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

This study predicts that strain-tunable multipiezo effects in the Janus monolayer Cr2SSe enable the selective reversal of valley polarization and a single-spin-channel anomalous valley Hall effect, offering a promising pathway for low-power, non-volatile valleytronic and spintronic devices.

The Gist

Imagine you have a tiny, magical sheet of material so thin it's only one atom thick. Scientists call this a "monolayer." In this paper, the researchers are studying a specific magical sheet made of Chromium, Sulfur, and Selenium, arranged in a special "Janus" shape (named after the two-faced Roman god). One side of the sheet is made of Sulfur, and the other is Selenium. This asymmetry is the key to all the magic.

Here is the story of what they found, explained simply:

1. The "Perfectly Balanced" Magnet

Usually, magnets have a North and a South pole. But this material is special: it is an Altermagnet. Think of it like a perfectly balanced seesaw. On one side of the seesaw, you have "spin-up" electrons (let's call them happy, red marbles), and on the other side, you have "spin-down" electrons (sad, blue marbles). Because they are perfectly balanced, the whole sheet has zero net magnetism. It doesn't stick to your fridge.

However, even though the total magnetism is zero, the individual marbles are still very organized. The red marbles like to hang out in one spot, and the blue marbles in another. This is called Spin-Valley Locking. Imagine a dance floor where the red dancers only dance on the left side, and the blue dancers only dance on the right.

2. The "Stretchy" Magic

The researchers discovered that if you stretch or squeeze this sheet (like stretching a rubber band), something amazing happens. Because the sheet is so thin and flexible, pulling it changes how the electrons behave. This is called the Multipiezo Effect. It's like a Swiss Army knife of physics: one action (stretching) triggers three different superpowers at once:

• The Piezovalley Effect (The Traffic Director):
  Normally, the red and blue dancers are equally happy on both sides of the dance floor. But when you stretch the sheet, you break the symmetry. Suddenly, the red dancers must go to the left, and the blue dancers must go to the right. You can control which side they go to just by changing the direction you pull the sheet.

  • The Cool Part: If you pull one way, the red dancers go left. If you pull the other way, they go right. It's like a light switch for electron traffic.

• The Piezoelectric Effect (The Battery):
  Because the top and bottom of the sheet are different (Janus structure), stretching it creates an electric charge, like a tiny battery. The more you stretch it, the stronger the battery gets.

• The Piezomagnetic Effect (The Magnetizer):
  Remember the perfectly balanced seesaw? When you stretch it, the balance gets slightly tipped. Suddenly, the sheet isn't perfectly balanced anymore; it becomes a weak magnet. You turned a non-magnet into a magnet just by pulling it!

3. The "Selective Reversal" Trick (The Magic Trick)

This is the most impressive part of the discovery. Usually, if you change the rules for the red dancers, the blue dancers have to change too. But in this material, the researchers found a way to change the rules for only the red dancers without touching the blue ones.

Imagine a two-story building. The red dancers live on the top floor, and the blue dancers live on the bottom. By squeezing the building just the right amount (specifically, compressing it by 2% to 3%), the red dancers decide to flip their direction and run the other way, while the blue dancers keep running in their original direction.

This is called Selective Reversal. It means scientists can control the "top floor" and "bottom floor" electrons completely independently. This is huge for making faster, smarter computer chips.

4. The "One-Way Street" Highway (Single-Spin-Channel AVHE)

Finally, because of all this stretching and flipping, the electrons start moving in a very specific way. Imagine a highway where, usually, cars of all colors mix together. But here, under the right stretch, the highway becomes a one-way street for only one color of car.

If you put a voltage on the material, only the "spin-up" electrons (the red marbles) move sideways to create a signal. The "spin-down" electrons (the blue marbles) just sit there and do nothing. This is called the Single-Spin-Channel Anomalous Valley Hall Effect.

Why Does This Matter?

Think of our current computers as busy highways with traffic jams. They use a lot of energy to move data. This new material is like a smart, self-driving highway that:

1. Uses almost no energy (low power).
2. Can be controlled by simply stretching or squeezing it (mechanical control).
3. Can sort data by "spin" (color) perfectly, creating a super-efficient flow of information.

In short, the researchers found a material that acts like a mechanical remote control for electrons. By just pulling or pushing it, we can turn on/off magnets, create electricity, and direct traffic of information with incredible precision. This could lead to the next generation of super-fast, ultra-efficient electronics that don't overheat and use very little battery power.

Technical Summary

1. Problem Statement

The field of valleytronics and spintronics seeks materials that allow for the precise control of spin and valley degrees of freedom. While two-dimensional (2D) antiferromagnets (AFMs) offer advantages like immunity to stray fields, their spin-degenerate band structures hinder the generation of spin-polarized currents. The recent discovery of altermagnetism (AM)—a magnetic order with zero net magnetization but alternating spin polarization in reciprocal space—offers a solution. However, current research faces two main limitations:

1. Integration Gap: Individual piezo-induced effects (piezovalley, piezoelectric, piezomagnetic) have been reported separately, but their simultaneous integration within a single material system remains unexplored.
2. Control Limitations: Conventional valley selection rules typically couple the valley polarization of the valence and conduction bands, preventing independent control. Furthermore, achieving a single-spin-channel transport regime (where only one spin channel contributes to transport) in AM systems is a significant challenge.

2. Methodology

The authors employed first-principles calculations based on Density Functional Theory (DFT) to investigate the Janus monolayer Cr2SSe.

• Software & Parameters: Calculations were performed using VASP with the PBE-GGA functional. Strong correlation effects of Cr 3d electrons were addressed using the DFT+U method ($U_{eff} = 3.5$ eV).
• Structural Setup: A vacuum layer of ~30 Å was used to isolate the monolayer. Structural optimization utilized a $13\times13\times1$ k-point grid.
• Stability Analysis: Dynamic stability was confirmed via phonon dispersion calculations (PHONOPY), and thermal stability was verified through ab initio molecular dynamics (AIMD) simulations at 300 K.
• Property Evaluation:
  • Electronic/Valley: Band structures were calculated with and without spin-orbit coupling (SOC). Valley polarization was quantified as the energy difference between X and Y valleys.
  • Magnetic: Net magnetization and Bader charge analysis were performed to understand magnetic moment evolution.
  • Piezoelectric: Spontaneous polarization was calculated using the Berry-phase method.
  • Transport: Berry curvature and the Anomalous Valley Hall Effect (AVHE) were computed using the Kubo formula and Maximally Localized Wannier Functions (WANNIER90).
• Strain Engineering: Uniaxial strains ranging from -4% (compressive) to +4% (tensile) were applied along orthogonal crystallographic directions ($x$ and $y$) to modulate symmetry and physical properties.

3. Key Contributions

The paper identifies Janus monolayer Cr2SSe as a versatile platform exhibiting a multipiezo effect (simultaneous piezovalley, piezoelectric, and piezomagnetic responses) driven by symmetry breaking. The primary contributions include:

• Discovery of Multipiezo Coupling: Demonstrating that a single material can concurrently exhibit tunable valley polarization, electric polarization, and net magnetization under strain.
• Selective Reversal Mechanism: Revealing a unique mechanism where compressive strain selectively reverses the valley polarization of the valence band while leaving the conduction band polarization unchanged, enabling independent band control.
• Single-Spin-Channel AVHE: Predicting a regime where strain-induced valley inversion leads to a transport state where 100% of charge carriers (regardless of doping type) utilize a single spin channel, realizing a single-spin-channel Anomalous Valley Hall Effect.

4. Key Results

A. Structural and Magnetic Stability

• Cr2SSe crystallizes in a tetragonal structure ($p4mm$) with intrinsic inversion symmetry breaking.
• It hosts an altermagnetic (AM) ground state (AFM1 configuration) with zero net magnetization, protected by diagonal mirror ($M_{xy}$) and $C_{4v}$ symmetries.
• The material is dynamically, thermally, and mechanically stable.

B. Piezovalley Effect

• Mechanism: Valley degeneracy in Cr2SSe is protected by $M_{xy}$ symmetry (C-paired valleys), not time-reversal symmetry. Uniaxial strain breaks this symmetry, lifting degeneracy.
• Performance: Under +4% tensile strain, the conduction band valley polarization reaches 57.6 meV, exceeding most reported ferrovalley materials.
• Reversibility: Applying strain along the $x$-direction vs. $y$-direction flips the sign of the valley polarization, allowing deterministic control.

C. Piezomagnetic and Piezoelectric Effects

• Piezomagnetic: Strain breaks the spin compensation between inequivalent Cr sublattices (Cr(I) and Cr(II)), inducing a weak but finite net magnetic moment (transitioning from AM to FM-like). This occurs without carrier doping.
• Piezoelectric: Due to the Janus structure, the material possesses an intrinsic spontaneous polarization of 4.13 pC/m. This value is tunable (up to 4.37 pC/m under -4% strain), indicating strong electromechanical coupling.

D. Selective Reversal of Valley Polarization

• Under compressive strains of -2% and -3%, the system exhibits a decoupled response:
  • Conduction Band: Valley polarization magnitude increases monotonically; sign remains unchanged.
  • Valence Band: Valley polarization undergoes a sign reversal between -2% and -3%.
• Origin: This is attributed to the different orbital characters: the valence band is dominated by Se $p$-orbitals (highly sensitive to strain direction), while the conduction band is dominated by Cr $d$-orbitals (intermediate sensitivity).

E. Single-Spin-Channel Anomalous Valley Hall Effect (AVHE)

• Strain breaks $M_{xy}$ symmetry, generating finite Berry curvature at the X and Y valleys.
• At -3% strain, the selective reversal of the valence band valley polarization aligns the transport channels such that both holes (in the Y valley) and electrons (in the X valley) are transported exclusively via the spin-up channel.
• This results in a single-spin-channel AVHE, where the opposite spin channel contributes negligibly, enabling highly efficient spin transport without external magnetic fields.

5. Significance

This work provides a theoretical foundation for the design of low-power, non-volatile valleytronic and spintronic devices.

• Multifunctionality: It demonstrates that a single 2D material can integrate piezovalley, piezoelectric, and piezomagnetic functionalities, offering a compact platform for multifunctional sensors and actuators.
• Independent Control: The ability to selectively reverse valley polarization in specific bands breaks conventional selection rules, allowing for complex logic operations and independent manipulation of charge carriers.
• Quantum Transport: The realization of a single-spin-channel AVHE bridges fundamental quantum transport physics with practical device applications, promising enhanced spin transport efficiency and new strategies for energy-efficient computing.