Altermagnetic materials, with real-space antiferromagnetic arrangement and reciprocal-space anisotropic spin splitting, have attracted much attention. However, the spin splitting is small in most altermagnetic materials, which is a disadvantage to their application in electronic devices. In this study, based on symmetry analysis and the first-principles electronic structure calculations, we predict for the first time two Luttinger compensated bipolarized magnetic semiconductors Mn(CN)2 and Co(CN)2 with isotropic spin splitting as in the ferromagnetic materials. Our further analysis shows that the Luttinger compensated magnetism here depends not only on spin group symmetry, but also on the crystal field splitting and the number of d-orbital electrons. In addition, the polarized charge density indicates that both Mn(CN)2 and Co(CN)2 have the quasi-symmetry T{\tau} , resulting from the crystal field splitting and the number of d-orbital electrons. The Luttinger compensated magnetism not only has the zero total magnetic moment as the antiferromagnetism, but also has the isotropic spin splitting as the ferromagnetism, thus our work not only provides theoretical guidance for searching Luttinger compensated magnetic materials with distinctive properties, but also provides a material basis for the application in spintronic devices.
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.
Shuo Mi#, Manyu Wang#, Bingxian Shi#, Songyang Li, Xiaoxiao Pei, Yanyan Geng, Shumin Meng, Rui Xu, Li Huang, Wei Ji, Fei Pang, Peng Cheng*, Jianfeng Guo*, and Zhihai Cheng*
Abstract:
Strain engineering offers a compelling route to modulate magnetism in two-dimensional (2D) materials, yet most approaches rely on externally applied strain. An in-plane anisotropic 2D-layered ferromagnet FePd2Te2 provides a suitable platform to study intrinsic strain-magnetism coupling due to its twinning domains. Here, we report spatially modulated internal compressive/tensile(C/T) strain regions in FePd2Te2 and their strong impact on local magnetic properties in real space by using atomic/magnetic force microscopy (AFM/MFM) combined with scanning tunneling microscopy (STM). Field- and strain-dependent spin transformations reveal the modulation of its intrinsic C/T regions. Notably, C regions retain intact Fe zigzag chains and exhibit larger, abruptly switching magnetic moments, while T regions display fragmented chains with reduced, gradually rotating spins. The intrinsic strain-induced intact ferromagnetic (FM), field-induced polarized-FM states, and their transitions are comparatively discussed during magnetic measurements. Temperature- and field-dependent evolution are further investigated in the FM and paramagnetic (PM) states and summarized to obtain an H-T phase diagram of FePd2Te2. Our work provides key results for understanding real-space tunable magnetic states through internal structural heterogeneity and suggests potential strategies for manipulating intrinsic strain-engineered magnetic devices.
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, intra- and interchain magnetic couplings, we identify four out of 30 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 interchain magnetic coupling and predict three intrinsic altermagnets, CrBr3, VBr3, and MnBr3, due to their ferromagnetic interchain couplings and five extrinsic ones, CrF3, CrCl3, CrI3, FeCl3, and CoTe3, ascribed to their neglectable or antiferromagnetic interchain couplings. Moreover, the interchain magnetic coupling here is highly tunable by manipulating the interchain 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.
Jinghao Deng#, Deping Guo#, Yao Wen, Shuangzan Lu, Zhengbo Cheng, Zemin Pan, Tao Jian, Yusong Bai, Hui Zhang, Wei Ji*, Jun He*, Chendong Zhang*
Abstract:
Multiferroicity allows magnetism to be controlled using electric fields or vice versa, which has gained tremendous interest in both fundamental research and device applications. A reduced dimensionality of multiferroic materials is highly desired for device miniaturization, but the coexistence of ferroelectricity and magnetism at the two-dimensional limit is still debated. Here, we used a NbSe2 substrate to break both the C3 rotational and inversion symmetries in monolayer VCl3 and thus introduced exceptional in-plane ferroelectricity into a two dimensional magnet. Scanning tunnelling spectroscopy directly visualized ferroelectric domains and manipulated their domain boundaries in monolayer VCl3, where coexisting antiferromagnetic order with canted magnetic moments was verified by vibrating sample magnetometer measurements. Our density functional theory calculations highlight the crucial role that highly directional interfacial Cl–Se interactions play in breaking the symmetries and thus in introducing in-plane ferroelectricity, which was further verified by examining an ML-VCl3/graphene sample. Our work demonstrates an approach to manipulate the ferroelectric states in monolayered magnets through van der Waals interfacial interactions.
Fig. 1. Morphology and atomic structure of ML-VCl3 on a NbSe2 substrate.
Fig. 2. IP electric polarizations characterized by band bending near DWs.
Fig. 3. Experimental and theoretical investigations of the magnetic order in epitaxy ML-VCl3.
Fig. 4. Anisotropic charge transfer–induced IP ferroelectricity and comparison with the VCl3-graphene interface.
