Effects of crystal deformation on spin-valley interplay and topological phase transition: a case study on VSi2X4 (X = N or P) monolayers

Abstract

Achieving spin-valley coupled states is essential to promote the fantastic integration of spintronics and valleytronics. Two-dimensional transition metal systems with the D_3h point group, by breaking both time-reversal symmetry and structural inversion symmetry, are ideal candidates to explore the manifestation of spin-valley physics. Here, we present a detailed ab initio study on two-dimensional VSi₂X₄ (X = N and P) ferromagnetic semiconductors with contrasting Berry curvatures and inequivalent valleys when spin orientations are along the out-of-plane direction. The magnetic anisotropy can be well explained by the second-order perturbation theory, and the valley polarization derived from non-degenerated d orbitals under the trigonal prismatic crystal field can be expressed by the effective spin-orbital coupling Hamiltonian model. Importantly, a general picture regarding crystal deformation is uncovered which demonstrates the valley-flipping behavior with inverted V-d orbitals. The crystal field deformation index η, which is the ratio of height to base length (h/w) in V-centered trigonal prismatic coordination, can dominate the behavior of the hole- or electron-based valley polarization. We uncover that single valley flipping results in a nontrivial topological phase with the Chern number being 1 and nontrivial edge states. We also provide a general band evolution and topological phase diagram as a function of η. The anomalous Hall conductivity and the regime of unbalanced-carrier transport are also clarified. Crystal deformation effects on the spin-valley interplay provide a practical way for flexible valley-related regulations. Our work not only enriches the research on the regulation of valley-related behaviors, but also provides an ideal platform for exploring the valley-polarized topological and transport properties in spintronic and valleytronic devices.