarization and spin-orbit coupling. Under an in-plane electric field, the valley-dependent Berry curvature results in the anomalous valley Hall effect (AVHE). Moreover, under a suitable in-plane biaxial strain, the TiTeBr monolayer transforms into a Chern insulator with a nonzero Chern number, yet retains its ferrovalley characters and thus the emergent quantum anomalous valley Hall effect (QAVHE). Our study indicates that the TiTeBr monolayer is a promising ferrovalley material, and it provides a platform for investigating the valley-dependent Hall effect.

Tunable valley polarization effect and second-order topological state in monolayer FeClSH.

In two-dimensional (2D) materials, breaking the inversion symmetry plays an important role in valleytronics. Ferrovalley (FV) materials can achieve spontaneous valley polarization (VP) without additional modulation due to the magnetic exchange interaction and strong spin-orbit coupling. Using first-principles calculations, we predict a new 2D material, Janus FeClSH, which exhibits a large spontaneous VP. This monolayer is a perfect FV material, where the valence band maximum and conduction band minimum are located at the K/K' point. A large VP of 102.95 meV is spontaneously generated for the case of out-of-plane magnetization. Additionally, we propose that the irradiating circularly polarized light can be used to realize VP for the case of in-plane magnetization. Remarkably, a triangular nanoflake of FeClSH with armchair edges can show nontrivial corner states, exhibiting a second-order topological insulator (SOTI) state. The VP effect and SOTI state are tunable with the Hubbard U parameter, making the FeClSH monolayer promising for the study of the coupling between VP and SOTI.

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.

Valley-dependent topological phase transition in monolayer ferrovalley materials RuXY (X, Y = F, Cl, Br)

Due to the breaking of the time reversal symmetry and spatial inversion symmetry, hexagonal ferrovalley materials have intrinsic large valley polarization. Model analysis shows that tuning the two different band gaps of valleys can realize phase transitions between ferrovalley semiconductors, half valley metals, and valley-polarized quantum anomalous Hall semiconductors. Through first-principle calculations, monolayer ferrovalley materials RuXY (X, Y = F, Cl, Br), which exhibit valley splitting at the top valence band and the bottom conduction band, are predicted to achieve this valley-dependent topological phase transition. Due to the different orbital proportions of d orbitals, the valley splitting at the top valence band is much greater than that at the bottom conduction band. Strain can regulate the interaction between orbitals, thus producing valley-dependent band inversion, leading to the quantum spin or valley Hall effect. The chiral edge states are demonstrated under appropriate biaxial strain. The topological phase transition is related to the inversion of the band structure and Berry curvatures at K and K′ valleys. These results have certain significance for the design of two-dimensional valley-dependent quantum materials and the application of valleytronic devices.

Tunable valley polarization and magneto-crystal anisotropy in two-dimensional VI3/WSe2 Van der Waals heterostructure

In this work, the effects of magnetic proximity coupling on electronic structures, valley polarization and magneto-crystal anisotropy of VI3/WSe2 heterostructure are studied in detail based on density functional theory. The results show that the spin-valley polarization characters of WSe2 monolayer can be induced by the proximity effect of ferromagnetic VI3 monolayer. Based on the effective Hamiltonian [Formula: see text] model, a large valley polarization of 8.7[Formula: see text]meV is observed, which is mainly contributed by the SOC effect and not magnetic exchange field. Meanwhile, the magneto-crystal anisotropy of VI3 layer is also obviously altered from the [100] to [001] magnetic axis compared to the isolated VI3 monolayer. The reduction in the interlayer space strengths the W–V atomic coupling, resulting in a significant increase in the spin and valley polarization. Compression strain shows weakening effect on the valley polarization, while the tensile strain largely enhances the valley polarization of VI3/WSe2 heterostructure, which can reach the maximum value of 29.1[Formula: see text]meV at the tensile strain of 8%. The V spin direction ([Formula: see text]) has significant effect on valley polarization of WSe2 layer, which is positively correlated with the magnetization strength of V atom in the vertical direction. Furthermore, constructing the VI3/WSe2/VI3 sandwich heterostructure can induce a larger valley polarization, which can reach a maximum value of 32.4[Formula: see text]meV. These results indicate that the VI3/WSe2 heterostructure is a potential candidate for valleytronics.

Large valley polarization and high Curie temperature in single layer XI2 (X = Sc, Y)

Ferrovalley materials with spontaneous valley polarization are the key to valleytronics applications. Therefore, it is important to find materials with relatively large valley polarization. In this work, we theoretically designed two novel two-dimensional ferrovalley materials namely XI2 (X = Sc, Y), which have both high Curie temperature and large valley polarization. The Curie temperature of monolayer ScI2 and YI2 are 138 K and 58 K, the large valley polarization of 97 meV and 108 meV are also predicted in monolayer ScI2 and YI2. The anomalous valley Hall effect is also proposed based on the valley contrasting Berry curvature. In addition, strain engineering can effectively modulate the valley polarization and Curie temperature of monolayer XI2 (X = Sc, Y). The Curie temperature of ScI2 increases with increasing strain, and the valley polarization of YI2 increases with increasing strain. Our findings suggest that monolayer XI2 (X = Sc, Y) is a promising material for valleytronics.

Controllable valley magnetic response in phase-transformed tungsten diselenide

Achieving valley pseudospin with large polarization is crucial in the implementation of quantum information applications. Transition metal dichalcogenides (TMDC) with different phase structures provide an ideal platform for valley modulation. The valley splitting has been achieved in hybrid phase WSe2, while its valley polarization remains unstudied. Magnetic field controllable valley polarization is explored in WSe2 with coexistence of H and T phases by an all-optical route. A record high valley polarization of 58.3% is acquired with a 19.9% T phase concentration under a 4-T magnetic field and nonresonant excitation. The enhanced valley polarization is dependent on the phase component and shows various increasing slopes, owing to the synergy between the T phase WSe2 and the magnetic field. The magnetic field controlled local magnetic momentums are revealed as the mechanism for the large valley polarization in H / T-WSe2. This speculation is also verified by theoretical simulations of the nonequilibrium spin density. These results display a considerable valley magnetic response in phase-engineered TMDC and provide a large-scale scheme for valley polarization applications.

Large spontaneous valley polarization and high magnetic transition temperature in stable two-dimensional ferrovalley YX2(X=I, Br, and Cl )

Ferrovalley materials with spontaneous valley polarization are crucial to valleytronic application. Based on first-principles calculations, we demonstrate that two-dimensional (2D) $\mathrm{Y}{X}_{2}(X=\mathrm{I}, \mathrm{Br}, \text{and} \mathrm{Cl})$ in a 2H structure constitutes a series of promising ferrovalley semiconductors with large spontaneous valley polarization and high magnetic transition temperature. Our calculations reveal that $\mathrm{Y}{X}_{2}$ are dynamically, energetically, thermally and mechanically stable 2D ferromagnetic semiconductors with a magnetic transition temperature about 200 K. Due to the natural noncentrosymmetric structure, intrinsic ferromagnetic order and strong spin orbital coupling, the large spontaneous valley polarizations of 108.98, 57.70, and 22.35 meV are also predicted in single-layer $\mathrm{Y}{X}_{2}(X=\mathrm{I}, \mathrm{Br}, \text{and} \mathrm{Cl})$, respectively. The anomalous valley Hall effect is also proposed based on the valley contrasting Berry curvature. Moreover, the ferromagnetism and valley polarization are found to be effectively tuning by applying a biaxial strain. Interestingly, the suppressed valley physics of ${\mathrm{YBr}}_{2}$ and ${\mathrm{YCl}}_{2}$ can be switched on via applying a moderate compression strain. The present findings promise $\mathrm{Y}{X}_{2}$ as competitive candidates for the further experimental studies and practical applications in valleytronics.

Two-dimensional ferromagnetic semiconductors of rare-earth Janus 2H-GdIBr monolayers with large valley polarization.

Based on a rare-earth Gd atom with 4f electrons, through first-principles calculations, we demonstrate that a Janus 2H-GdIBr monolayer exhibits an intrinsic ferromagnetic (FM) semiconductor character with an indirect band gap of 0.75 eV, a high Curie temperature Tc of 260 K, a significant magnetic moment of 8μB per f.u. (f.u. = formula unit), in-plane magnetic anisotropy (IMA) and a large spontaneous valley polarization of 118 meV. The MAE, inter-atomic distance or angle, and Tc can be efficiently modulated by in-plane strains and charge carrier doping. Under a strain range from -5% to 5% and charge carrier doping from -0.3 e to 0.3 e per f.u., the system still retains its FM ordering and the corresponding Tc can be modulated by strains from 233 K to 281 K and by charge carrier doping from 140 K to 245 K. Interestingly, under various strains, the matrix element differences (dz2, dyz), (dx2-y2, dxy) and (px, py) of Gd atoms dominate the MAE behaviors, which originates from the competition between the contributions of the Gd-d orbitals, Gd-p orbitals, and p orbitals of halogen atoms based on the second-order perturbation theory. Inequivalent Dirac valleys are not energetically degenerate due to the time-reversal symmetry breaking in the Janus 2H-GdIBr monolayer. A considerable valley gap between the Berry curvature at the K and K' points provides an opportunity to selectively control the valley freedom and states. External tensile (compressive) strain further increases (decreases) the valley gap up to a maximum (minimum) value of 158 (37) meV, indicating that the valley polarization in the Janus 2H-GdIBr monolayer is robust to external strains. This study provides a novel paradigm and platform to design spintronic devices for next-generation quantum information technology.

Distinct ferrovalley characteristics of the Janus RuClX (X = F, Br) monolayer.

Two-dimensional ferrovalley materials should simultaneously possess three characteristics, that is, a Curie temperature beyond atmospheric temperature, perpendicular magnetic anisotropy, and large valley polarization for potential commercial applications. In this report, we predict two ferrovalley Janus RuClX (X = F, Br) monolayers by first-principles calculations and Monte Carlo simulations. The RuClF monolayer exhibited a valley-splitting energy as large as 194 meV, perpendicular magnetic anisotropy energy of 187 μeV per f.u., and Curie temperature of 320 K. Thus, spontaneous valley polarization at room temperature will be present in the RuClF monolayer, which is nonvolatile for spintronic and valleytronic devices. Although the valley-splitting energy of the RuClBr monolayer was as high as 226 meV with magnetic anisotropy energy of 1.852 meV per f.u., the magnetic anisotropy of the RuClBr monolayer was in-plane, and its Curie temperature was only 179 K. The orbital-resolved magnetic anisotropy energy revealed that the interaction between the occupied spin-up states of dyz and the unoccupied spin-down states of dz2 dominated the out-of-plane magnetic anisotropy in the RuClF monolayer, but the in-plane magnetic anisotropy of the RuClBr monolayer was mostly contributed by the coupling of the dxy and dx2-y2 orbitals. Interestingly, the valley polarizations in the Janus RuClF and RuClBr monolayers appeared in their valence band and conduction band, respectively. Thus, two anomalous valley Hall devices are proposed using the present Janus RuClF and RuClBr monolayers with hole and electron doping, respectively. This study provides interesting and alternative candidate materials for the development of valleytronic devices.

Computational discovery of two-dimensional rare-earth iodides: promising ferrovalley materials for valleytronics

Two-dimensional Ferrovalley materials with intrinsic valley polarization are rare but highly promising for valley-based nonvolatile random access memory and valley filter devices. These ferromagnetic materials exhibit valleys at or near the Fermi level with intrinsic magnetism. The strong coupling between magnetism and spin–orbit coupling induces intrinsic valley polarization. Using Kinetically Limited Minimization, an unconstrained crystal structure prediction algorithm, and prototype sampling based on first-principles calculations, we have discovered new Ferrovalley materials, rare-earth iodides RI2, where R is a rare-earth element belonging to Sc, Y, or La-Lu, and I is Iodine. The rare-earth iodides are layered and demonstrate either 2H, 1T, or 1T d phase as the ground state in bulk, analogous to transition metal dichalcogenides (TMDCs). The calculated exfoliation energy of monolayers (MLs) is comparable to that of graphene and TMDCs, suggesting possible experimental synthesis. The MLs in the 2H phase exhibit ferromagnetism due to unpaired electrons in d and f orbitals. Throughout the rare-earth series, d bands have valley polarization at K and points in the Brillouin zone in the vicinity of the Fermi level. Large intrinsic valley polarization in the range of 15–143 meV without external stimuli is observed in these Ferrovalley materials, which can be enhanced further by applying an in-plane bi-axial strain. These valleys can selectively be probed and manipulated for information storage and processing, potentially offering superior performance beyond conventional electronics and spintronics. We further show that the 2H ferromagnetic phase of RI2 MLs possesses non-zero Berry curvature and exhibits anomalous valley Hall effect with considerable anomalous Hall conductivity. Our work will incite exploratory synthesis of the predicted Ferrovalley materials and their application in valleytronics and beyond.

Spontaneous Valley Polarization Caused by Crystalline Symmetry Breaking in Nonmagnetic LaOMX2 Monolayers.

In order to achieve valley polarization, breaking the time-reversal symmetry in two-dimensional hexagonal lattices with inversion asymmetry is the heart of current valleytronic research, which, however, has caused studies to stagnate due to the inevitable drawbacks. In this work, we go beyond the conventional paradigm and demonstrate the novel valley physics caused by lowering the crystalline symmetry instead of breaking the time-reversal symmetry. In particular, we translate our concept into concrete nonmagnetic LaOMX2 monolayers with a tetragonal lattice, confirming that a spontaneous structure distortion can cause the long-sought, considerably large valley polarization. In detail, the physics of valley-orbital coupling, valley-orbital-layer coupling, valley-contrasting linear dichroism, and interlayer exciton valleytronics are discussed.

Two-dimensional intrinsic ferrovalley Janus 2H-VSeS monolayer with high Curie temperature and robust valley polarization

Inspired by the successful synthesis of two-dimensional (2D) V-based Janus dichloride monolayers with intrinsic ferromagnetism and high Curie temperature (T$_{c}$), the electronic structure, spin-valley splitting and magnetic anisotropy of Janus 2H-VSeS monolayers are investigated in detailed using first-principles calculations. The results show that the Janus 2H-VSeS monolayer exhibits a large valley splitting of 105meV, high T$_{c}$ of 278K and good magnetocrystalline anisotropy (0.31meV) contributed by the in-plane d$_{x^{2}-y^{2}}$/d$_{xy}$ orbitals of V atoms. The biaxial strain ($-$8%<$\varepsilon$<8%) can effectively tune the magnetic moments of V atom, valley splitting $\Delta$E, T$_{c}$ and MAE of Janus 2H-VSeS monolayer. The corresponding $\Delta$E and T$_{c}$ are adjusted from 72meV to 106.8meV and from 180K to 340K, respectively. The electronic phase transition from bipolar magnetic semiconductor (BMS) to half-semiconductor (HSC), spin gapless semiconductor (SGS), and half-metal (HM) is also observed due to the change of V 3d-orbital occupation. Due to the broken space- and time-reversal symmetry, the opposite valley charge carriers carry opposite Berry curvature, which leads to prominent anomalous Hall conductivity at the K and K$^{\prime}$ valleys. The maximum modulation of Berry curvature can reach to 45% and 9.5% by applying the biaxial strain and charge carrier doping, respectively. The stable in-plane magnetocrystalline anisotropy and large spontaneous valley polarization make the ferromagnetic Janus 2H-VSeS monolayer a promising material for achieving the spintronics and valleytronics devices.

Tunable magnetocrystalline anisotropy and valley polarization in an intrinsic ferromagnetic Janus 2H -VTeSe monolayer

Two-dimensional Janus monolayers with specular asymmetry exhibit excellent physicochemical properties and are a good candidate for optoelectronic, valley electronic, and nanoelectronics devices. Based on the density functional theory, the Janus $2H$-VTeSe monolayer is an intrinsic ferromagnetic semiconductor with an indirect band gap of 0.324 eV and exhibits a good thermodynamic and kinetic stability, in-plane magnetocrystal anisotropy, large spontaneous valley polarization of 155 meV, and high Curie temperature (${T}_{c}$) of 380 K. The biaxial strain ($\ensuremath{-}6%&lt;\ensuremath{\varepsilon}&lt;6%$) can effectively tune the Janus $2H$-VTeSe monolayer from the bipolar magnetic semiconductor phase to half-semiconductor, spin gapless semiconductor, and half-metallic phases. Moreover, the magnetocrystal anisotropy energy (MAE) is modulated by the strain from 0.54 meV ($\ensuremath{\varepsilon}=\ensuremath{-}6%$) to 1.32 meV ($\ensuremath{\varepsilon}=\ensuremath{-}2%$), and the easy [100] and hard [001] magnetic axes could be switched from each other by charge carrier doping. The calculated valley optical response of the Janus $2H$-VTeSe monolayer exhibits a valley-selective circular dichroism. Due to the broken inversion and time-reversal symmetry, the valley polarization and Berry curvature can be continuously tuned by applying biaxial strains (modulation range 24.2%), external electric field (modulation range 2%), and varying the magnetization angle (0 to 180 degrees). The Janus $2H$-VTeSe monolayer possesses intrinsic ferromagnetic ordering, large spontaneous valley polarization, high ${T}_{c}$ of 380 K, and considerable MAE of 1.15 meV, giving it a potential application in the two-dimensional spintronic devices.

Single-layer intrinsic 2H-phase LuX 2 (X = Cl, Br, I) with large valley polarization and anomalous valley Hall effect

Manipulation of the valley degree of freedom provides a new path for quantum information technology, but the real intrinsic large valley-polarization materials are rarely reported up to date. Here, we perform first-principles calculations to predict a class of 2H-phase single layer (SL) materials LuX 2 (X = Cl, Br, I) to be ideal candidates. SL-LuX 2 are ferrovalley materials with a giant valley-polarization of 55 meV–148 meV as a result of its large spin–orbital coupling (SOC) and intrinsic ferromagnetism (FM). The magnetic transition temperatures of SL-LuI2 and SL-LuCl2 are estimated to be 89 K–124 K, with a sizable magnetic anisotropy at out-of-plane direction. Remarkably, the anomalous valley Hall effect (AVHE) can be controlled in SL-LuX 2 when an external electric field is applied. Moreover, the intrinsic valley-polarization of SL-LuI2 is highly robust for biaxial strain. These findings provide a promising ferrovalley material system for the experimentation of valleytronics and subsequent applications.

Intrinsic valley-related multiple Hall effect in the two-dimensional organometallic lattice of NbTa-benzene

Valley-related multiple Hall effect in two-dimensional (2D) lattice is a fundamental transport phenomenon in the fields of condensed matter physics and materials science. Most proposals for its realization are limited to toy models or extrinsic effects. Here, based on a tight-binding model and first-principles calculations, we report the discovery of intrinsic valley-related multiple Hall effect in the 2D organometallic lattice of NbTa-benzene. Protected by the breaking of both time-reversal and inversion symmetry, NbTa-benzene exhibits large valley polarization spontaneously in both the conduction and valence bands, guaranteeing the anomalous valley Hall effect. Simultaneously, because of the exchange interaction and strong spin-orbit coupling, intrinsic band inversion occurs at one valley, which ensures the valley-polarized quantum anomalous Hall (QAH) effect, thus presenting the extraordinary valley-related multiple Hall effect in nature. In addition, it can be transformed into the phase with a ferrovalley or the QAH effect solely through strain engineering. These insights are not only useful for the fundamental research in valley-related physics but also enable a wide range of device applications.