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Topological spin textures in 2D altermagnetic chromium chalcogenides: Interplay between magnetic frustration and Dzyaloshinskii-Moriya interaction

This study utilizes first-principles calculations and atomistic simulations to demonstrate that the interplay between intrinsic exchange frustration and symmetry-breaking Dzyaloshinskii-Moriya interactions in two-dimensional altermagnetic chromium chalcogenides drives the formation of diverse non-collinear topological spin textures through distinct synergistic and competitive mechanisms.

Original authors: Zirui Zhang, Shiwei Zhu, Ruixiao Ma, Qiuyao Zhang, Xiaoping Wu, Changsheng Song

Published 2026-09-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Zirui Zhang, Shiwei Zhu, Ruixiao Ma, Qiuyao Zhang, Xiaoping Wu, Changsheng Song

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

In the microscopic world of solid materials, magnetism is usually thought of as a simple tug-of-war between two opposing forces. In a standard magnet, tiny atomic spins all point in the same direction, creating a strong pull. In an antiferromagnet, they point in opposite directions, canceling each other out so the material feels no magnetic pull to the outside world. For decades, scientists believed that if you wanted to create complex, swirling patterns of magnetism—structures that could store information or carry data without electricity—you needed a material that was either strongly magnetic or had a very specific, unbalanced internal structure. However, a new class of materials called altermagnets has recently challenged this view. These materials have the zero net magnetism of an antiferromagnet but possess a hidden, momentum-dependent spin splitting that makes them behave like magnets in surprising ways. The question now is whether these unique materials can also host the intricate, swirling magnetic knots known as topological spin textures, which are prized for their stability and potential use in ultra-dense, low-power computer memory.

A team of researchers at Zhejiang Sci-Tech University has taken a deep dive into this question by studying a family of two-dimensional crystals made of chromium and various chalcogen elements like oxygen, sulfur, selenium, and tellurium. Using powerful computer simulations that model the behavior of individual atoms, they explored how these materials behave when they are just a single layer thick. They focused on two types of arrangements: a symmetric version where the top and bottom layers are identical, and an asymmetric "Janus" version where the top and bottom layers are made of different elements. The researchers found that the symmetric versions, while interesting, could not support these swirling magnetic knots on their own because their internal symmetry prevented a crucial twisting force from forming. However, the asymmetric Janus versions told a different story. By breaking the symmetry between the top and bottom layers, the researchers unlocked a powerful interaction that, when combined with the material's natural internal conflicts, created a playground for these exotic magnetic states.

The key to this discovery lies in the interplay between two competing factors inside the crystal. First, there is magnetic frustration. Imagine a group of friends trying to sit in a circle where everyone wants to sit next to someone they dislike, but the circle is too small for everyone to get their way. In these chromium crystals, the atoms want to align their spins in opposite directions with their neighbors, but the geometry of the lattice makes it impossible for everyone to be satisfied at once. This creates a state of constant tension or "frustration." Second, in the asymmetric Janus crystals, the researchers found that the heavy atoms in the bottom layer generate a twisting force, known as the Dzyaloshinskii-Moriya interaction, which tries to twist the spins into a spiral. In the symmetric crystals, this twisting force is forbidden by the material's mirror-like symmetry, but in the Janus crystals, the broken symmetry allows it to emerge.

When the researchers simulated the behavior of these Janus crystals, they discovered that the tension from the frustration and the twist from the interaction worked together to stabilize a variety of magnetic shapes that would otherwise be impossible. Depending on the specific combination of elements used, the material settled into different patterns. Some configurations formed clusters of magnetic knots, while others stretched into chains or isolated single knots. The researchers found that the type of pattern that formed depended on a delicate balance. In materials where the internal tension was the strongest force, the magnetic spins formed complex, high-complexity knots with many twists. In materials where the twisting force was stronger, the spins settled into simpler, single knots.

What makes this finding particularly significant is that the researchers identified two distinct ways these forces interact. In one scenario, the internal tension actually helps the twisting force by making it easier for the magnetic knots to form, effectively lowering the threshold needed to create them. In another scenario, the two forces compete directly: the tension pushes the system toward complex, multi-twisted knots, while the twisting force pushes it toward simple, single-twist knots. This competition allows scientists to tune the material's behavior simply by changing the chemical ingredients. For instance, by swapping a lighter element for a heavier one, they could shift the balance from a state of high complexity to a state of simple, robust knots. The simulations also showed that these knots are remarkably stable, with energy barriers that prevent them from unraveling easily, suggesting they could survive in real-world conditions.

The study confirms that these two-dimensional chromium crystals are a versatile platform for exploring how magnetic forces compete and cooperate. The researchers showed that by breaking the symmetry of the crystal layers, they could activate the necessary twisting forces to create these topological textures without needing an external magnetic field to hold them in place. This is a crucial step forward, as most magnetic storage devices currently require external fields to write data, which consumes energy and limits how small the devices can be. By demonstrating that these complex magnetic structures can exist naturally in a zero-field environment, the work opens the door to designing new types of magnetic memory that are both denser and more energy-efficient. The findings provide a clear roadmap for future experiments, suggesting that by carefully selecting the chemical composition of these Janus crystals, engineers can design materials with specific magnetic textures tailored for next-generation spintronic devices.

Technical Summary: Topological Spin Textures in 2D Altermagnetic Chromium Chalcogenides

Problem Statement
While altermagnetism (AM) has recently been established as a distinct magnetic paradigm characterized by zero net magnetization and momentum-dependent spin splitting, the exploration of topological spin textures (such as skyrmions and bimerons) within two-dimensional (2D) altermagnetic backgrounds remains limited. In conventional magnetic systems, the formation of such textures is typically governed by the interplay between magnetic frustration and the Dzyaloshinskii-Moriya interaction (DMI). However, previous studies have largely treated these mechanisms separately, and the specific interplay governing topological states in emerging altermagnetic phases is poorly understood. Specifically, symmetric 2D chromium chalcogenides ( $Cr_2X_2$ ) possess intrinsic exchange frustration but lack the necessary symmetry breaking to support net in-plane DMI, limiting the stabilization of chiral textures. The central question addressed is whether and how the interplay between exchange frustration and a tunable in-plane DMI can stabilize topological spin textures in 2D altermagnets, particularly in asymmetric Janus configurations ( $Cr_2XY$ ).

Methodology
The study employs a combined approach of first-principles calculations and atomistic spin-model simulations:

First-Principles Calculations: Density Functional Theory (DFT) calculations were performed using the VASP package with the PBE functional and GGA+U ( $U=3.5$ eV for Cr 3d electrons). Structural optimization, electronic band structure analysis, and phonon spectrum calculations (via PHONOPY) were conducted to assess lattice stability and dynamical properties.
Spin-Hamiltonian Parameterization: Magnetic interaction parameters, including Heisenberg exchange constants ( $J_1, J_2, J'_2, J_3$ ), DMI vectors ( $D_{\parallel}, D_{\perp}$ ), and single-ion anisotropy ( $K$ ), were extracted from DFT total-energy differences between collinear and non-collinear spin configurations.
Atomistic Spin Simulations: Equilibrium spin configurations under zero external magnetic field were obtained by solving the Landau–Lifshitz–Gilbert (LLG) equation using the SPIRIT code.
Phase Space Analysis: Systematic scans of the frustration parameters ( $\eta_1, \eta_2$ ) versus in-plane DMI ( $D_{\parallel}$ ) were performed to map phase diagrams. The Geodesic Nudged Elastic Band (GNEB) method was utilized to calculate minimum-energy paths and energy barriers for the collapse of topological textures into the uniform altermagnetic ground state.

Key Contributions and Results
The authors investigated monolayer $Cr_2X_2$ (symmetric) and Janus $Cr_2XY$ (asymmetric) altermagnets ( $X, Y = O, S, Se, Te$ ).

Structural and Magnetic Properties:
- Symmetric $Cr_2X_2$ monolayers retain out-of-plane mirror symmetry ( $M_z$ ), forbidding net in-plane DMI ( $D_{\parallel} = 0$ ).
- Janus $Cr_2XY$ monolayers break $M_z$ , activating a substantial in-plane DMI mediated by the strong spin-orbit coupling (SOC) of heavy chalcogen ligands (Fert-Levy mechanism).
- Both systems exhibit strong intrinsic exchange frustration arising from the competition between nearest-neighbor ( $J_1$ ) and further-neighbor ( $J_2, J_3$ ) antiferromagnetic (AFM) interactions, described by a frustrated square-lattice $J_1-J_2-J_3$ model.
- Néel temperatures ( $T_N$ ) range from 70 K to 161 K, with dynamical stability confirmed for most materials (except Janus $Cr_2TeO$ , which shows soft phonon modes due to extreme structural distortion).
Topological Spin Textures:
- In symmetric $Cr_2X_2$ , exchange frustration alone is insufficient to stabilize non-collinear states; the systems remain in collinear AFM states.
- In Janus $Cr_2XY$ , the interplay between frustration and $D_{\parallel}$ stabilizes diverse non-collinear chiral structures, including bimeron clusters, bimeron chains, isolated skyrmions ( $Q=1$ ), and labyrinthine stripe domains.
- The specific texture depends on the balance between frustration, $D_{\parallel}$ , and magnetic anisotropy ( $K$ ). For instance, high-Q bimeron clusters are stabilized in systems with strong frustration and weak $D_{\parallel}$ , while isolated $Q=1$ skyrmions appear in systems with strong $D_{\parallel}$ and out-of-plane anisotropy.
Mechanisms of Interplay:
The study identifies two distinct mechanisms governing the frustration-DMI interplay:
- Synergistic Effect: Exchange frustration "softens" the collinear altermagnetic order, thereby lowering the critical $D_{\parallel}$ threshold required to initiate the formation of topological spin configurations.
- Competitive Effect: Frustration and $D_{\parallel}$ favor different topological charges. Frustration promotes high-topological-charge (high- $Q$ ) states (e.g., bimeron clusters, $Q=3$ skyrmions), whereas $D_{\parallel}$ favors low-charge states (e.g., isolated $Q=1$ skyrmions).
- Energy Barriers: GNEB calculations reveal that the stability of high- $Q$ bimerons is primarily governed by exchange frustration, while the stability of $Q=1$ skyrmions is dominated by the DMI energy contribution.

Significance
The paper establishes a general framework for understanding the interplay between magnetic frustration and DMI in 2D altermagnets. By demonstrating that the Janus configuration $Cr_2XY$ provides a platform where strong exchange frustration and tunable in-plane DMI coexist, the work identifies these materials as versatile candidates for realizing field-free topological spin textures. The findings suggest that the frustration-DMI balance can be used as a tuning handle to control the topological charge and morphology of spin textures, offering a pathway for designing next-generation spintronic devices based on altermagnetic materials. The study clarifies that in altermagnets, frustration arises from same-sign AFM competition rather than conventional ferro-antiferro competition, and that the symmetry breaking in Janus structures is the key to activating the DMI necessary for chiral textures.

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