Two‑dimensional multiferroics promise low‑power, multifunctional devices, yet the intrinsic coexistence and mutual control of three coupled ferroic orders in a single layer remains elusive. Here, we identify pentagonal monolayer FeO2 as an intrinsic triferroic altermagnet where ferroelectric (FE), ferroelastic (FA), and altermagnetic (AM) orders coexist and tightly coupled, accompanied by a competing antiferroelectric (AFE) phase using first‑principles calculations. The solely presence of glide mirror Mx symmetry in a FeO2 sublayer, with the breaking of four‑fold rotation C4z symmetry, induces in‑plane vector ferroelectricity and twin‑related ferroelastic strains. Both FE and AFE phases break combined parity–time symmetry and display sizable altermagnetic spin splitting with Néel temperatures over 200 K. Electric‑field induced rotation of the FE polarization reverses the sign of the spin splitting, while in‑plane uniaxial strain triggers ferroelastic switching that simultaneously rotates the FE polarization vector by 90° and reverses the AM state. These electric‑field‑ and strain‑mediated pathways interlink six distinct polarization states that can be selected purely by electric fields and/or mechanical strain. This work extends intrinsic triferroicity to pentagonal monolayers and outlines a symmetry‑based route toward mechanically and electrically configurable altermagnetic spintronics.
Altermagnetism has recently drawn considerable attention in three- and two dimensional materials. Here, we extend this concept to quasi-one-dimensional (Q1D) monolayers assembled from single-atomic magnetic chains. Through systematically examining nine types of structures, two stacking orders, and intra /inter-chain magnetic couplings, we identify four out of thirty promising structural prototypes for hosting altermagnetism, which yields 192 potential monolayer materials. We further confirm eight thermodynamically stable Q1D monolayers via high-throughput calculations. Using symmetry analysis and first-principles calculations, we find that the existence of altermagnetism is determined by the type of inter-chain magnetic coupling and predict three intrinsic altermagnets, CrBr3, VBr3, and MnBr3, due to their ferromagnetic inter-chain couplings and five extrinsic ones, CrF3, CrCl3, CrI3, FeCl3, and CoTe3, ascribed to their neglectable or antiferromagnetic inter-chain couplings. Moreover, the inter-chain magnetic coupling here is highly tunable by manipulating the inter-chain spacing, leading to experimentally feasible transitions between altermagnetic and nodal-line semiconducting states. In addition, applying external electric fields can further modulate the spin splitting. Our findings establish a highly tunable family of Q1D altermagnets, offering fundamental insights into the intricate relationship between geometry, electronic structure, and magnetism. These discoveries hold significant promises for experimental realization and future spintronic applications.
FIG. 1. (a) Summary of the emergence of altermagnetism in 1D magnetic chains with different stoichiometric ratios under AA and AB stacking configurations. FM and AFM represent interchain magnetic ordering. The symbol “×” indicates the absence of altermagnetism, while “ ” signifies its emergence. The symbol “/” represents the absence of the AB stacking configuration. Top (upper panel) and side (lower panel) views of the AA-stacked (b) and AB-stacked (c) γ -phase XY2 (X = transition metal, Y = chalcogen/halogen atom) and AA-stacked (d) and AB-stacked (e) β-phase XY3 monolayers. Orange arrows and blue lines illustrate symmetry operations C2x and Mx that connect the sublattices with opposite spins. Red dots P1 to P3 marked in panel (d) indicate structural inversion centers. Orange and blue spheres represent magnetic atoms with up and down majority spins, respectively. J1, J2, and J3 marked in panel (e) represent spin-exchange parameters for the nearest, second-nearest, and third-nearest neighbors, respectively. (f) Diagram of spin-splitting symmetry in the Brillouin zone.
FIG. 2. (a) The screening process of Q1D altermagnets. (b) Top view of spin density distribution and (c) band structure of the CrCl3 monolayer at the interchain spacing of 6.0 Å. The red dot represents the inversion center. The illustration shows the high-symmetry path in the Brillouin zone. (d), (e) The same scheme of (b), (c) for the CrCl3 monolayer with an expanded interchain spacing of 6.40 Å. The red dashed box highlights nodal-line electronic states.
TABLE I. Lattice constants (a and b) and spin-exchange parameters [J1, J2, J3, labeled in Fig. 1(e), in units of meV per magnetic atom] of the eight dynamically stable AA-stacked intrachain AFM β-XY3 Q1D monolayers.
FIG. 3. (a) The energy difference (EAFM -EFM ) as a function of interchain spacing for Q1D VBr3 monolayer. The vertical dashed line indicates the freestanding interchain distance. (b) Band structure of the monolayer VBr3 under interchain of 6.80 Å [labeled as red pentagram in 3(a)]. (c) The energy difference as a function of interchain spacing for Q1D CoTe3 monolayer. (d) Band structure of the monolayer CoTe3 under interchain of 5.10 Å [labeled as red pentagram in 3(c)].
FIG. 4. (a) Band dispersion plots of the highest valence band in freestanding CrCl3 monolayer with interchain FM coupling under varied external electric field. The orange dots indicate the band crossing point along the -S direction. Spin splitting mappings of the highest valence band in the freestanding CrCl3 monolayer (b) without electric field and (c) under an electric field of 0.2 V/Å.
The search for novel one-dimensional (1D) materials with exotic physical properties is crucial for advancing nanoelectronics and spintronics. Here, we perform a comprehensive high-throughput, first-principles study to explore the vast landscape of 1D transition-metal chalcogenides and halides. Starting with 6,832 candidate structures derived from 28 metals and 8 non-metals, we systematically evaluated their thermodynamic stability by comparing the formation energies of 1D chains against competing 2D phases, mimicking thermodynamic selectivity during nucleation. This screening identified 210 stable 1D magnetic chains. Furthermore, representation learning models revealed that chemical stoichiometry and the electron affinity of the non-metal element are key factors governing 1D stability. The stable materials exhibit a rich spectrum of properties, including diverse magnetic orders (FM, AFM) and Luttinger compensated antiferromagnetism in MnTe. We discovered 20 ferroelastic chains, with FeTe showing a giant magnetostriction of -5.57 %. Other emergent phenomena include Charge Density Wave (CDW) chains in FeTe and NiSe. Finally, our findings propose concrete platforms for quantum applications, such as the predicted realization of Majorana zero modes in a ferromagnetic CrCl2 chain on a superconducting NbSe2 substrate.
Yangjin Lee#, Linxuan Li#, Weihan Zhang#, Uje Choi, Kihyun Lee, Young-Min Kim, Wei Ji*, Wu Zhou*, Kwanpyo Kim*, and Alex Zettl*
Abstract:
Low-dimensional magnetic materials have garnered significant interest due to their unique physical properties and potential applications. Nevertheless, the synthesis of one-dimensional (1D) magnetic materials presents challenges, and the properties of these 1D materials at the single-chain limit have not been well investigated. We here explore experimentally and theoretically 1D CrX2 (X= Cl, Br, I) magnetic single-chains residing within carbon nanotubes. Single chains of CrX2 are confirmed by atomic-resolution scanning transmission electron microscopy imaging and spectroscopy analysis. Electron energy loss spectroscopy clearly reveals the high-spin state of Cr atoms within the chain. Notably, we present the first precise measurement and analysis of Cr spin state at the single-chain level, revealing that these spin states can be controlled by the local atomic bonding configuration (CrX2 versus CrX3 phases). Density functional theory calculations support the structural stability and provide the magnetic and electronic properties of the 1D CrX2 chains.
Zeyu Liu, Xianghua Kong, Zewen Wu, Linwei Zhou, Jingsi Qiao and Wei Ji
Abstract:
Many exotic electronic states were discovered in moiré superlattices hosted in twisted homo-bilayers in the past decade, including unconventional superconductivity and correlated insulating states. However, it is technically challenging to precisely and orderly stack two or more layers into certain twisting angles. Here, we presented a theoretical strategy that introduces moiré superlattices in untwisted homo-bilayers by applying different in-plane strains on the two layers of a graphene homo-bilayer, respectively. Our density functional theory calculations indicate that the graphene bilayer exhibits substantial out-of-plane corrugations that form a coloring-triangular structure in each moiré supercell under gradient in-plane strains. Such structure leads to a set of kagome bands, namely one flat-band and, at least, one Dirac band, developing along the M-K path after band-folding. For comparison, uniformly applied in-plane strain only yields a nearly flat band within path K-G, which is originated from local quantum confinement. These findings highlight the gradient strain as a route to feasibly fabricate exotic electronic states in untwisted flexible homo-bilayers.
