First-principles work on bilayer ScI2_2 (Pan et al., Appl. Phys. Lett. 127, 221601 (2025)) predicts that interlayer sliding and 180° rotation switch the interlayer magnetic coupling between antiferromagnetic (AA, AB*, BA*) and ferromagnetic (AA*, AB, BA) orders, coexist with sliding-induced ferroelectricity at the AB/BA stackings, and — once spins are rotated out of plane — produce spontaneous valley polarization. These predictions are unverified and now contested: an independent 2026 DFT+U plus Monte Carlo study (Sarkar and Chandra) — whose AA/AB/BA bilayers are built from the octahedral 1T polymorph, which their total-energy calculations place about 0.11 eV per formula unit below the trigonal-prismatic 1H phase studied by Pan et al. — reports the opposite exchange-sign pattern for the correspondingly named stackings, a robust out-of-plane easy axis with an anisotropy two orders of magnitude larger, and ordering temperatures near room temperature instead of tens of kelvin, yet, while citing Pan et al. and describing its own results as consistent with them, it reconciles none of these discrepancies. The open problem is to settle, in a methodologically robust way, the stacking-to-interlayer-exchange sign map, the easy axis, and the ordering temperatures of bilayer ScI2_2 — including which monolayer polymorph (1H or 1T) is the ground state and hence which bilayer object the predictions concern — with the experimental realization and detection of the predicted stacking-controlled multiferroic switching, including the required spin reorientation and the kinetics of interlayer sliding and rotation, as a source-suggested confirming direction.

Background

Two-dimensional (2D) van der Waals (vdW) magnets — crystalline solids one or a few atoms thick, held together by weak interlayer forces — have made layer number and stacking geometry itself a control knob for magnetism. The canonical example is bilayer CrI3_3, whose two layers couple antiferromagnetically in one stacking registry and ferromagnetically in another, as observed directly by magneto-optical experiments (Chen et al., Science 366, 983 (2019)). In parallel, 'sliding ferroelectricity' — a switchable electric polarization created merely by laterally shifting one layer of a nonpolar bilayer — has been demonstrated electrically in vdW devices (Yasuda et al., Science 385, 53 (2024)). A material in which the same interlayer sliding switches both magnetic order and electric polarization, i.e. a stacking-tunable multiferroic, is an attractive target for multifunctional 2D devices.

Monolayer ScI2_2 is a ferromagnetic metal built from scandium atoms in trigonal-prismatic coordination (the so-called 1H phase, the same structural family as monolayer MoS2_2); the single Sc 3d electron sits predominantly in the dz2d_{z^2}-derived band at the Fermi level. Earlier first-principles work found that the free monolayer prefers an in-plane magnetization direction (He et al., 2021). Pan et al. (2025) studied the bilayer with density functional theory including an on-site Hubbard correction UU (the 'DFT+U' scheme that penalizes spurious delocalization of localized d electrons; they used U=2.5U=2.5 eV in the Dudarev form) and a semi-empirical dispersion correction. Mapping total energies of different spin arrangements onto a Heisenberg exchange Hamiltonian (an effective model in which each Sc magnetic moment interacts with its neighbors through exchange constants JJ), they found a large intralayer ferromagnetic exchange (J1≈−67J_1\approx-67 meV, negative sign meaning ferromagnetic in their convention) but tiny interlayer exchanges: the AA stacking favors antiferromagnetic (AFM) interlayer coupling by only 0.50 meV per formula unit, while the aligned AB and BA stackings favor ferromagnetic (FM) coupling by 0.33 meV per formula unit, and the antialigned stackings (produced by a 180° in-plane rotation of one layer, denoted AA*, AB*, BA*) show the opposite pattern. The microscopic origin is interlayer superexchange — virtual hopping of the d electron through intervening iodine p orbitals, whose strength and sign depend on the stacking geometry. In the aligned stackings, lateral sliding also breaks inversion symmetry between the layers, inducing a switchable out-of-plane electric polarization (sliding ferroelectricity), maximal at AB/BA. Because the magnetic anisotropy energy (MAE, the energy cost of rotating the spin away from the preferred 'easy axis') is small (about 0.4 meV per formula unit, with the easy axis in-plane), the authors propose that spin-orbit torque — current-induced twisting of the magnetization — or an external field could rotate the spins out of plane, where inversion-symmetry breaking plus spin-orbit coupling produces unequal energies of the K and K' valleys ('valley polarization', a breaking of the two inequivalent band extrema of a hexagonal crystal useful for 'valleytronics'). A Heisenberg-model Monte Carlo estimate put the monolayer ordering temperature at only about 85 K.

A recent independent study (Sarkar and Chandra, 2026), using a different code (Quantum ESPRESSO vs VASP), a different Hubbard parameter (Ueff=1.7U_{\mathrm{eff}}=1.7 eV), a different dispersion treatment, and a different structural polymorph — their bilayers are built from the octahedral 1T monolayer, which their total-energy calculations place about 0.11 eV per formula unit below the trigonal-prismatic 1H phase studied by Pan et al. — studied the AA, AB, and BA stackings of this 1T-based bilayer and reached conflicting conclusions: ferromagnetic interlayer coupling for AA and BA but antiferromagnetic for AB (the opposite sign pattern from Pan et al.'s 1H-based bilayer for two of the three correspondingly named stackings), a robust out-of-plane easy axis with a monolayer MAE of about 0.07 eV per formula unit (0.05–0.06 eV in the bilayer; roughly two orders of magnitude larger than Pan et al.'s value and of opposite sign), and Monte Carlo ordering temperatures of 360–375 K — above room temperature — obtained from Binder cumulant crossings (a standard finite-size-scaling diagnostic for locating magnetic phase transitions in simulation) on lattices of linear size L=30L=30 up to 200200. The published version of that study cites Pan et al. and asserts that its results are 'fully consistent' with that report, yet none of the specific discrepancies — the different structural polymorph of the bilayers, the exchange signs of the AA and AB stackings, the easy-axis direction, the MAE magnitude, and the ordering temperature — is mentioned or reconciled; moreover, its stated MAE sign-convention label ('positive MAE corresponds to an in-plane easy axis') contradicts its own formula ΔEMAE=E110−E001\Delta E_{\mathrm{MAE}}=E_{110}-E_{001}, under which its positive value implies the out-of-plane easy axis it reports — exactly the kind of convention opacity that a robust determination must audit. The contradiction thus stands unadjudicated in the published literature, and it includes the structural question of which monolayer polymorph, 1H or 1T, is the ground state of monolayer ScI2_2 and hence which bilayer is physically relevant, alongside the sensitivity to the Hubbard parameter, exchange-correlation functional, dispersion treatment, code, and sign conventions. No experimental synthesis of monolayer or bilayer ScI2_2 has been reported: ScI2_2 is known only as a bulk layered dihalide, so every experimental ingredient of the proposal (growth, stacking-registry control and identification, magnetic readout) remains to be developed.

Problem Statement

Does bilayer ScI2_2 realize stacking-tunable multiferroicity as predicted — i.e., can the sign of the interlayer magnetic coupling be switched reversibly between antiferromagnetic and ferromagnetic by interlayer sliding and 180° rotation, with coexisting sliding ferroelectricity and, under out-of-plane spin orientation, valley polarization — and is this switching robust and realizable? The core requirement is a methodologically robust, convention-audited theoretical determination, for all six stackings of the 1H-phase bilayer (AA, AB, BA and their antialigned counterparts AA*, AB*, BA*), of (a) the sign and magnitude of the interlayer exchange coupling (the sub-meV-per-formula-unit FM/AFM energy differences and Heisenberg interlayer constants), (b) the magnetic easy axis and anisotropy energy of monolayer and bilayer, and (c) the magnetic ordering temperatures, reported for the 1H-phase bilayer in every case and, whenever the monolayer ground state is found to be a polymorph other than 1H, also for the bilayer built from that ground-state polymorph for the correspondingly named stackings (AA, AB, BA) — a determination that must quantify the sensitivity to the Hubbard parameter, exchange-correlation functional, dispersion treatment, and code/pseudopotential choices and must reconcile or adjudicate the published contradictions between Pan et al. (1H-phase bilayer; in-plane easy axis, AA antiferromagnetic, AB/BA ferromagnetic, ordering near 85 K) and Sarkar and Chandra (1T-based bilayer; out-of-plane easy axis with ~0.07 eV/f.u. monolayer anisotropy, AA/BA ferromagnetic and AB antiferromagnetic, ordering at 360–375 K), including which monolayer polymorph (1H vs 1T) is the ground state of monolayer ScI2_2 and hence which bilayer object is physically relevant. Experimental realization — synthesizing or isolating monolayer/bilayer ScI2_2, identifying and controlling the stacking registry, and measuring the interlayer magnetic coupling as a function of stacking, including the feasibility, required field strengths or spin–orbit torques, and thermal robustness of whatever spin reorientation is required to reach the out-of-plane orientation (in particular, rotating the spins from an in-plane axis if the easy-axis determination of item (b) confirms the in-plane easy axis predicted by Pan et al.), and the kinetics and reversibility of interlayer sliding and 180° rotation under realistic conditions (substrates, strain, defects) — is a source-suggested future direction and a natural route of confirmation, not a completion criterion for this problem; extension of the same stacking-control principles to other 1H-phase transition-metal dihalide bilayers is likewise a follow-on direction explicitly flagged by the source, not a completion criterion for this problem. The mandatory completion criterion of this problem is the (a)-(c) determination with its sensitivity study and the reconciliation or adjudication of the published contradictions; the coexisting sliding ferroelectricity and the out-of-plane valley polarization predicted by the sources characterize the phenomenon under test but are not themselves separately mandated deliverables.

References

  1. Yaxin Pan, Chongze Wang, Shuyuan Liu, Fengzhu Ren, Chang Liu, Bing Wang, Jun-Hyung Cho (2025), 'Tunable multiferroic properties of bilayer ScI2 via stacking engineering' (arXiv preprint titled 'Stacking-tunable multiferroic states in bilayer ScI2'), Applied Physics Letters 127, 221601, DOI: 10.1063/5.0298703, arXiv:2510.16379, https://doi.org/10.1063/5.0298703, https://arxiv.org/abs/2510.16379
  2. Soumyajit Sarkar, Soham Chandra (2026), 'Stacking-dependent magnetic ordering in bilayer ScI2', Physica Scripta 101, 205905, DOI: 10.1088/1402-4896/ae6a46, arXiv:2602.11781, https://doi.org/10.1088/1402-4896/ae6a46, https://arxiv.org/abs/2602.11781
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