Strain-tunable multipiezo effects in Janus monolayer Cr2SSe: Selective reversal of valley polarization and single-spin-channel anomalous valley Hall effect

Abstract: Altermagnetism, the third class of collinear magnetic order, uniquely combines a zero net magnetization with spin polarized bands in reciprocal space, opening new avenues for two dimensional valleytronics and spintronics. Here, using first principles calculations, we predict that the Janus monolayer Cr2SSe, which possesses intrinsic inversion symmetry breaking, hosts a strain tunable multipiezo effect and exhibits distinctive valleytronic properties. The system displays pronounced spin splitting and band inversion at the X and Y high symmetry points in the Brillouin zone, giving rise to robust spin-valley locking. The degeneracy of these valleys is protected by diagonal mirror symmetry. Application of uniaxial strain breaks this symmetry, concurrently inducing piezovalley, piezoelectric, and piezomagnetic responses, a manifestation of the multipiezo effect. Critically, strain applied along orthogonal crystallographic directions yields opposite valley polarization, while under small compressive strain, we achieve selective reversal of valley polarization, enabling independent control of valence and conduction band valleys and promoting a single-spin-channel anomalous valley Hall effect. These findings establish a pathway for low-power, non volatile manipulation of valley degrees of freedom and enhanced spin transport efficiency, providing a theoretical foundation for the design of energy-efficient valleytronic devices.

• The paper demonstrates that uniaxial strain in Cr₂SSe induces selective valley polarization reversal, achieving a 57.6 meV conduction band polarization difference.
• The study uses DFT+U and Berry curvature calculations to reveal robust multipiezo effects, including both piezoelectric and piezomagnetic responses, in the Janus monolayer.
• The paper reports a strain-induced single-spin-channel anomalous valley Hall effect, paving the way for energy-efficient, non-volatile spintronic device applications.

Strain-Tunable Multipiezo Effects and Valley Control in Janus Monolayer Cr₂SSe

Introduction

This work delivers a comprehensive first-principles analysis of multipiezo effects and emergent valleytronic phenomena in the Janus monolayer Cr₂SSe, an archetype of two-dimensional (2D) altermagnetic (AM) materials. The study advances fundamental understanding of symmetry-mediated coupling among spin, valley, and lattice degrees of freedom and establishes Cr₂SSe as a robust platform for the independent, strain-mediated manipulation of valley polarization and for the realization of a single-spin-channel anomalous valley Hall effect (AVHE).

Material Stability, Magnetic Order, and Electronic Structure

Cr₂SSe exhibits a tetragonal Janus structure with space group $p4mm$, confirming both inversion symmetry breaking and presence of a diagonal mirror ($M_{xy}$) symmetry. Phonon dispersion and ab initio molecular dynamics simulations underline its dynamic and thermal stability. Magnetic ground state calculations identify an in-plane staggered AM order, with the two Cr sublattices coupled through $C_{4v}$ and $M_{xy}$ symmetries, leading to zero net magnetization but spin-polarized electronic bands.

The spin-resolved band structure (PBE+$U$, $U_{eff}=3.5\,$eV) discloses a direct bandgap of 0.82 eV with pronounced spin splitting at $X$ and $Y$ points, producing a robust spin-valley locking and concurrent non-relativistic band inversion characteristics. The electronic ground state is confirmed to remain within the AM regime even with inclusion of spin-orbit coupling, indicating negligible relativistic corrections to the band topology.

Strain-Induced Multipiezo Effects

Piezovalley Effect and Valley Polarization Control

Upon application of uniaxial strain, Cr₂SSe undergoes symmetry-lowering transitions due to the explicit breaking of $M_{xy}$ symmetry. This breaks the degeneracy of the C-paired valleys (distinct from conventional T-paired valleys), and induces large, controllable valley polarization. Numerical calculations reveal that tensile strain up to +4% yields a maximum conduction band valley polarization of 57.6 meV, with the polarization sign entirely reversed for strain along orthogonal crystallographic directions (i.e., $x$ vs.\ $M_{xy}$0 axes), a direct consequence of the underlying symmetry constraints.

Piezoelectric and Piezomagnetic Effects

The Janus structure, with robust inversion asymmetry, sustains an intrinsic electric polarization of 4.13 pC/m, tunable up to 4.37 pC/m under $M_{xy}$14% compressive strain. This polarized response not only exceeds values typical for other 2D piezoelectrics but also maintains a linear dependence on strain.

Simultaneously, strain induces a finite net magnetization—realizing a direct piezomagnetic effect within this AM phase—without necessitating carrier doping. The strain-induced disparity in local Bader charges between the two Cr sublattices, as determined from DFT+U calculations, encapsulates the correlation between electron transfer and net moment, confirming theoretical predictions for AM materials under symmetry breaking.

Selective Valley Polarization Reversal

A notable finding is the strain-tunable, decoupled control of valley polarization in the conduction and valence bands, enabled by the differing orbital character (Cr $M_{xy}$2 vs.\ Se $M_{xy}$3 bands). At moderate compressive strain ($M_{xy}$42% to $M_{xy}$53% along $M_{xy}$6), the conduction band valley polarization increases monotonically, maintaining sign, while the valence band valley polarization undergoes a sign reversal. This allows independent reversibility of valley polarization for conduction and valence states, breaking traditional selection rules that otherwise couple these valley degrees of freedom.

Single-Spin-Channel Anomalous Valley Hall Effect

Calculation of Berry curvature (via Wannier90 and Kubo formalism), demonstrates that uniaxial strain not only generates finite, valley-contrasting Berry curvature but also enables single-spin-channel transport under certain conditions. Specifically, with $M_{xy}$73% strain, both relevant valley states governing transport are fully spin-polarized in a single channel, i.e., transport occurs exclusively via spin-up carriers. This 100% spin selection in AVHE is the first demonstration of a strain-controlled, single-spin transport channel in a 2D AM system, which could be crucial for ultralow-power spintronic and valleytronic device architectures.

Implications and Future Directions

This study clarifies the theoretical underpinnings for controlling valley and spin degrees of freedom through mechanical means in monolayer Janus AMs. Crucially, the selective decoupling of valley polarization in distinct bands and realization of single-spin-channel AVHE underpin new device paradigms where logical operations can be assigned to independent, orthogonally controlled quantum numbers. The magnitude of strain-induced responses and absence of reliance on external fields or carrier injection mark a significant advancement toward scalable, non-volatile, energy-efficient device integration.

Future research will focus on experimental verification of strain control via flexible substrates and in situ gating, exploring stochastic/robust switching mechanisms for device logic, as well as topological manifestations and dynamic switching in nanostructured and stacked Janus-AM heterostructures. The interplay of multipiezo effects with other ferroic orders (e.g., ferrotoroidicity, magnetoelectric coupling) also warrants examination.

Conclusion

Cr₂SSe monolayer establishes a prototype for strain-engineered valleytronic and spintronic functionality in two-dimensional AM systems. The strain-tunable multipiezo effects, symmetry-driven and decoupled valley control, and demonstration of a single-spin-channel AVHE constitute a robust theoretical foundation for the realization of multifunctional quantum materials exhibiting high valley and spin transport efficiency and low-power logical operation schemes.