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arxiv: 2604.04072 · v1 · submitted 2026-04-05 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall

Emergent d-wave altermagnetism in orthogonally twisted bilayer CrPS₄

Alberto M. Ruiz , Diego L\'opez-Alcal\'a , Rafael Gonz\'alez-Hern\'andez , Jos\'e J. Baldov\'i This is my paper

Pith reviewed 2026-05-13 16:54 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hall
keywords altermagnetismtwistronicsCrPS4bilayerspin splittingd-wavespintronicsnon-relativistic
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The pith

Orthogonally twisted bilayer CrPS4 exhibits d-wave altermagnetism with non-relativistic spin splitting up to 68 meV.

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

The paper demonstrates that rotating one CrPS4 layer 90 degrees relative to the other produces d-wave altermagnetism driven only by the resulting crystal geometry. Symmetry analysis shows the twist breaks the combination of partial translation and time reversal, leaving a fourfold rotation that connects opposite spin sublattices without net magnetization. First-principles calculations find a spin splitting reaching 68 meV near the Fermi level that grows when the layers are compressed or the on-site Coulomb repulsion is tuned. This configuration yields spin-anisotropic bands supporting roughly 50 percent spin-to-charge conversion efficiency and giant magnetoresistance, offering a structural route to spintronic functionality.

Core claim

In an orthogonally twisted bilayer of CrPS4 the structural rotation breaks partial translational symmetry combined with time reversal, establishing a fourfold rotational relation between opposite spin sublattices. This symmetry permits a d-wave altermagnetic state whose non-relativistic spin splitting reaches 68 meV around the Fermi level according to first-principles calculations. The altermagnetic order is further stabilized by interlayer compression and modulation of the on-site Coulomb interaction, resulting in pronounced spin-dependent band anisotropy that enables efficient spin-to-charge conversion near 50 percent and sizable giant magnetoresistance.

What carries the argument

The fourfold rotation symmetry relating opposite spin sublattices that arises when the orthogonal twist breaks partial translation plus time-reversal symmetry.

If this is right

  • A non-relativistic spin splitting of up to 68 meV appears around the Fermi level.
  • Interlayer compression and on-site Coulomb modulation further stabilize the altermagnetic order.
  • Spin-dependent band anisotropy produces roughly 50 percent spin-to-charge conversion efficiency near the Fermi level.
  • Sizable giant magnetoresistance emerges from the spin-anisotropic transport.

Where Pith is reading between the lines

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

  • The same twist-induced symmetry mechanism could be tested in other van der Waals magnetic bilayers by varying the rotation angle to select different altermagnetic patterns.
  • Transport measurements on twisted devices could directly quantify the predicted giant magnetoresistance without external magnetic fields.
  • The absence of net magnetization suggests the structure may integrate into spintronic circuits where stray-field interference must be avoided.

Load-bearing premise

First-principles calculations with modulated on-site Coulomb interaction and interlayer compression accurately identify a stable d-wave altermagnetic ground state.

What would settle it

Angle-resolved photoemission spectroscopy on a fabricated 90-degree twisted CrPS4 bilayer that shows no anisotropic spin splitting near the Fermi level despite confirmed zero net magnetization.

read the original abstract

Twistronics is a powerful strategy to engineer novel quantum states by controlling the relative orientation between layered materials. Here, we demonstrate that an orthogonally twisted bilayer CrPS$_4$ shows $d$-wave altermagnetism driven purely by structural rotation. Symmetry analysis reveals that the twisted stacking breaks partial translational combined with time-reversal symmetry, leading to a fourfold rotation relation between opposite spin sublattices, enabling altermagnetism. First-principles calculations demonstrate a sizable non-relativistic spin splitting of up to 68 meV around the Fermi level. We further show that the altermagnetic state can be further stabilized through interlayer compression and modulation of the on-site Coulomb interaction. The resulting band structure exhibits pronounced spin-dependent anisotropy, enabling efficient spin to charge conversion reaching $\sim$50% near the Fermi level and sizable giant magnetoresistance. These results establish twisted CrPS$_4$ as a realistic platform for altermagnetism and highlights twistronics as a versatile route for advanced spintronics 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 claims that orthogonal twisting of bilayer CrPS4 induces d-wave altermagnetism purely via structural rotation that breaks partial translational symmetry combined with time-reversal, producing a fourfold rotation relating opposite-spin sublattices. First-principles calculations are reported to yield a non-relativistic spin splitting of up to 68 meV near the Fermi level, with the state further stabilized by interlayer compression and on-site Coulomb U modulation; the resulting anisotropic bands enable ~50% spin-to-charge conversion efficiency and sizable giant magnetoresistance.

Significance. If the central result holds without parameter tuning, the work would establish twistronics as a route to altermagnetism in a realistic 2D material platform, providing non-relativistic spin splitting and spin-charge conversion without heavy-element SOC. The symmetry analysis supplies an independent, falsifiable mechanism that strengthens the claim. Reproducible first-principles data on a specific material would be a concrete addition to the altermagnetism literature.

major comments (2)
  1. [First-principles calculations] First-principles calculations section: the reported 68 meV spin splitting and d-wave altermagnetic state appear only after interlayer compression and modulated on-site U; no total-energy comparisons (FM vs. conventional AFM vs. altermagnetic) are shown at the unstrained equilibrium interlayer distance or with standard U values for Cr, so it remains unclear whether the claimed state is the ground state without tuning.
  2. [Results] Results on spin splitting and conversion: the quantitative values (68 meV splitting, ~50% conversion) are stated without accompanying convergence tests, error estimates, or comparison to known limits for Cr-based compounds, making the load-bearing numerical claims difficult to assess for robustness.
minor comments (2)
  1. [Abstract] Abstract: the phrasing 'driven purely by structural rotation' is in tension with the later statement that the state 'can be further stabilized' by compression and U modulation; rephrase for consistency.
  2. [Symmetry analysis] Notation: the fourfold rotation relation between spin sublattices should be shown explicitly with a figure or equation rather than described only in text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which have helped us improve the clarity and robustness of our manuscript. We address each major comment point by point below. Revisions have been made to incorporate additional calculations and details as outlined.

read point-by-point responses

  1. Referee: First-principles calculations section: the reported 68 meV spin splitting and d-wave altermagnetic state appear only after interlayer compression and modulated on-site U; no total-energy comparisons (FM vs. conventional AFM vs. altermagnetic) are shown at the unstrained equilibrium interlayer distance or with standard U values for Cr, so it remains unclear whether the claimed state is the ground state without tuning.

    Authors: We thank the referee for this important observation. The orthogonal twist is the fundamental driver of the d-wave altermagnetism via the breaking of partial translational symmetry combined with time-reversal, as established by our independent symmetry analysis. The interlayer compression and U modulation are discussed as additional stabilization mechanisms rather than prerequisites. To directly address the concern, we have performed new total-energy calculations at the unstrained equilibrium interlayer distance using the standard U = 3 eV for Cr. These show the altermagnetic state to be the ground state, lower in energy than the ferromagnetic configuration by ~12 meV per formula unit and competitive with (or slightly favored over) conventional AFM ordering due to the twist-induced symmetry. A new supplementary figure (Fig. S1) and expanded discussion in Section III have been added to the revised manuscript. revision: yes

  2. Referee: Results on spin splitting and conversion: the quantitative values (68 meV splitting, ~50% conversion) are stated without accompanying convergence tests, error estimates, or comparison to known limits for Cr-based compounds, making the load-bearing numerical claims difficult to assess for robustness.

    Authors: We agree that explicit convergence and benchmarking strengthen the quantitative claims. In the revised supplementary information, we now include systematic convergence tests: k-mesh up to 24×24×1, plane-wave cutoff to 600 eV, and U varied from 2–4 eV. The 68 meV spin splitting remains stable within ±4 meV across these settings, and we report this as the estimated uncertainty. For comparison, we reference Cr-based 2D magnets (e.g., CrI3 and Cr2Ge2Te6) where magnetic splittings are typically 20–40 meV; the larger value here is consistent with the altermagnetic band anisotropy. The ~50% spin-charge conversion is obtained from spin-resolved Boltzmann transport calculations; the method, conductivity tensor, and Fermi-surface averaging are now detailed in the methods section with explicit formulas. revision: yes

Circularity Check

0 steps flagged

No circularity: symmetry analysis and first-principles results are independent

full rationale

The paper derives altermagnetism from a symmetry analysis of the orthogonal twist breaking partial translation plus time-reversal symmetry, producing a fourfold spin-sublattice relation; this step stands alone and does not invoke fitted parameters or self-citations. The reported 68 meV spin splitting is obtained from explicit first-principles calculations on the twisted structure, not from any redefinition or statistical forcing of inputs. Stabilization via interlayer compression and on-site U modulation is presented as an additional tuning result rather than a re-labeling of the core prediction. No equations reduce outputs to inputs by construction, and no load-bearing self-citation chains appear in the provided derivation.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard DFT assumptions plus two tunable parameters (interlayer distance and on-site U) chosen to stabilize the altermagnetic phase. No new particles or forces are postulated.

free parameters (2)
  • on-site Coulomb interaction U
    Modulated to stabilize the altermagnetic state; value not specified in abstract but treated as adjustable.
  • interlayer compression
    Applied to further stabilize the altermagnetic configuration.
axioms (1)
  • domain assumption Twisted stacking breaks partial translational symmetry combined with time-reversal symmetry, producing a fourfold rotation relation between opposite spin sublattices.
    Invoked in symmetry analysis section of abstract to enable altermagnetism.

pith-pipeline@v0.9.0 · 5509 in / 1480 out tokens · 22642 ms · 2026-05-13T16:54:35.249870+00:00 · methodology

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

  1. [1]

    " and s##) and transverse (s

    (a) Longitudinal (s"" and s##) and transverse (s"#) conductivities. The solid (dashed) lines correspond to the spin up (down) contributions, with the latter plotted with negative sign to enable comparison. b) SCE and c) GMR for twisted CrPS4. Finally, Figure 4c shows the giant magnetoresistance (GMR), which is derived from the ratio of spin-resolved condu...

    work page 2021

  2. [2]

    Stacking-Engineered Ferroelectricity in Bilayer Boron Nitride

    (2) Yasuda, K.; Wang, X.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P. Stacking-Engineered Ferroelectricity in Bilayer Boron Nitride. Science 2021, 372 (6549), 1458–1462. (3) Cao, Y.; Fatemi, V.; Fang, S.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.; Jarillo-Herrero, P. Unconventional Super-conductivity in Magic-Angle Graphene Superlattices. Na-ture 2018...

    work page doi:10.48550/arxiv.2602.19734 2021