Spontaneous valley splitting and valley pseudospin field effect transistors of monolayer VAgP2Se6

Independent Electrical Control of Spin and Valley Degrees in 2D Breathing Kagome Ta3I8 with Intrinsic Triferroicity

Independent electrical control of spin and valley degrees of freedom (DOFs) in 2D materials is difficult due to the coupling of spin and valley DOFs. Here we propose that spin-filter transport and valley polarization can be independently manipulated by an electric field in 2D breathing kagome Ta3I8 due to the possession of both triferroic (ferromagnetism, ferroelectric, and ferrovalley) and bipolar magnetic semiconducting characteristics. The spin-filter transport can be realized by applying a bias voltage without altering the semiconducting characteristic. The flip of valley polarization is fulfilled by switching the ferroelectric polarization with a gate voltage. Our results demonstrate the potential to control different DOFs independently by adjusting the direction of the electric field.

Layer-Polarized Anomalous Hall Effects from Inversion-Symmetric Single-Layer Lattices

In the field of physics and materials science, the discovery of the layer-polarized anomalous Hall effect (LP-AHE) stands as a crucial development. The current research paradigm is rooted in topological or inversion-asymmetric valleytronic systems, making such a phenomenon rather rare. In this work, a universal design principle for achieving the LP-AHE from inversion-symmetric single-layer lattices is proposed. Through tight-binding model analysis, we demonstrate that by stacking into antiferromagnetic van der Waals bilayer lattices, the coupling physics between PT symmetry and vertical external bias can be realized. This coupling reveals the previously neutralized layer-locked Berry curvature, compelling the carriers to move in a specific direction within a given layer, thereby realizing the LP-AHE. Intriguingly, the chirality of the LP-AHE can be effectively switched by modulating the direction of vertical external bias. First-principles calculations validate this mechanism in bilayer T-FeCl2 and MnPSe3. Our results pave the way for new explorations of the LP-AHE.

Strain Engineering of Intrinsic Ferromagnetism in 2D van der Waals Materials

Since the discovery of the low-temperature, long-range ferromagnetic order in monolayers Cr2Ge2Te6 and CrI3, many efforts have been made to achieve a room temperature (RT) ferromagnet. The outstanding deformation ability of two-dimensional (2D) materials provides an exciting way to mediate their intrinsic ferromagnetism (FM) with strain engineering. Here, we summarize the recent progress of strain engineering of intrinsic FM in 2D van der Waals materials. First, we introduce how to explain the strain-mediated intrinsic FM on Cr-based and Fe-based 2D van der Waals materials through ab initio Density functional theory (DFT), and how to calculate magnetic anisotropy energy (MAE) and Curie temperature (TC) from the interlayer exchange coupling J. Subsequently, we focus on numerous attempts to apply strain to 2D materials in experiments, including wrinkle-induced strain, flexible substrate bending or stretching, lattice mismatch, electrostatic force and field-cooling. Last, we emphasize that this field is still in early stages, and there are many challenges that need to be overcome. More importantly, strengthening the guideline of strain-mediated FM in 2D van der Waals materials will promote the development of spintronics and straintronics.

Spontaneous valley polarization and valley-nonequilibrium quantum anomalous Hall effect in Janus monolayer ScBrI

Topology and ferrovalley (FV) are two essential concepts in emerging device applications and the fundamental research field. To date, relevant reports are extremely rare about the coupling of FV and topology in a single system. By Monte Carlo (MC) simulations and first-principles calculations, a stable intrinsic FV ScBrI semiconductor with high Curie temperature (T_C) is predicted. Because of the combination of spin-orbital coupling (SOC) and exchange interaction, the Janus monolayer ScBrI shows a spontaneous valley polarization of 90 meV, which is located in the top valence band. For the magnetization direction perpendicular to the plane, the changes from FV to half-valley-metal (HVM), to valley-nonequilibrium quantum anomalous Hall effect (VQAHE), to HVM, and to FV can be induced by strain engineering. It is worth noting that there are no particular valley polarization and VQAHE states for in-plane (IP) magnetic anisotropy. By obtaining the real magnetic anisotropy energy (MAE) under different strains, due to spontaneous valley polarization, intrinsic out-of-plane (OOP) magnetic anisotropy, a chiral edge state, and a unit Chern number, the VQAHE can reliably appear between two HVM states. The increasing strains can induce VQAHE, which can be clarified by a band inversion between d_x²-y²/d_xy and d_z² orbitals, and a sign-reversible Berry curvature. Once synthesized, the Janus monolayer ScBrI would find more significant applications in topological electronic, valleytronic, and spintronic nanodevices.

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 T_c of 260 K, a significant magnetic moment of 8μ_B 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 T_c 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 T_c 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 (d_z², d_yz), (d_x²-y², d_xy) and (p_x, p_y) 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 d_yz and the unoccupied spin-down states of d_z² 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 d_xy and d_x²-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.

Combined piezoelectricity, valley splitting and Dzyaloshinskii-Moriya interaction in Janus GdXY (X, Y = Cl, Br, I) magnetic semiconductors

Janus materials, as a family of multifunctional materials with broken mirror symmetry, have played a great role in piezoelectric, valley-related, and Rashba spin-orbit coupling (SOC) applications. Using first-principles calculations, it is predicted that monolayer 2H-GdXY (X, Y = Cl, Br, I) will combine giant piezoelectricity, intrinsic valley splitting and a strong Dzyaloshinskii-Moriya interaction (DMI), resulting from the intrinsic electric polarization, spontaneous spin polarization and strong spin-orbit coupling. Opposite Berry curvatures and unequal Hall conductivities at the K- and K'-valleys of monolayer GdXY are promising for storing information through the anomalous valley Hall effect (AVHE). Through construction of the spin Hamiltonian and micromagnetic model, we obtained the primary magnetic parameters of monolayer GdXY as a function of the biaxial strain. Due to the dimensionless parameter κ having strong tunability, monolayer GdClBr is promising to host isolated skyrmions. The present results are expected to enable the application of Janus materials in piezoelectricity, spin- and valley-tronics and the formation of chiral magnetic structures.

Layered Semiconductor Cr0.32Ga0.68Te2.33 with Concurrent Broken Inversion Symmetry and Ferromagnetism: A Bulk Ferrovalley Material Candidate

The valleytronic state found in group-VI transition-metal dichalcogenides such as MoS2 has attracted immense interest since its valley degree of freedom could be used as an information carrier. However, valleytronic applications require spontaneous valley polarization. Such an electronic state is predicted to be accessible in a new ferroic family of materials, i.e., ferrovalley materials, which features the coexistence of spontaneous spin and valley polarization. Although many atomic monolayer materials with hexagonal lattices have been predicted to be ferrovalley materials, no bulk ferrovalley material candidates have been reported or proposed. Here, we show that a new non-centrosymmetric van der Waals (vdW) semiconductor Cr0.32Ga0.68Te2.33, with intrinsic ferromagnetism, is a possible candidate for bulk ferrovalley material. This material exhibits several remarkable characteristics: (i) it forms a natural heterostructure between vdW gaps, a quasi-two-dimensional (2D) semiconducting Te layer with a honeycomb lattice stacked on the 2D ferromagnetic slab comprised of the (Cr, Ga)-Te layers, and (ii) the 2D Te honeycomb lattice yields a valley-like electronic structure near the Fermi level, which, in combination with inversion symmetry breaking, ferromagnetism, and strong spin-orbit coupling contributed by heavy Te element, creates a possible bulk spin-valley locked electronic state with valley polarization as suggested by our DFT calculations. Further, this material can also be easily exfoliated to 2D atomically thin layers. Therefore, this material offers a unique platform to explore the physics of valleytronic states with spontaneous spin and valley polarization in both bulk and 2D atomic crystals.

2D electrene LaH2monolayer: an ideal ferrovalley direct semiconductor with room-temperature ferromagnetic stability

In developing nonvolatile valleytronic devices, ferromagnetic (FM) ferrovalley semiconductors are critically needed due to the existence of spontaneous valley polarization. At present, however, the known real materials have various drawbacks towards practical applications, including the in-plane FM ground state, low Curie temperature (TC), small valley polarization, narrow energy window with clean polarized valley, and indirect bandgap. From first-principles calculations, here we predict anideal ferrovalley semiconductor, honeycomb LaH₂monolayer (ML), whose intrinsic properties can overcome all these shortcomings. We demonstrate that LaH₂ML, having satisfied structural stability, is a FM half-semiconducting electrene (La3+2H-⋅e-) with its magnetic moments localized at the lattice interstitial sites rather than La atoms. At the same time, LaH₂ML holds the following desired attributes: a robust out-of-plane FM ground state with a highTC(334 K), a sizable valley polarization (166 meV), a wide energy window (137 meV) harboring clean single-valley carriers, and a direct bandgap. These results identify a much needed ideal ferrovalley semiconductor candidate, holding the promising application potential in valleytronics and spintronics devices.

Spontaneous Valley Polarization and Electrical Control of Valley Physics in Single-Layer TcIrGe2S6

The modulation of valley polarization in one single system is of important fundamental and practical importance in quantum information technology. Here, through the first-principles calculations, we identify single-layer TcIrGe₂S₆ as a tantalizing candidate for realizing the modulation of valley polarization. Arising from the combination of inversion symmetry breaking and intrinsic magnetic exchange interaction, single-layer TcIrGe₂S₆ exhibits spontaneous valley polarization. The value of valley polarization in the conduction band is 161 meV, favorable for achieving the intriguing anomalous valley Hall effect. Furthermore, single-layer TcIrGe₂S₆ possesses ferroelectric order. More remarkably, its ferroelectric and valley physics can be strongly coupled, namely, the valley properties can be switched off and on electrically. These findings not only provide a compelling candidate for two-dimensional valleytronic research but also open a new avenue for modulating valley physics.

Intrinsic Valley Splitting and Direct-to-Indirect Band Gap Transition in Monolayer HfZrSiCO2

Both a reasonably large valley splitting (VS) and a sufficiently long valley exciton lifetime are crucial in valleytronics device applications. Currently, no single system possesses both attributes simultaneously. Herein, we demonstrate that a Janus monolayer HfZrSiCO2 concurrently hosts a giant intrinsic VS and excitonic quasi-particles with long valley lifetime due to valley-sublayer coupling and built-in electric field. In addition, the band structure of the monolayer HfZrSiCO2 can be continuously manipulated by either an external electric field or a biaxial strain, giving rise to a tunable VS and driving a direct-to-indirect band gap transition. Moreover, the system exhibits valley-contrasting linear dichroism in exciton absorption. These results suggest that the Janus monolayer HfZrSiCO2 is a promising candidate for information applications.

Janus 2H-VSSe monolayer: two-dimensional valleytronic semiconductor with nonvolatile valley polarization

Valleytronic as a hot topic in recent years focuses on electrons' valley degree of freedom as a quantum information carrier. Here, by combining two-bandk.pmodel with high-throughput density functional theory (DFT) calculations, the valley states of Janus 2H-VSSe monolayer are studied which have spontaneous polarization. Nonvolatile valley polarization state is mainly arises from intrinsic ferromagnetism contributed by V-3d electronic configuration and not the spontaneous out-of-plane dipole moment of VSSe monolayer. The effective Hamiltonian model and DFT calculations both showed that the valley splitting mainly originates from the smaller spin splitting coming from the spin-orbit coupling effect rather than the spin splitting of magnetic exchange field. By using the effective Dirac Hamiltonian and Kubo formula, we further calculated the longitudinal and transversal conductivities and absorption spectra of VSSe monolayer which exhibits an anomalous valley Hall effect and clear valley-selective circular dichroism. Our calculations indicate that the modification of valley and spin splitting related to Berry curvature by applying an external strain is more noticeable than by the change of the magnetic moment orientation and electric field. We found that carriers accumulation with particular spin and valley label can be manipulated by tuning effective Hamiltonian parameters. The coexistence of robust in-plane magnetic ordering and spontaneous valley polarization of 2H-VSSe monolayer supports the possibility of applications in spintronics, valleytronics and optoelectronics devices.

Monolayer gadolinium halides, GdX2 (X = F, Cl, Br): intrinsic ferrovalley materials with spontaneous spin and valley polarizations

Two-dimensional (2D) intrinsic ferrovalley semiconductors provide unprecedented opportunities to investigate valley physics as well as providing promising device applications due to their exceptional combination of spontaneous spin and valley polarizations. Here, we have predicted from first-principles calculations and Monte Carlo simulations that monolayers (MLs) GdX₂ are such extremely rare excellent materials. Apart from their robust stabilities energetically, dynamically, thermally, and mechanically, these 2D materials are found to be semiconducting intrinsic ferromagnets where the magnetic coupling is ascribed to 5d-electron-mediated 4f-4f exchange interactions. Moreover, MLs GdX₂ (X = F, Cl, Br) not only exhibit significant magnetic anisotropy energy of 351, 268, and 30 μeV per Gd, but also have a high Curie temperature of 300, 245, and 225 K, respectively. In particular, spontaneous valley polarization in three systems occurs due to the cooperative interplay between the spin-orbit coupling and magnetic exchange interactions, whose magnitude is as sizable as 55, 38, and 82 meV for MLs GdF₂, GdCl₂, and GdBr₂, respectively. Under the action of an in-plane longitudinal electrical field, the valley-contrasting Berry curvatures arising from the broken space-inversion and time-reversal symmetries in MLs GdX₂ could yield opposite transverse velocities of the carriers, giving rise to the occurrence of a spin-polarized anomalous valley Hall effect. Overall, these findings render 2D GdX₂ a class of promising candidate materials for experimental studies and practical spintronics and valleytronics applications.

Valley polarization transition driven by biaxial strain in Janus GdClF monolayer

The valley degree of freedom of carriers in crystals is useful to process information and perform logic operations, and it is a key factor for valley application to realize valley polarization. Here, we propose a model that the valley polarization transition at different valley points (-K and K points) is produced by biaxial strain. Using first-principles calculations, we illustrate our idea with a concrete example of a Janus GdClF monolayer. The predicted GdClF monolayer is dynamically, mechanically and thermally stable, and is a ferromagnetic (FM) semiconductor with perpendicular magnetic anisotropy (PMA), valence band maximum (VBM) at valley points and a high Curie temperature (T_C). Due to its intrinsic ferromagnetism and spin-orbit coupling (SOC), a spontaneous valley polarization will be induced, but the valley splitting is only -3.1 meV, which provides an opportunity to achieve valley polarization transition at different valley points by strain. In the considered strain range (a/a₀: 0.94-1.06), the strained GdClF monolayer always has an energy bandgap, strong FM coupling and PMA. The compressive strain is in favour of -K valley polarization, while the tensile strain is favorable for K valley polarization. The corresponding valley splittings at 0.96 and 1.04 strains are -44.5 meV and 29.4 meV, respectively, which are higher than the thermal energy at room temperature (25 meV). Due to its special Janus structure, both in-plane and out-of-plane piezoelectric polarizations can be observed. It is found that the direction of in-plane piezoelectric polarization can be overturned by strain, and the d₁₁ values at 0.96 and 1.04 strains are -1.37 pm V^-1 and 2.05 pm V^-1, respectively. Our work paves the way to design ferrovalley materials for application in multifunctional valleytronic and piezoelectric devices by strain.

Potential 2D Materials with Phase Transitions: Structure, Synthesis, and Device Applications

Layered materials with phase transitions, such as charge density wave (CDW) and magnetic and dipole ordering, have potential to be exfoliated into monolayers and few-layers and then become a large and important subfamily of two-dimensional (2D) materials. Benefitting from enriched physical properties from the collective interactions, long-range ordering, and related phase transitions, as well as the atomic thickness yet having nondangling bonds on the surface, 2D phase-transition materials have vast potential for use in new-concept and functional devices. Here, potential 2D phase-transition materials with CDWs and magnetic and dipole ordering, including transition metal dichalcogenides, transition metal halides, metal thio/selenophosphates, chromium silicon/germanium tellurides, and more, are introduced. The structures and experimental phase-transition properties are summarized for the bulk materials and some of the obtained monolayers. In addition, recent experimental progress on the synthesis and measurement of monolayers, such as 1T-TaS₂ , CrI₃ , and Cr₂ Ge₂ Te₆ , is reviewed.

Two-dimensional ferromagnetism and driven ferroelectricity in van der Waals CuCrP2S6

Multiferroic materials have the potential to be applied in novel magnetoelectric devices, for example, high-density non-volatile storage devices. During the last decades, research on multiferroic materials was focused on three-dimensional (3D) materials. However, 3D materials suffer from dangling bonds and quantum tunneling in nano-scale thin films. Two-dimensional (2D) materials might provide an elegant solution to these problems, and thus are highly in demand. Using first-principles calculations, we predicted ferromagnetism and electric-field-driving ferroelectricity in the monolayer and even in the few-layers of CuCrP2S6. Although the total energy of the ferroelectric phase of the monolayer is higher than that of the antiferroelectric phase, the ferroelectric phases can be realized by applying a large electric field. Besides the degrees of freedom in the common multiferroic materials, the valley degree of freedom is also polarized, according to our calculations. The spins, electric dipoles and valleys are coupled with each other as shown in the computational results. In our experiment, we observed the out-of-plane ferroelectricity in few-layer CuCrP2S6 (approximately 13 nm thick) at room temperature. 2D ferromagnetism of few-layers is inferred from the magnetic hysteresis loops of the massively stacked nanosheets at 10 K. The experimental observations support our calculations very well. Our findings may provide a series of 2D materials for further device applications.