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Interplay of Altermagnetism and Coupled Quasi-Altermagnetic states in Sliding Two-dimensional Square Lattice

This paper proposes a new classification of altermagnetic states in two-dimensional square lattices, identifying a distinct "coupled quasi-altermagnetic" phase where interlayer sliding controls reversible non-relativistic spin splitting, and demonstrates this mechanism using Mn2WS4 and its Janus derivative Mn2WS2Se2.

Original authors: Bhautik R Dhori, Deepak Upadhyay, Prafulla K Jha

Published 2026-06-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Bhautik R Dhori, Deepak Upadhyay, Prafulla K Jha

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a dance floor where two groups of dancers (representing electrons with "up" and "down" spins) are moving in perfect opposition. Usually, in a standard magnetic dance, one group dominates, creating a net magnetic pull. But in antiferromagnets, these two groups are perfectly balanced; for every dancer spinning up, there is one spinning down, canceling each other out so the whole floor has zero net magnetism.

For a long time, scientists thought these balanced dancers moved in lockstep, meaning their energy levels were identical. However, a new discovery called Altermagnetism changed the script. It showed that even without a net magnetic pull, these dancers can still have different energy levels depending on where they are on the dance floor (their position in the crystal lattice). It's like having two groups of dancers who are perfectly balanced in number, but one group is dancing a fast waltz while the other dances a slow tango, depending on which corner of the room they are in.

The New Discovery: "Quasi-Altermagnetism"

This paper introduces a new, slightly different version of this dance called Quasi-Altermagnetism.

Think of the dance floor as a sliding glass door.

The Standard Dance (Altermagnetism): If you slide the top layer of the floor exactly on top of the bottom layer (or slide it diagonally to a specific spot), the two groups of dancers remain perfectly balanced and connected by symmetry. They are "Altermagnetic."
The New Dance (Quasi-Altermagnetism): If you slide the top layer just a tiny bit off that perfect spot (specifically, sliding it halfway along one direction but not the other), the perfect symmetry breaks. The two groups of dancers are no longer mirror images of each other in the same way. They are still balanced in total number (zero net magnetism), but they have lost their "twin" connection. This is the Quasi-Altermagnetic state.

The Magic of Sliding

The researchers found that by simply sliding one layer of a 2D material over another (like shifting a rug on a floor), you can switch the material back and forth between these two states:

Altermagnetic: The "perfectly balanced but different" state.
Quasi-Altermagnetic: The "slightly unbalanced but still zero-net" state.

This sliding acts like a switch. When you slide the layers into the "Quasi" position, something special happens: the energy levels of the dancers split apart right in the center of the room (the $\Gamma$ point), even without any external magnetic forces or relativistic effects. In the standard "Altermagnetic" state, this center point usually remains a neutral meeting place where the dancers overlap. In the "Quasi" state, they are forced apart.

The Real-World Example: The Mn2WS4 Material

To prove this, the scientists looked at a specific material made of Manganese, Tungsten, and Sulfur (Mn2WS4), which forms a square grid.

They built a model of this material as a two-layer sandwich.
They simulated sliding the top layer.
Result: When they slid it to the "AC1" or "AC2" positions (the specific off-center slides), the material turned into a Quasi-Altermagnet. The electrons at the center of the energy map split apart, creating a distinct "spin-split" signature that didn't exist before.

The "Janus" Twist

The researchers also looked at a cousin of this material, Mn2WS2Se2, where some sulfur atoms were swapped for Selenium. This created a "Janus" structure (named after the two-faced Roman god), where the top and bottom of the material are chemically different.

They found that this chemical change also breaks the symmetry, creating similar "Quasi-Altermagnetic" effects.
Just like sliding the layers, changing the chemical makeup of the local environment can force the material into this new state.

Why Does This Matter? (According to the Paper)

The paper suggests these states are crucial for spintronics (electronics that use electron spin instead of just charge).

The Switch: Because you can slide the layers to switch between these states, you can control how electrons move.
The Hall Effect: The researchers found that when they applied an electric field, the "Quasi" states created a strange, one-way traffic jam for electrons (called the Anomalous Hall Effect). In one sliding position, the traffic jam went one way; in the other, it went the opposite way.
The Device: They proposed a device that acts like a tunnel. If the layers on both sides are in the same "Quasi" state, electrons flow easily (low resistance). If one side is in a different state, the flow is blocked (high resistance). This creates a switch controlled by sliding, not by magnets.

Summary Analogy

Imagine a two-story building where the floors are made of magnetic tiles.

Normal Magnet: One floor is all North, the other all South.
Antiferromagnet: Every North tile on the top floor is directly above a South tile on the bottom. They cancel out.
Altermagnet: The tiles are still North/South balanced, but the "North" tiles on the top floor are dancing differently than the "South" tiles on the bottom, creating a split in their energy.
Quasi-Altermagnet (This Paper): You slide the top floor just enough so the North tiles are no longer directly above the South tiles. They are still balanced in total, but the "dance" is now completely different and unique to that specific slide. This slide creates a new, controllable way to split the energy of the electrons, offering a new way to build switches for future computers.

Technical Summary: Interplay of Altermagnetism and Coupled Quasi-Altermagnetic States in Sliding Two-dimensional Square Lattice

Problem Statement
While the emergence of non-relativistic spin splitting (NRSS) in altermagnets (AMs) has established a new paradigm for antiferromagnets with vanishing net magnetization, a comprehensive classification of sliding-induced phases in two-dimensional (2D) systems remains lacking. Recent demonstrations of sliding-induced valley-polarized phases in 2D altermagnets represent only a partial manifestation of altermagnetism. Specifically, there is no established framework to distinguish between standard altermagnetic states and other sliding-induced phases that exhibit spin splitting but lack the strict symmetry requirements of traditional AMs. Furthermore, the direct correspondence between reciprocal-space spin splitting and real-space magnetic configuration switching in these systems requires systematic exploration.

Methodology
The authors employ a multi-faceted approach combining first-principles calculations, general stacking theory, and spin-Laue symmetry analysis:

Computational Framework: Calculations were performed using Density Functional Theory (DFT) within the Vienna ab initio simulation package (VASP) using the Projector Augmented-Wave (PAW) method and the PBE-GGA functional. To account for strong correlations in Mn-3d electrons, the DFT+U approach was utilized with $U = 3.0$ eV.
Symmetry Analysis: Spin-group symmetries $[R_i || R_j]$ were analyzed to characterize the magnetic order. The study distinguishes between systems where opposite-spin sublattices are connected by symmetry operations (preserving spin degeneracy at the $\Gamma$ point) and those where such connections are broken.
Model Systems: The study investigates a 2D square Lieb-lattice model and applies it to specific materials: monolayer and bilayer Mn $_2$ WS $_4$ and its Janus derivative Mn $_2$ WS $_2$ Se $_2$ .
Transport Properties: Anomalous Hall Conductivity (AHC) was calculated using the Kubo formalism by integrating Berry curvature over occupied bands, including spin-orbit coupling (SOC) effects.

Key Contributions and Classification
The primary contribution of this work is the proposal and classification of a distinct subclass of altermagnetism termed "coupled quasi-altermagnetic states." The authors classify sliding-induced phases into two categories:

Altermagnetic States: These include monolayers and specific bilayer stackings (AA and AB) where the system preserves specific symmetries (e.g., $[C_2 || M_\phi]$ ) that connect opposite-spin sublattices. In these states, spin degeneracy at the high-symmetry $\Gamma$ point is preserved in the absence of SOC.
Quasi-Altermagnetic States: These arise in specific sliding configurations (AC1 and AC2) where interlayer translation breaks the symmetry operations connecting opposite-spin sublattices (specifically the $G-H$ set becomes empty). Crucially, these states exhibit Type-IV NRSS, characterized by the lifting of spin degeneracy at the $\Gamma$ point even without SOC.

The authors establish that these two quasi-altermagnetic states (AC1 and AC2) are "coupled" via a real-space symmetry operation $[C_2 || M]$ , which induces simultaneous spin and valley reversal. This creates a direct correspondence between the real-space sliding configuration and the reciprocal-space spin splitting pattern.

Results

Symmetry and Band Structure: In Mn $_2$ WS $_4$ , AA and AB bilayers retain altermagnetic characteristics with degenerate $\Gamma$ points. In contrast, AC1 and AC2 configurations (generated by sliding along $(1/2, 0)$ and $(0, 1/2)$ ) break the $M_\phi$ symmetry. This results in finite spin splitting at the $\Gamma$ point without SOC, distinguishing them from standard AMs.
Structural Origin: Structural analysis reveals that the lifting of degeneracy in quasi-altermagnetic states correlates with a volume disproportionation between the tetrahedra formed by up-spin and down-spin Mn atoms ( $\Delta V \approx 3 \times 10^{-3}$ Å $^3$ ). This local structural asymmetry breaks the equivalence of the magnetic sublattices.
Transport Signatures:
- In AA and AB configurations, Berry curvature is symmetric and opposite at X and X' valleys, leading to a valley Hall effect (VHE) but zero net Anomalous Hall Conductivity (AHC) near band edges.
- In AC1 and AC2 configurations, the breaking of symmetry leads to asymmetric Berry curvature distributions. This results in a non-zero, sign-reversible AHC. Under hole doping, an in-plane electric field drives spin-up holes in AC1 and spin-down holes in AC2 to opposite sample edges, generating transverse Hall voltages of opposite signs.
Janus Derivatives: The study extends these findings to Mn $_2$ WS $_2$ Se $_2$ . The Type-II Janus phase (altermagnetic) supports similar sliding-induced transitions between altermagnetic and quasi-altermagnetic states, confirming the mechanism's applicability to materials with modified local environments.
Device Concept: The reversible switching between AC1 and AC2 states suggests a mechanism for sliding-controlled tunneling magnetoresistance (TMR). A device architecture using hole-doped AC1/AC2 electrodes separated by an AA barrier could exhibit low-resistance (parallel) and high-resistance (antiparallel) states based on the alignment of spin and valley degrees of freedom.

Significance
The paper claims to uncover a sliding-induced interplay between altermagnetic and quasi-altermagnetic phases, revealing their crucial role in controlling spin degeneracy at the Brillouin-zone center ( $\Gamma$ point). By establishing a classification framework based on spin-splitting characteristics and symmetry analysis, the study provides a theoretical basis for understanding reversible Type-IV NRSS. The authors posit that these findings pave the way for future spintronic technologies that utilize interlayer sliding to manipulate spin and valley degrees of freedom without relying on external magnetic fields or intrinsic electric polarization. The mechanism is presented as broadly applicable to a wide class of 2D square-lattice systems.