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

Ferro-Valleytricity with In-Plane Spin Magnetization

Ferro-valleytricity that manifests spin-orbit coupling (SOC)-induced spontaneous valley polarization is generally considered to occur in two-dimensional (2D) materials with out-of-plane spin magnetization. Here, we propose a mechanism to realize SOC-induced valley polarization and ferro-valleytricity in 2D materials with in-plane spin magnetization, wherein the physics correlates to non-collinear magnetism in triangular lattice. Our model analysis provides comprehensive ingredients that allow for ferro-valleytricity with in-plane spin magnetization, revealing that mirror symmetry favors remarkable valley polarization and time-reversal-mirror joint symmetry should be excluded. Through modulating the in-plane spin magnetization offset, the SOC-induced valley polarization could be reversed. Followed by first-principles, such a mechanism is demonstrated in a multiferroic triangular lattice of single-layer W3Cl8. We further show that the reversal of valley polarization could also be driven by applying an electric field that modulates ferroelectricity. Our findings greatly enrich valley physics research and significantly extend the scope for material classes of ferro-valleytricity.

Single layer TlX (X = Cl/Br/I) with a ferroelectric-valley coupling potential for an electrically tunable polarizer

Ferrovalley materials are generally hexagonal lattice systems with a ferromagnetism-valley coupling, in which the intrinsic ferromagnetism can induce valley polarization. However, as of now the number of ferrovalleys found is still limited. In this article, TlX (X = Cl/Br/I) single-layers (SLs) are proposed with a tetragonal lattice structure as well as ferroelectricity-valley coupling. Furthermore, they possess good mechanical and dynamic stability, and are expected to be synthesized in experiments. When applying an in-plane electric field or uniaxial strain, the SL-TlX (X = Cl/Br/I) show a robust valley polarization. Because the direction of polarization of SL-TlX (X = Cl/Br/I) can be controlled with a rapid reversal of the electric field direction, SL-TlX (X = Cl/Br/I) are potential valleytronic materials with an electrically controllable valley polarization. The SL-TlX (X = Cl/Br/I) have linear optical selection rules, different from those of traditional hexagonal lattice systems, giving them potential for manufacturing electrically controllable optical filters.

Ferrovalleytricity in a two-dimensional antiferromagnetic lattice

Control over and manipulation of valley physics via ferrovalleytricity is highly desirable for advancing valleytronics. Current research focuses primarily on two-dimensional ferromagnetic systems, while antiferromagnetic counterparts are seldom explored. Here, we present a general mechanism for extending the ferrovalleytricity paradigm to antiferromagnetic lattices to achieve spin control over valley physics. Our symmetry analysis and k·p model reveal that by introducing a Zeeman field aroused by the proximity effect, spin-switchable non-uniform potential is imposed on the two sublattices of an antiferromagnetic lattice. This enables spin control over the anomalous valley Hall effect, thereby realizing ferrovalleytricity. This mechanism is confirmed in a CrBr3-MnPSe3-CrBr3 heterotrilayer from first principles, where the spin-switchable non-uniform Zeeman effect is exerted on two Mn sublattices when the antiferromagnetic MnPSe3 layer is sandwiched between ferromagnetic CrBr3 layers. Such a non-uniform Zeeman effect combined with valley physics guarantees spin control over the anomalous valley Hall effect, i.e., ferrovalleytricity, in the MnPSe3 layer. Our work will shed light on potential applications of valley physics in antiferromagnetic systems.

Large valley splitting and vacancy-induced valley polarization in two-dimensional WSeNH

The investigation and manipulation of valley pseudospin in promising two-dimensional (2D) semiconductors are essential for accelerating the development of valleytronics. Based on first-principles, we herein report that the WSeNH monolayer is a potential 2D valleytronic material. It is found that stable 2D WSeNH exhibits a semiconducting character with broken inversion symmetry, forming a pair of energy-degenerate but inequivalent valleys at the K and K' points. Arising from the strong spin-orbit coupling strength governed by the W-dxy/dx2-y2 orbitals, it exhibits a large valley splitting of 425 meV at the top of the valence band, which makes it highly plausible for generating the attractive valley Hall effect. Moreover, both valley splitting and optical transition energy can be efficiently modulated by external strain. Furthermore, we find that a considerable valley polarization of 23 meV can be readily realized in 2D WSeNH by introducing hydrogen vacancies. These findings not only broaden the family of 2D valleytronic materials but also provide alternative avenues for valley manipulation.

Enhancement and modulation of valley polarization in Janus CrSSe with internal and external electric fields

The valley polarization, induced by the magnetic proximity effect, in monolayer transition metal dichalcogenides (TMDCs), has attracted significant attention due to the intriguing fundamental physics. However, the enhancement and modulation of valley polarization for real device applications is still a challenge. Here, using first-principles calculations we investigate the valley polarization properties of monolayer TMDCs CrS2 and CrSe2 and how to enhance the valley polarization by constructing Janus CrSSe (with an internal electric field) and modulate the polarization in CrSSe by applying external electric fields. Janus CrSSe exhibits inversion symmetry breaking, internal electric field, spin-orbit coupling, and compelling spin-valley coupling. A magnetic substrate of the MnO2 monolayer can induce a modest magnetic moment in CrSe2, CrSe2, and CrSSe. Notably, the Janus structure with an internal electric field has a much larger valley p compared with its non-Janus counterparts. Moreover, the strength of valley polarization can be further modulated by applying external electric fields. These findings suggest that Janus materials hold promise for designing and developing advanced valleytronic devices.

Engineering Layertronics in Two-Dimensional Ferromagnetic Multiferroic Lattice

Layertronics, rooted in the layer Hall effect (LHE), is an emerging fundamental phenomenon in condensed matter physics and spintronics. So far, several theoretical and experimental proposals have been made to realize LHE, but all are based on antiferromagnetic systems. Here, using symmetry and tight-binding model analysis, we propose a general mechanism for engineering layertronics in a two-dimensional ferromagnetic multiferroic lattice. The physics is related to the band geometric properties and multiferroicity, which results in the coupling between Berry curvature and layer degree of freedom, thereby generating the LHE. Using first-principles calculations, we further demonstrate this mechanism in bilayer (BL) TcIrGe2S6. Due to the intrinsic inversion and time-reversal symmetry breakings, BL TcIrGe2S6 exhibits multiferroicity with large Berry curvatures at both the center and corners of the Brillouin zone. These Berry curvatures couple with the layer physics, forming the LHE in BL TcIrGe2S6. Our work opens a new direction for research on layertronics.