Robust $d$-wave altermagnetism in $\mathrm{RbCr_2Se_2O}$

Abstract: The $\mathrm{KV_2Se_2O}$, $\mathrm{Rb_{1-δ}V_2Te_2O}$ and $\mathrm{Cs_{1-δ}V_2Te_2O}$ are experimentally confirmed to adopt either C-type or G-type antiferromagnetic configuration, corresponding to apparent or hidden altermagnetism. However, their nearly degenerate energies lead to inconsistent experimental assignments between the two antiferromagnetic configurations. Here, we predict that the experimentally synthesized $\mathrm{RbCr_2Se_2O}$ is a robust $d$-wave altermagnetic metal, since the energy difference between C-type and G-type configurations is large, which is independent of electron correlation strength and van der Waals interaction. Upon applying in-plane uniaxial strain, $\mathrm{RbCr_2Se_2O}$ can generate a net total magnetic moment via a direct piezomagnetic effect, which is distinct from semiconductor that typically requires carrier doping in addition to strain. This provides an experimental strategy for distinguishing the G-type antiferromagnetic configuration, in which the total magnetic moment remains zero under uniaxial strain. Our work presents an isostructural $d$-wave altermagnetic $\mathrm{RbCr_2Se_2O}$ analogous to $\mathrm{KV_2Se_2O}$, $\mathrm{Rb_{1-δ}V_2Te_2O}$ and $\mathrm{Cs_{1-δ}V_2Te_2O}$, which can facilitate further experimental verification. Furthermore, these results are universal across materials of this family $\mathrm{XCr_2Y_2O}$ (X=K, Rb, Cs; Y=S,Se, Te), thus expanding the family of altermagnets.

• The paper establishes RbCr₂Se₂O as a robust d-wave altermagnet by revealing a significant energy gap between C-type and G-type AFM configurations.
• It employs DFT calculations with Hubbard U corrections and van der Waals interactions to uncover strain-tunable piezomagnetic effects and distinct spin-resolved band structures.
• The study extends these findings to the XCr₂Y₂O family, indicating potential spintronic applications through symmetry-protected spin splitting.

Robust $d$-Wave Altermagnetism in $\mathrm{RbCr_2Se_2O}$

Introduction

This paper investigates $\mathrm{RbCr_2Se_2O}$ as a model system for robust $d$-wave altermagnetism, a class of magnetism that supports spin-split electronic bands without net magnetization or spin-orbit coupling, yet permits compensated collinear order. The work distinguishes the material from earlier quasi-two-dimensional candidates such as $\mathrm{KV_2Se_2O}$, $\mathrm{Rb_{1-\delta}V_2Te_2O}$, and $\mathrm{Cs_{1-\delta}V_2Te_2O}$, which display near-degeneracy between C-type and G-type AFM configurations. In contrast, $\mathrm{RbCr_2Se_2O}$ exhibits a substantial energy gap between these configurations, conferring robust, unambiguous $d$-wave altermagnetic order. This distinction is validated across a family of isostructural compounds $\mathrm{XCr_2Y_2O}$ (X=K, Rb, Cs; Y=S, Se, Te), extending the relevance of the findings.

Materials, Magnetic Structures, and Methodology

$\mathrm{RbCr_2Se_2O}$0 is crystallographically analogous to other known $\mathrm{RbCr_2Se_2O}$1-wave altermagnetic materials, adopting the $\mathrm{RbCr_2Se_2O}$2 space group and a layered structure of Rb and $\mathrm{RbCr_2Se_2O}$3 stacks.

Figure 1: The crystal structure, four magnetic configurations (F-, A-, C-, G-type), relative energies versus $\mathrm{RbCr_2Se_2O}$4, and C-type AFM band structures for $\mathrm{RbCr_2Se_2O}$5.

The paper considers four primary magnetic configurations:

• F-type: FM intralayer, FM interlayer,
• A-type: FM intralayer, AFM interlayer,
• C-type: AFM intralayer, FM interlayer (apparent altermagnetic),
• G-type: AFM intralayer, AFM interlayer (hidden altermagnetic).

The interplay of crystal and spin symmetries ($\mathrm{RbCr_2Se_2O}$6 with $\mathrm{RbCr_2Se_2O}$7) dictates distinct electronic characteristics. Density functional theory calculations are performed with Hubbard $\mathrm{RbCr_2Se_2O}$8 corrections and van der Waals interactions, ensuring robust determination of the electronic and magnetic ground state.

Ground-State Magnetism and Electronic Structure

The C-type configuration emerges as the ground state of $\mathrm{RbCr_2Se_2O}$9, with a pronounced energy separation from G-type—an essential result, as in prior vanadium-based systems these energies are nearly degenerate. This large energy difference, maintained across all reasonable $\mathrm{RbCr_2Se_2O}$0 values and when including van der Waals corrections, eliminates ambiguity in experimental assignments of the microscopic magnetic order.

The calculated electronic band structure in the C-type phase manifests $\mathrm{RbCr_2Se_2O}$1-wave altermagnetism, characterized by spin degeneracy along the $\mathrm{RbCr_2Se_2O}$2-M line and alternating spin splittings along the M-Y-$\mathrm{RbCr_2Se_2O}$3 and M-X-$\mathrm{RbCr_2Se_2O}$4 directions.

Figure 2: Spin-resolved band projections onto sectors A and B of the $\mathrm{RbCr_2Se_2O}$5 layers in the C-type configuration, without uniaxial strain.

Projections onto individual layers (sectors A and B) confirm equivalent spin textures, validating that net moments are absent but local spin-polarized transport is symmetry-allowed. In contrast, the G-type configuration retains $\mathrm{RbCr_2Se_2O}$6 symmetry with compensated and locally split states.

Strain-Tunable Magnetoelectronic Response

A key result is the direct piezomagnetic effect realized under in-plane uniaxial strain. Application of strain along the $\mathrm{RbCr_2Se_2O}$7-axis induces a net magnetic moment exclusively in the C-type configuration, transitioning the system from altermagnetic to ferrimagnetic with an $\mathrm{RbCr_2Se_2O}$8-wave symmetry component in the spin-split bands.

Figure 3: Energy band structure evolution in C-type $\mathrm{RbCr_2Se_2O}$9 for varying uniaxial strain ($d$0).

Figure 4: G-type energy relative to C-type as function of $d$1 and the total magnetic moment versus strain for both C- and G-types.

The system supports a measurable magnetic moment up to $d$2 per formula unit at $d$3, with a nearly linear strain response. In contrast, the G-type configuration remains robustly compensated with zero net moment for all strains, demonstrating the discriminative power of combined transport and magnetization measurements under strain.

Extension to the $d$4 Family

Comprehensive calculations are repeated for isostructural compounds $d$5, $d$6, $d$7, $d$8, $d$9, $\mathrm{KV_2Se_2O}$0, $\mathrm{KV_2Se_2O}$1, and $\mathrm{KV_2Se_2O}$2. Across this series, the C-type phase maintains the lowest energy, and the corresponding $\mathrm{KV_2Se_2O}$3-wave spin-splitting patterns in the band structures are consistently observed.

Figure 5: Magnetic energies versus $\mathrm{KV_2Se_2O}$4 and strain dependence of net magnetic moment for the broader $\mathrm{KV_2Se_2O}$5 series.

Figure 6: Band structures with C-type configuration for the nine $\mathrm{KV_2Se_2O}$6 compounds, consistently exhibiting $\mathrm{KV_2Se_2O}$7-wave spin splitting.

All variants display significant net piezomagnetic moments under in-plane strain, suggesting experimental generality of these responses.

Experimental and Theoretical Implications

The existence of a robust energy gap between C-type and G-type configurations in $\mathrm{KV_2Se_2O}$8 enables unambiguous assignment of magnetic ground states in experimental settings, overcoming the difficulties of near degenerate states and domain averaging. The direct piezomagnetic effect does not require carrier doping, in contrast to semiconductor piezomagnetism, facilitating clear discrimination between apparent and hidden altermagnetic orders. The $\mathrm{KV_2Se_2O}$9-wave altermagnetic states offer symmetry-protected spin splitting ideal for spintronic application, and strain engineering provides a viable route for tunable spin transport phenomena.

Theoretically, the findings reinforce the generality of altermagnetic order beyond vanadium-based compounds and delineate the symmetry constraints that enable observable, controllable spin physics even in net-compensated antiferromagnets.

Conclusion

The paper establishes $\mathrm{Rb_{1-\delta}V_2Te_2O}$0 as a robust $\mathrm{Rb_{1-\delta}V_2Te_2O}$1-wave altermagnet, distinguished by a sizable and $\mathrm{Rb_{1-\delta}V_2Te_2O}$2-independent energetic preference for the C-type AFM configuration, strong symmetry-protected spin splitting, and a strain-tunable piezomagnetic response. The extension to the $\mathrm{Rb_{1-\delta}V_2Te_2O}$3 class points to a broad family of materials poised for experimental exploration and exploitation in spintronic technology. The approach for distinguishing apparent and hidden altermagnetic states via strain-induced magnetization provides a practical diagnostic tool relevant to both fundamental magnetism and device applications. Future research may focus on the experimental realization of predicted phenomena, interface engineering for device integration, and investigation of coupled electronic and lattice dynamics in the altermagnetic state.