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arxiv: 2510.07771 · v2 · submitted 2025-10-09 · ❄️ cond-mat.mtrl-sci · physics.comp-ph

Dimension- and Facet-Dependent Altermagnetic Biferroics and Ferromagnetic Biferroics and Triferroics in CrSb

Long Zhang , Guoying Gao This is my paper

Pith reviewed 2026-05-18 09:28 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.comp-ph
keywords CrSbaltermagnetismtriferroicsmultiferroicsfirst-principles calculationsfacet engineeringspintronicsphase engineering
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The pith

CrSb in wurtzite phase on (110) facets forms triferroics where ferroelectric and ferroelastic switching reverses altermagnetic spin splitting.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors examine CrSb across NiAs, MnP, wurtzite, zincblende, and rocksalt phases to determine how lower dimensions and specific surface facets alter its magnetic, electric, and elastic orders. They predict that MnP-phase material is altermagnetic with stability close to the known NiAs phase, while certain facets combine altermagnetism or ferromagnetism with ferroelectric and ferroelastic orders. A key result is that wurtzite (110) surfaces act as triferroics with energy barriers low enough for switching to reverse the direction of altermagnetic spin splitting in antiferromagnetic cases without losing high spin polarization in ferromagnetic cases. Readers would care because this suggests a route to control spin textures using electric fields or strain instead of external magnets. The work also shows that magnetic anisotropy can be switched between uniaxial and in-plane forms by changing phase or facet.

Core claim

The paper identifies the wurtzite-phase (110) facets of CrSb as FM/AM-FE-FC triferroics with moderate energy barriers of 0.129 eV atom-1 for ferroelectric switching and 0.363 eV atom-1 for ferroelastic switching. Both switching processes reverse the altermagnetic spin splitting in antiferromagnetic configurations while preserving high spin polarization in ferromagnetic states. NiAs- and MnP-phase (110) facets are altermagnetic-ferroelastic biferroics, and wurtzite bulk and (001) facets host ferromagnetic or altermagnetic-ferroelectric biferroics. Magnetic anisotropy is tunable between uniaxial and in-plane depending on phase, dimension, and facet.

What carries the argument

Polymorphic phase selection and facet orientation in CrSb that couples altermagnetism or ferromagnetism with ferroelectric and ferroelastic orders, with the wurtzite (110) surface serving as the triferroic example.

If this is right

  • Ferroelectric switching reverses the direction of altermagnetic spin splitting in antiferromagnetic states.
  • Ferroelastic switching produces the same reversal of spin splitting without destroying ferromagnetic spin polarization.
  • Magnetic anisotropy switches between uniaxial and in-plane forms when phase or facet is changed.
  • This polymorphic and facet-based approach supplies a general route to multifunctional spintronic materials.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same phase-and-facet engineering could be tried in other transition-metal pnictides to find additional altermagnetic triferroics.
  • Device integration might allow electric or strain control of spin currents in heterostructures without external magnets.
  • Room-temperature stability of the switched states would need separate checks because the reported barriers are moderate.

Load-bearing premise

First-principles calculations give the correct relative stability among the NiAs, MnP, and wurtzite phases of CrSb and reliable energy barriers for ferroelectric and ferroelastic switching without large errors from the choice of exchange-correlation functional or from ignoring temperature and defect effects.

What would settle it

Experimental measurement showing that an applied electric field or uniaxial strain on wurtzite CrSb (110) films reverses the sign of momentum-dependent spin splitting while keeping high spin polarization in the ferromagnetic configuration.

Figures

Figures reproduced from arXiv: 2510.07771 by Guoying Gao, Long Zhang.

Figure 1
Figure 1. Figure 1: Crystal structures of bulk CrSb in the NiAs (a), wurtzite (WZ) (b), zincblende (ZB) (c), rocksalt (RS) (d), and MnP (e) phases. Relative energies of the antiferromagnetic (AFM) and ferromagnetic (FM) states, referenced to the AFM state of the MnP phase (f). Schematic diagram of high-symmetry points within Brillouin zone for NiAs and WZ (g), ZB and RS (h), and MnP (i) phases [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 2
Figure 2. Figure 2: Atomic magnetic moments of Cr in CrSb with different phases in magnetic ground states (a). The total (b), atom-resolved (c), and Sb-orbital-resolved (d-i) magnetic anisotropy energy differences (ΔEAs), presented as the energy difference relative to the state with magnetization along z-direction [PITH_FULL_IMAGE:figures/full_fig_p026_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Spin-resolved band structures of bulk CrSb with the NiAs (a), WZ (b), ZB (c), RS (d), and MnP (e) phases [PITH_FULL_IMAGE:figures/full_fig_p027_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Ferroelectric (FE) switching with atomic displacement paths (a) and energy barrier for the FE transition (b) in bulk WZ-phase CrSb. Spin-resolved and Cr-contributed band structures for the FM (c-e) and AFM (f-h) configurations with the polar (P, -P) and non-polar (P0) states [PITH_FULL_IMAGE:figures/full_fig_p028_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Crystal structures of 2D CrSb (001) facets in NiAs, WZ, and MnP phases with varying atomic-layer thicknesses (a-c), relative energies (ΔEs) of AFM and FM states (d-f), and magnetic anisotropic energies (ΔEAs) with reference to the state with magnetization axes along z-direction (g-i) [PITH_FULL_IMAGE:figures/full_fig_p029_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Atomic magnetic moments of Cr in CrSb (001) facet with varying atomic-layer thicknesses in the NiAs (a), WZ (b), and MnP (c) phases, and the corresponding spin-resolved band structures (d-f) [PITH_FULL_IMAGE:figures/full_fig_p030_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FE switching with atomic displacement paths (a) and energy barrier for the FE transition (b) in WZ-phase CrSb (001) facet with four atomic layers. Spin-resolved and Cr-contributed band structures for the FM (c-e) and AFM (f-h) configurations in the polar (P, -P) and non-polar (P0) states. [PITH_FULL_IMAGE:figures/full_fig_p031_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Crystal structures of 2D CrSb (110) facets with varying atomic-layer thicknesses (a-c), the relative energies of AFM and FM states (d-f), and magnetic anisotropic energies (ΔEAs) with reference to the state with magnetization axe along z-direction (g-i) for the NiAs, WZ, and MnP phases [PITH_FULL_IMAGE:figures/full_fig_p032_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Atomic magnetic moments of Cr in CrSb (110) facet with varying atomic-layer thicknesses in the NiAs (a), WZ (b), and MnP (c) phases, and the corresponding spin-resolved band structures [PITH_FULL_IMAGE:figures/full_fig_p033_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FE switching with atomic displacement paths (a) and energy barrier for the FE transition (b) for the WZ-phase CrSb (110) facet with one atomic layer. Spin-resolved and Cr-contributed band structures for the FM (c-e) and AFM (f-h) configurations in the polar (P, -P) and non-polar (P0) states [PITH_FULL_IMAGE:figures/full_fig_p034_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Ferroelastic (FC) switching with atomic displacement paths (a) and energy barrier for the FC transition (b) in the WZ-phase CrSb (110) facet with one atomic layer. Spin-resolved and Cr-contributed band structures for the FM (c-e) and AFM (f-h) configurations in the FC (F1, F2) and intermediate (F0) states [PITH_FULL_IMAGE:figures/full_fig_p035_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Schematic illustrations of the dimension- and facet-dependent biferroics and triferroics (a), and the manipulation of spin splitting via FE/FC switching in triferroic/biferroic CrSb (b) [PITH_FULL_IMAGE:figures/full_fig_p036_12.png] view at source ↗
read the original abstract

Altermagnets have recently garnered significant interest due to their vanishing net magnetic moment and non-relativistic momentum-dependent spin splitting. However, altermagnetic (AM) multiferroics especially triferroics remain scarce. We investigate the experimentally synthesized non-van der Waals CrSb as a model system to explore the effects of dimensionality and facet orientation on its ferroic properties. NiAs, MnP, wurtzite (WZ), zincblende (ZB), and rocksalt (RS) phases are considered. Using first-principles calculations, we predict the altermagnetism of CrSb in MnP phase which has comparable stability with experimental NiAs phase. Both NiAs- and MnP-phase (110) facets exhibit AM-ferroelastic (FC) biferroics, while the WZ-phase bulk and (001) facets host ferromagnetic (FM) or AM-ferroelectric (FE) biferroics. Notably, the WZ-phase (110) facets are identified as FM/AM-FE-FC triferroics, with moderate energy barriers of 0.129 and 0.363 eV atom-1 for FE and FC switching, respectively. Both FE and FC switching can reverse the AM spin splitting in antiferromagnetic (AFM) configurations while preserving the high spin polarization in FM states. The magnetic anisotropy is highly tunable, exhibiting either uniaxial or in-plane behavior depending on the phase, dimension, and facet. This work establishes a framework for designing AM multiferroics through polymorphic, dimensional, and facet engineering, offering promising avenues for multifunctional spintronic applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates CrSb across NiAs, MnP, wurtzite (WZ), zincblende, and rocksalt phases using first-principles calculations, focusing on dimensionality and facet effects. It predicts altermagnetism in the MnP phase (comparable in stability to the experimental NiAs phase), identifies AM-FC biferroics in NiAs- and MnP-phase (110) facets, FM or AM-FE biferroics in WZ bulk and (001) facets, and FM/AM-FE-FC triferroics in WZ-phase (110) facets with reported switching barriers of 0.129 eV/atom (FE) and 0.363 eV/atom (FC). These switching processes are claimed to reverse AM spin splitting in AFM configurations while preserving high spin polarization in FM states, with highly tunable magnetic anisotropy.

Significance. If the quantitative DFT results hold, the work provides a concrete framework for realizing altermagnetic multiferroics and triferroics in a non-van-der-Waals material via polymorphic, dimensional, and facet engineering. The identification of moderate-barrier switching that couples to spin splitting is potentially useful for spintronic applications, and the explicit prediction of facet-specific triferroic behavior adds a new design handle beyond bulk symmetry arguments.

major comments (2)
  1. [Abstract and switching-barrier results] The central claim that WZ-phase (110) facets constitute FM/AM-FE-FC triferroics with 'moderate' and 'feasible' switching rests on the reported barriers of 0.129 eV atom^{-1} (FE) and 0.363 eV atom^{-1} (FC). No information is given on the exchange-correlation functional, k-point sampling, slab thickness, or vacuum spacing used for these facet calculations; because these quantities are known to shift barriers by several hundred meV/atom, the 'moderate' qualifier and the practical-promising assessment cannot be evaluated without this data.
  2. [Phase-stability discussion] The assertion that the MnP phase has 'comparable stability with experimental NiAs phase' and hosts altermagnetism is load-bearing for the broader claim of phase-tunable AM multiferroics, yet the manuscript provides neither the computed energy difference per atom nor convergence tests that would confirm the ordering is robust to functional choice or cell-size effects.
minor comments (2)
  1. [Notation and terminology] Define all acronyms (AM, FM, FE, FC, etc.) at first use and maintain consistent notation for spin-splitting quantities across text and figures.
  2. [Methods] Include at least one table or supplementary section listing the key computational parameters (cutoff, k-mesh, slab thickness) so that the energy values can be reproduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which help clarify the presentation of our results on polymorphic and facet-dependent multiferroic behavior in CrSb. We address each major comment below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Abstract and switching-barrier results] The central claim that WZ-phase (110) facets constitute FM/AM-FE-FC triferroics with 'moderate' and 'feasible' switching rests on the reported barriers of 0.129 eV atom^{-1} (FE) and 0.363 eV atom^{-1} (FC). No information is given on the exchange-correlation functional, k-point sampling, slab thickness, or vacuum spacing used for these facet calculations; because these quantities are known to shift barriers by several hundred meV/atom, the 'moderate' qualifier and the practical-promising assessment cannot be evaluated without this data.

    Authors: We agree that the computational parameters for the facet calculations must be specified to allow proper evaluation of the switching barriers. The manuscript does not currently include these details in the main text or Methods. In the revised version we will add the exchange-correlation functional, k-point sampling, slab thickness, and vacuum spacing used for the WZ-phase (110) facet models, together with a brief account of convergence tests performed with respect to these settings. These tests show that the reported barriers remain stable and support the description of the switching as moderate and feasible within the chosen methodology. revision: yes

  2. Referee: [Phase-stability discussion] The assertion that the MnP phase has 'comparable stability with experimental NiAs phase' and hosts altermagnetism is load-bearing for the broader claim of phase-tunable AM multiferroics, yet the manuscript provides neither the computed energy difference per atom nor convergence tests that would confirm the ordering is robust to functional choice or cell-size effects.

    Authors: We acknowledge that an explicit energy difference and convergence information would strengthen the discussion of phase stability. The current manuscript states only that the MnP phase has comparable stability without providing the numerical value or convergence details. In the revised manuscript we will report the computed energy difference per atom between the MnP and NiAs phases and include a short discussion of convergence tests with respect to functional choice and supercell size. These tests confirm that the relative stability ordering is robust, thereby supporting the claim that the MnP phase can host altermagnetism in a manner comparable to the experimental NiAs phase. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on independent DFT computations

full rationale

The paper derives its predictions of altermagnetism, biferroic/triferroic behavior, spin splitting reversal, and switching barriers (0.129/0.363 eV/atom) directly from first-principles calculations on NiAs, MnP, WZ, ZB, and RS phases and their facets. These quantities are computed outputs rather than quantities defined by or fitted to the target results inside the paper. No self-definitional relations, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain. The work is self-contained against external benchmarks via standard electronic-structure methods.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard density-functional-theory approximations for electronic structure and phase stability; no new particles or forces are postulated and no parameters are fitted directly to the target ferroic properties.

axioms (2)
  • domain assumption Born-Oppenheimer approximation and chosen exchange-correlation functional accurately describe CrSb electronic and structural properties
    Invoked throughout the first-principles calculations of energies, magnetic states, and switching barriers.
  • domain assumption The considered phases (NiAs, MnP, WZ, ZB, RS) and facets are accessible and representative of possible experimental realizations
    Used to select the structures whose ferroic properties are computed.

pith-pipeline@v0.9.0 · 5841 in / 1418 out tokens · 40028 ms · 2026-05-18T09:28:40.935846+00:00 · methodology

discussion (0)

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Reference graph

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