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Valley, the energy extrema in the electronic band structure at momentum space, is regarded as a new degree of freedom of electrons, in addition to charge and spin. The studies focused on valley degree of freedom now form an emerging field of condensed-matter physics, i.e., valleytronics, whose development is exactly following that of spintronics, which focuses on the spin degree of freedom. Here, in analogy to half-metals in spintronics where one spin channel is conducting, whereas the other is insulating, we propose the concept of half-valley metal, in which conduction electrons are intrinsically 100% valley polarized, as well as 100% spin polarized even when spin–orbit interactions are considered. Combining first-principle calculations with a two-band k·p model, the physical mechanism to form the half-valley metal is illuminated. Taking the ferrovalley H-FeCl2 monolayer with strong exchange interaction as an example, we find that the strong electron correlation effect can induce the ferrovalley to half-valley-metal transition. Due to the valley-dependent optical selection rules, such a system could be transparent to, e.g., left-circularly polarized light, yet the right-circularly polarized light will be reflected, which can in turn be used as a crucial method to detect the half-valley-metal state. Interestingly, with the increase of the correlation effect, the system becomes insulating again with all valleys following the same optical selection rule. We confirm that in this specific case, the valence bands, which consist of single spin, possess nonzero Chern number and consequently an intrinsic quantum anomalous valley Hall effect emerges. Our findings open an appealing route toward functional 2D materials design of valleytronics.

In analogy to all-electric spintronics, all-electric valleytronics, i.e., valley manipulation via electric means, becomes an exciting new frontier as it may bring revolutions in the field of data storage with ultra-high speed and ultra-low power consumption. The existence of the anomalous valley Hall effect in ferrovalley materials demonstrates the possibility of electrical detection for valley polarization. However, in previously proposed valley-polarized monolayers, the anomalous valley Hall effect is controlled by external magnetic fields. Here, through elaborate structural design, we propose the antiferrovally bilayer as an ideal candidate for realizing all-electric valleytronic devices. Using the minimal k·p model, we show that the energy degeneracy between valley indexes in such system can be lifted by electric approaches. Subsequently, the anomalous valley Hall effect strongly depends on the electric field as well. Taking the bilayer VSe2 as an example, all-electric tuning and detecting of anomalous valley Hall effect is confirmed by density-functional theory calculations, indicating that the valley information in such antiferrovalley bilayer can be reversed by an electric field perpendicular to the plane of the system and easily probed through the sign of the Hall voltage. First-principles calculations reveal that the anomalous valley Hall effect can be detected and tuned through an external electric field in bilayer VSe2. In transition-metal dichalcogenides, the local maxima or minima of the energy bands (so called valleys) are degenerate; in analogy to spintronics, manipulation of the electronic valley degree of freedom is promising for valleytronics applications. Monolayer 2H-VSe2 has already been put forth as a ferrovalley material, capable to exhibit spontaneous valley polarization and control its polarity under external magnetic fields. Now, Wen-Yi Tong and Chun-Gang Duan report that the valley Hall effect can be present in VSe2 bilayers without external stimuli. A perpendicular electric field enhances the accumulation of the majority carriers in the two layers in opposite directions, induces the anomalous valley Hall effect, and controls the sign of the Hall voltage. Such a way to access and control the valley information, is significant for valleytronics applications.

Engineering the electronic band structure of material systems enables the unprecedented exploration of new physical properties that are absent in natural or as-synthetic materials. Half metallicity, an intriguing physical property arising from the metallic nature of electrons with singular spin polarization and insulating for oppositely polarized electrons, holds a great potential for a 100% spin-polarized current for high-efficiency spintronics. Conventionally synthesized thin films hardly sustain half metallicity inherited from their 3D counterparts. A fundamental challenge, in systems of reduced dimensions, is the almost inevitable spin-mixed edge or surface states in proximity to the Fermi level. Here, we predict electric field-induced half metallicity in bilayer A-type antiferromagnetic van der Waals crystals (i.e., intralayer ferromagnetism and interlayer antiferromagnetism), by employing density functional theory calculations on vanadium diselenide. Electric fields lift energy levels of the constituent layers in opposite directions, leading to the gradual closure of the gap of singular spin-polarized states and the opening of the gap of the others. We show that a vertical electrical field is a generic and effective way to achieve half metallicity in A-type antiferromagnetic bilayers and realize the spin field effect transistor. The electric field-induced half metallicity represents an appealing route to realize 2D half metals and opens opportunities for nanoscale highly efficient antiferromagnetic spintronics for information processing and storage.

Multiferroic and magnetoelectric materials are considered as major candidates for next-generation information storage technologies due to their simultaneous presence and interplay of two or more ferroic orders. In this paper, we briefly review our theoretical progress relating to the all-electric spintronics, i.e., spin manipulation via an electric means rather than a magnetic field. Special focus is given to interface/surface magnetoelectric effect, electric field control of magnetocrystalline anisotropy, Rashba spin–orbit coupling, spin transport, and other generalized all-electric modulation of magnetism. Our recently developed method, i.e., the orbital selective external potential method, is also expounded. This method might be a powerful tool in finding the mechanisms responsible for the intriguing phenomena occurred in multiferroics or magnetoelectric materials.

Transition-metal dichalcogenide (TMD) monolayers $MXY\phantom{\rule{0.16em}{0ex}}(M=\mathrm{Mo},\phantom{\rule{0.16em}{0ex}}\mathrm{W};X\phantom{\rule{0.16em}{0ex}}\ensuremath{\ne}\phantom{\rule{0.16em}{0ex}}Y=\mathrm{S},\phantom{\rule{0.16em}{0ex}}\mathrm{Se},\phantom{\rule{0.16em}{0ex}}\mathrm{Te})$ are two-dimensional polar semiconductors. Setting the WSeTe monolayer as an example and using density functional theory calculations, we investigate the manipulation of Rashba spin-orbit coupling (SOC) in the MXY monolayer. It is found that the intrinsic out-of-plane electric field due to the mirror symmetry breaking induces the large Rashba spin splitting around the $\mathrm{\ensuremath{\Gamma}}$ point, which, however, can be easily tuned by applying the in-plane biaxial strain. Through a relatively small strain (from $\ensuremath{-}2%$ to 2%), a large tunability (from around $\ensuremath{-}50%$ to 50%) of Rashba SOC can be obtained due to the modified orbital overlap, which can in turn modulate the intrinsic electric field. The orbital selective external potential method further confirms the significance of the orbital overlap between $\mathrm{W}\text{\ensuremath{-}}{d}_{{z}^{2}}$ and $\mathrm{Se}\text{\ensuremath{-}}{p}_{z}$ in Rashba SOC. In addition, we also explore the influence of the external electric field on Rashba SOC in the WSeTe monolayer, which is less effective than strain. By calculating the electric-field-induced Rashba SOC in all six $M{X}_{2}$ monolayers, the rule of the electric-field influence on Rashba SOC in TMD monolayers is demonstrated. The large Rashba spin splitting, together with the valley spin splitting in MXY monolayers, may make a special contribution to semiconductor spintronics and valleytronics.

Multiferroics are materials where two or more ferroic orders coexist owing to the interplay between spin, charge, lattice and orbital degrees of freedom. The explosive expansion of multiferroics literature in recent years demonstrates the fast growing interest in this field. In these studies, the first-principles calculation has played a pioneer role in the experiment explanation, mechanism discovery and prediction of novel multiferroics or magnetoelectric materials. In this review, we discuss, by no means comprehensively, the extensive applications and successful achievements of first-principles approach in the study of multiferroicity, magnetoelectric effect and tunnel junctions. In particular, we introduce some our recently developed methods, e.g., the orbital selective external potential method, which prove to be powerful tools in the finding of mechanisms responsible for the intriguing phenomena occurred in multiferroics or magnetoelectric materials. We also summarize first-principles studies on three types of electric control of magnetism, which is the common goal of both spintronics and multiferroics. Our review offers in depth understanding on the origin of ferroelectricity in transition metal oxides, and the coexistence of ferroelectricity and ordered magnetism, and might be helpful to explore novel multiferroic or magnetoelectric materials in the future.

Multiferroics are materials where two or more ferroic orders coexist owing to the interplay between spin, charge, lattice and orbital degrees of freedom. The explosive expansion of multiferroics literature in recent years demon-strates the fast growing interest in this field. In these studies, the first-principles calculation has played a pioneer role in the experiment explanation, mechanism discovery and prediction of novel multiferroics or magnetoelectric materials. In this review, we discuss, by no means comprehensively, the extensive applications and successful achievements of first-principles approach in the study of multiferroicity, magnetoelectric effect and tunnel junc-tions. In particular, we introduce some our recently developed methods, e.g., the orbital selective external potential (OSEP) method, which prove to be powerful tools in the finding of mechanisms responsible for the intriguing phe-nomena occurred in multiferroics or magnetoelectric materials. We also summarize first-principles studies on three types of electric control of magnetism, which is the common goal of both spintronics and multiferroics. Our review offers in depth understanding on the origin of ferroelectricity in transition metal oxides, and the coexistence of fer-roelectricity and ordered magnetism, and might be helpful to explore novel multiferroic or magnetoelectric materi-als in the future., Comment: 44 pages, 30 figures. Review paper

Considerable progress in contemporary spintronics has been made in recent years for developing nanoscale data memory and quantum information processing. It is, however, still a great challenge to achieve the ultimate limit of storage bit. 2D materials, fortunately, provide an alternative solution for designing materials with the expected miniaturizing scale, chemical stability as well as giant magnetic anisotropy energy. By performing first-principles calculations, we have examined two possible doping sites on a WS2 monolayer using three kinds of transition metal (TM) atoms (Mn, Fe and Co). It is found that the TM atoms prefer to stay on the W atom site. Additionally, differently from the case of Mn, doping Co and Fe atoms on the W vacancy can achieve perpendicular magnetic anisotropy with a much larger magnitude, which provides a bright prospect for generating atomic-scale magnets of storage devices.

Rashba spin orbit coupling (SOC) in noble metal surfaces is of great importance for the application of metal films in spintronic devices. By combining the density-functional theory calculations with our recently developed orbital selective external potential method, we investigate the Rashba SOC in the Shockley surface states of Au(111) and Ag(111). We find that the large Rashba SOC in the sp-character surface states of Au(111) is mainly contributed by the minor d-orbitals in the surface states. While for the sd-character surface states, although they are dominated by the d-orbitals, Rashba splitting is found to be rather small. Band structure analysis reveals that this is mainly because the sd-character surface states are well below the Fermi level and can be less influenced by the asymmetric surface potential. We demonstrate that the Rashba SOC in noble metal surfaces can be effectively manipulated by shifting the d-orbitals in the surface states, which can be physically implemented through surface decoration. Our investigation provides a deep understanding on Rashba SOC in noble metal surfaces and could be helpful to their applications in spintronic devices.