2D Magnetic Systems Research Articles

Second‐Order Topological Insulator in Ferromagnetic Monolayer and Antiferromagnetic Bilayer CrSBr

Second‐order topological insulators (SOTIs) in 2D materials have attracted significant research interest. Recent theoretical predictions suggest that SOTIs can be achievable in 2D magnetic systems, especially within ferromagnetic (FM) materials. Yet, the quest for suitable 2D antiferromagnetic (AFM) materials capable of hosting magnetic SOTIs remains a challenge. Herein, utilizing first‐principles calculations and theoretical analysis, 2D CrSBr is proposed, including monolayer and bilayer forms, as a promising candidate for a magnetic high‐order topological insulator. The monolayer exhibits a FM ground state and features quantized fractional corner charge in its spin‐up channel in the absence of spin–orbital coupling (SOC), yielding fully spin‐polarized corner states. Intriguingly, the bilayer form adopts an AFM ground state while retaining the SOTI properties, with quantized corner charge in both spin channels. Remarkably, the SOTI properties in both monolayer and bilayer structures remain robust against the influence of SOC and symmetry‐breaking perturbations. The work not only identifies a tangible material for realizing 2D magnetic SOTIs, encompassing both FM and AFM phases, but also offers a path to explore the distinctive characteristics of SOTIs merged with magnetism.

An insulating and easy magnetization-plane magnet: The DFT + U and constrained electron population study of 1 T-FeCl2

The 1 T-FeCl2, as a typical and important 2D magnetic system, has attracted much attention. However, there are some debates on its ground-state and magnetic properties. We use the first-principles calculations based on the density functional theory to study the electronic structures and magnetic properties of 1 T-FeCl2. The linear response method was used to determinate the Hubbard U value as 5.467 eV. The electrons population controlling method was adopted to evident the system was fully filled in spin-up channel and dz2 single occupied in spin-down channel insulator. Further analysis of the total energy with the second-order perturbation theory confirmed the xy-plane is the magnetization easy plane, and the z axis is the magnetization hard axis. The weak ferromagnetic order was confirmed by energy-mapping and Monte Carlo simulations. Our results clarified the unique properties of 1 T-FeCl2 and deepen the understanding of the 2D magnetism.

Extraordinary Magnetic Response of an Anisotropic 2D Antiferromagnet via Site Dilution.

A prominent characteristic of 2D magnetic systems is the enhanced spin fluctuations, which reduce the ordering temperature. We report that a magnetic field of only 1000th of the Heisenberg superexchange interaction can induce a crossover, which for practical purposes is the effective ordering transition, at temperatures about 6 times the Néel transition in a site-diluted two-dimensional anisotropic quantum antiferromagnet. Such a strong magnetic response is enabled because the system directly enters the antiferromagnetically ordered state from the isotropic disordered state, skipping the intermediate anisotropic stage. The underlying mechanism is achieved on a pseudospin-half square lattice realized in the [(SrIrO3)1/(SrTiO3)2] superlattice thin film that is designed to linearly couple the staggered magnetization to external magnetic fields by virtue of the rotational symmetry-preserving Dzyaloshinskii-Moriya interaction. Our model analysis shows that the skipping of the anisotropic regime despite finite anisotropy is due to the enhanced isotropic fluctuations under moderate dilution.

Two-dimensional Heisenberg model with material-dependent superexchange interactions

The two-dimensional (2D) van der Waals ferromagnetic semiconductors, such as CrI$_3$ and Cr$_2$Ge$_2$Te$_6$, and the 2D ferromagnetic metals, such as Fe$_3$GeTe$_2$ and MnSe$_2$, have been obtained in recent experiments and attracted a lot of attentions. The superexchange interaction has been suggested to dominate the magnetic interactions in these 2D magnetic systems. In the usual theoretical studies, the expression of the 2D Heisenberg models were fixed by hand due to experiences. Here, we propose a method to determine the expression of the 2D Heisenberg models by counting the possible superexchange paths with the density functional theory (DFT) and Wannier function calculations. With this method, we obtain a 2D Heisenberg model with six different nearest-neighbor exchange coupling constants for the 2D ferromagnetic metal Cr$_3$Te$_6$, which is very different for the crystal structure of Cr atoms in Cr$_3$Te$_6$. The calculated Curie temperature Tc = 328 K is close to the Tc = 344 K of 2D Cr$_3$Te$_6$ reported in recent experiment. In addition, we predict two stable 2D ferromagnetic semiconductors Cr$_3$O$_6$ and Mn$_3$O$_6$ sharing the same crystal structure of Cr$_3$Te$_6$. The similar Heisenberg models are obtained for 2D Cr$_3$O$_6$ and Mn$_3$O$_6$, where the calculated Tc is 218 K and 208 K, respectively. Our method offers a general approach to determine the expression of Heisenberg models for these 2D magnetic semiconductors and metals, and builds up a solid basis for further studies.

A Quantum Monte Carlo Study of the Structural, Energetic, and Magnetic Properties of Two-Dimensional H and T Phase VSe2.

Previous works have controversially claimed near-room-temperature ferromagnetism in two-dimensional (2D) VSe2, with conflicting results throughout the literature. These discrepancies in magnetic properties between both phases (T and H) of 2D VSe2 are most likely due to the structural parameters being coupled to the magnetic properties. Specifically, both phases have a close lattice match and similar total energies, which makes it difficult to determine which phase is being observed experimentally. In this study, we used a combination of density functional theory, highly accurate diffusion Monte Carlo (DMC), and a surrogate Hessian line-search optimization technique to resolve the previously reported discrepancy in structural parameters and relative phase stability. With DMC accuracy, we determined the free-standing geometry of both phases and constructed a phase diagram. Our findings demonstrate the successes of the DMC method coupled with the surrogate Hessian structural optimization technique when applied to a 2D magnetic system.

Room-Temperature Intrinsic Ferromagnetic Chromium Tellurium Compounds with Thickness-Tunable Magnetic Texture.

2D ferromagnetic chromium tellurides exhibit intriguing spin configurations and high-temperature intrinsic ferromagnetism, providing unprecedented opportunities to explore the fundamental spin physics and build spintronic devices. Here, a generic van der Waals epitaxial approach is developed to synthesize the 2D ternary chromium tellurium compounds with thicknesses down to mono-, bi-, tri-, and few-unit cells(UC). The Mn0.14 Cr0.86 Te evolves from intrinsic ferromagnetic behavior in bi-UC, tri-UC, and few-UC to temperature-induced ferrimagnetic behavior as the thickness increases, resulting in a sign reversal of the anomalous Hall resistance. Temperature- and thickness-tunable labyrinthine-domain ferromagnetic behaviors are derived from the dipolar interactions in Fe0.26 Cr0.74 Te and Co0.40 Cr0.60 Te. Furthermore, the dipolar-interaction-induced stripe domain and field-induced domain wall (DW) motion velocity are studied, and multibit data storage is realized through an abundant DW state. The magnetic storage can function in neuromorphic computing tasks, and the pattern recognition accuracy can reach up to 97.93%, which is similar to the recognition accuracy of ideal software-based training (98.28%). Room-temperature ferromagnetic chromium tellurium compounds with intriguing spin configurations can significantly promote the exploration of the processing, sensing, and storage based on 2D magnetic systems.

Generation of magnetic skyrmions in two-dimensional magnets via interfacial proximity

Two-dimensional (2D) magnetic van der Waals materials provide a fertile platform for the design and control of topological spin textures such as skyrmions. However, despite studies reporting skyrmions in many 2D magnetic systems, the hosting van der Waals materials are still limited. Here, via first-principles calculations and Monte Carlo simulations, we propose a series of 2D magnetic heterostructures as a different materials' family hosting skyrmions. Unlike previously studied van der Waals heterostructures, a strong interface coupling generates here a significant inversion symmetry breaking, which then results in an inherently large Dzyaloshinskii-Moriya interaction (DMI). Furthermore, upon applying a moderate magnetic field, isolated skyrmions and skyrmions lattices emerge in various types of these heterostructures, and are robust within a relatively wide temperature range. Our work thus suggests a general method to induce DMI and paves the way toward topological magnetism in 2D materials through interfacial engineering.

Stacking influence on the in-plane magnetic anisotropy in a 2D magnetic system.

The magnetization patterns on three atomic layers thick islands of Co on Ru(0001) are studied by spin-polarized low-energy electron microscopy (SPLEEM). In-plane magnetized micrometer wide triangular Co islands are grown on Ru(0001). They present two different orientations correlated with two different stacking sequences which differ only in the last layer position. The stacking sequence determines the type of magnetization pattern observed: the hcp islands present very wide domain walls, while the fcc islands present domains separated by much narrower domain walls. The former is an extremely low in-plane anisotropy system. We estimate the in-plane magnetic anisotropy of the fcc regions to be 1.96 × 104 J m-3 and of the hcp ones to be 2.5 × 102 J m-3.

Design of Lanthanide Single-Chain Magnets Based on Tubular Segment Clusters

One-dimensional (1D) atomic chains that exhibit large magnetic anisotropy are highly relevant to spintronic applications. Such 1D magnetic systems have usually been produced by atom/molecular assembling on solid surfaces or by coordination polymers. Here, we demonstrate an alternative approach for the formation of a confined ferromagnetic holmium (Ho) atom chain, which is composed of repeating units of the tubular Ho doped boron (B) cluster HoB20. The tubular HoB20 is discovered by the global structural search of a series of small-sized boron clusters doped by a single Ho atom (HoBn, n = 12, 14, 16, 18, 20) using ab initio calculations. Electronic analysis reveals that the individual HoB20 cluster is stabilized by the double σ + π aromaticity. Extending the tubular structure results in a single Ho atom chain being confined inside a boron nanotube, which shows ferromagnetic behaviors and a large magnetic anisotropy of more than 40 meV/atom. Our findings indicate that the magnetic lanthanide chain is a promising candidate for high-density magnetic information storage.

Ultrafast Light-Induced Ferromagnetic State in Transition Metal Dichalcogenides Monolayers.

Ultrafast optical control of magnetism had great potential to revolutionize magnetic storage technology and spintronics, but for now, its potential remains mostly untapped in two-dimensional (2D) magnets. Here, using the state-of-the-art real-time time-dependent density functional theory (rt-TDDFT), we demonstrate that an ultrafast laser pulse can induce a ferromagnetic state in nonmagnetic MoSe2 monolayers interfaced with van der Waals (vdW) ferromagnetic MnSe2. Our results show that the transient ferromagnetism in MoSe2 derives from photoinduced direct ultrafast interlayer spin transfer from Mn to Mo via a vdW-coupled interface, albeit with a delay of approximately a few femtoseconds. This delay was strongly dependent on laser duration and interlayer coupling, which could be used to tune the amplitude and rate spin transfer. Furthermore, we have also shown that ferromagnetic states can be photoinduced in other transition metal dichalcogenides (TMDs), such as PtS2 and TaSe2 monolayers. Overall, our findings provide crucial physical insights for exploring light-induced interlayer spin and charge dynamics in 2D magnetic systems.

Coexistence of multiple Weyl fermions and quantum anomalous Hall effect in 2D half-metallic Cr2NT2

Topological state in two-dimensional (2D) magnetic system has attracted widespread attention due to its potential application in spintronics and quantum computing fields. As a novel topological states of matter, Weyl semimetals with multiple topological phases have been studied. However, realizing multiple topological phases in 2D magnetic system and studying their entanglement still face great challenges. In this work, using first-principles calculations, we predict that 2D monolayer Cr2NT2 (T = -OH, -F, =O) has multiple Weyl fermions (WFs) and large spin-down gap. Ferromagnetic ground states of monolayer Cr2NT2meet the dynamic, thermal and mechanical stabilities. Without spin-orbit coupling (SOC), these WPs are fully spin-polarized. When considering SOC, apart from WP3 in Cr2NO2, all WPs are opened the gap, and the chiral edge states are observed in Cr2NT2. In particular, there is a quantum anomalous Hall effect in Cr2NF2. Further, a biaxial strain in the a-b plane leads to the emergence of rich topological phases without SOC. In addtion, an effective four-band tight-binding model is constructed to clarify the origin of WFs in the non-trivial band topology. Finally, we calculate the Berry curvature and abnormal Hall conductivity of Cr2NT2, and find that they are a non-zero energy points around the Fermi level, indicating that monolayer Cr2NT2 are promising candidates for spintronic applications. Therefore, it is necessary to explore 2D magnetic materials with multiple types of WFs and QAH phases.

High-temperature magnetic skyrmions in BiCrX3 (X = Se and Te) monolayers.

Two-dimensional magnetic van der Waals materials provide a fertile platform for the design and control of topological spin textures such as skyrmions. However, despite studies reporting skyrmions in many 2D magnetic systems, those of the hosting van der Waals materials remain limited. Here, via first-principles calculations and Monte Carlo simulations, we propose BiCrX3 as a new family of materials for hosting skyrmions. Due to the large SOC of the X atom and intrinsic inversion asymmetry, an inherent large DMI occurs in all systems, enabling intriguing Néel-type skyrmions. Furthermore, upon applying a moderate magnetic field, isolated skyrmions and skyrmion lattices emerge in our systems, and are robust within a relatively wide temperature range.

Two-Dimensional Magnets beyond the Monolayer Limit.

Intrinsic two-dimensional (2D) magnetism has been demonstrated in various materials scaled down to a single monolayer. However, the question is whether 2D magnetism extends beyond the monolayer limit, to chemical species formed by sparse but regular 2D arrays of magnetic atoms. Here we show that sub-monolayer superstructures of Eu atoms self-assembled on the silicon surface exhibit strong magnetic signals. Robust easy-plane magnetism is discovered in both one- and two-dimensionally ordered structures with Eu coverage of half monolayer and above. The emergence of 2D magnetism manifests itself by a strong dependence of the effective transition temperature on weak magnetic fields. The results constitute a versatile platform for miniaturization of 2D magnetic systems and seed an expandable class of atomically thin magnets for applications in information technologies.

Density functional theory studies of transition metal doped Ti3N2 MXene monolayer

Spin-polarized density functional theory calculations with van der Waals correction were applied to investigate the presence of transition metal dopant atoms (Fe, Co, Ni, Pd and Pt) and their respective nitrogen vacancy complexes in the Ti3N2 MXene monolayer as candidate material for hydrogen evolution reaction (HER). We found that the transition metal dopant atoms as well as transition metal vacancy will feasibly form. However, the cation transition metal dopant atoms with nitrogen vacancy complexes and nitrogen vacancy are endothermic except for the PtTi + VN complex, thus would require additional energy to be realized. To evaluate for the HER activity, the Gibbs free energy and adsorption energetics were calculated. We found that the H atom stably bind to the considered surface configurations. However, the Gibbs free energy is far from optimal for the dopant complexes and the pristine Ti3N2 MXene monolayer. All the considered configurations have magnetic metallic ground state with possible application as 2D magnetic system.

Quarter-filled Kane-Mele Hubbard model: Dirac half metals

Recent experimental success in the realization of two-dimensional (2D) magnetism has stimulated the search for new magnetic 2D materials with strong magnetic anisotropy and high Curie temperature. One promising subgroup of 2D magnetic systems are Dirac half-metals (DHM) which have gained a lot of interest recently, as they host a high-temperature quantum anomalous Hall effect (QAHE). This article discusses predictions for intrinsic DHMs and identifies them as realizations of the Kane-Mele Hubbard model at quarter filling. This proposed unification contributes to a firmer understanding of these materials and suggests pathways for the discovery of new DHM systems.

Rational Design of Two-Dimensional Magnetic Chromium Borides Based on First-Principles CalculationSupported in part by the National Key Research and Development Program of China (Grant No. 2016YFB0700700), the National Natural Science Foundation of China (Grant No. 61904035), the Fudan Start-up Funding (Grant No. JIH1512034), and the Shanghai Sailing Program (Grant No. 19YF1403100).

Two-dimensional (2D) magnetic materials have been experimentally recognized recently, however, the Curie temperatures (T C) of known 2D systems are quite low. Generally, magnetic systems can be seen as constituent magnetic elements providing spins and the non-magnetic elements providing frameworks to host the magnetic elements. Short bond lengths between the magnetic and non-magnetic elements would be beneficial for strong magnetic interactions and thus high T C. Based on this, we propose to combine the magnetic element Cr and the non-magnetic element boron to design novel 2D magnetic systems. Using our self-developed software package IM2ODE, we design a series of chromium-boride based 2D magnetic materials. Nine stable magnetic systems are identified. Among them, we find that CrB4-I, CrB4-II and CrB5-I with common structural units [CrB8] are ferromagnetic metals with estimated T C of 270 K, 120 K and 110 K, respectively. On the other hand, five CrB3 phases with structural units [Cr2B12] are antiferromagnetic metals. Additionally, we also find one antiferromagnetic semiconductor CrB2-I. Our work may open new directions for identifying 2D magnetic systems with high T C.

Two-dimensional antiferromagnetic Dirac fermions in monolayer TaCoTe2

Dirac point in two-dimensional (2D) materials has been a fascinating subject of research. Recently, it has been theoretically predicted that Dirac point may also be stabilized in 2D magnetic systems. However, it remains a challenge to identify concrete 2D materials which host such magnetic Dirac point. Here, based on first-principles calculations and theoretical analysis, we propose a stable 2D material, the monolayers TaCoTe$_2$, as an antiferromagnetic (AFM) 2D Dirac material. We show that it has an AFM ground state with an out-of-plane N\'{e}el vector. It hosts a pair of 2D AFM Dirac points on the Fermi level in the absence of spin-orbit coupling (SOC). When the SOC is considered, a small gap is opened at the original Dirac points. Meanwhile, another pair of Dirac points appear on the Brillouin zone boundary below the Fermi level, which are robust under SOC and have a type-II dispersion. Such a type-II AFM Dirac point has not been observed before. We further show that the location of this Dirac point as well as its dispersion type can be controlled by tuning the N\'{e}el vector orientation.

Electric manipulation of magnetism in bilayer van der Waals magnets

The ferromagnetism of the two dimensional (2D) Cr2Ge2Te6 atomic layers with the perpendicular magnetic anisotropy and the Curie temperature 30–50 K has recently been experimentally confirmed. By performing the density-functional theory calculations, we demonstrate that the magnetic properties of bilayer Cr2Ge2Te6 can be flexibly tailored, due to the effective band structure tuning by the external electric field. The electric field induces the semiconductor-metal transition and redistributes charge and spin between the two layers. Furthermore, the magnetic anisotropy energy of the bilayer Cr2Ge2Te6 can be obviously enhanced by the electric field, which is helpful to stabilize the long-range ferromagnetic order. Our study about the electric manipulation of magnetism based on the band structure engineering generally exists in 2D magnetic systems and will be of great significance in low-dimensional all-electric spintronics.

Observation of unusual critical region behavior in the magnetic susceptibility of EuSe

The Europium Chalcogenides (EuCh: EuO, EuS, EuSe, and EuTe) have been regarded as model examples of simple, cubic, Heisenberg exchange coupled magnetic systems, with a ferromagnetic nearest-neighbor exchange constant J1 and an antiferromagnetic next-nearest-neighbor constant J2. Unlike the other EuCh, EuSe exhibits a range of complex magnetic behaviors, the latter being attributed to EuSe being near the point where J2=-J1, where its magnetism appears to consist of nearly de-coupled 2D ferromagnetic sheets. Analysis of precision SQUID measurements of the magnetic susceptibility χ in EuSe showed that in the region from ∼Tc to ∼2Tc, a fit of the data to the critical equation χ = χ2Tc(T/Tc-1)-γ gives γ=2.0, an exponent not predicted by any current theory. Additionally, this fit predicts that Tc should be ∼0K. We tentatively interpret this by saying that in the paramagnetic region the system "thinks" EuSe should not order above T=0. Tc=0K is predicted by the Mermin-Wagner theorem (MW) for Heisenberg-coupled 2D magnetic systems, and we can show that when J2=-J1, MW can also be applied to the J1, J2 exchange model of the EuCh to give a rigorous Tc=0 prediction. Under 10 kbar applied pressure EuSe exhibits a different γ and fitted Tc. An additional, and rather strange, critical-region effect was discovered. The EuSe sample was found to exhibit a relaxation effect in a small range of temperatures, just above and just below the actual Tc of 4.7K, with time constants of up to 5 minutes. We cannot yet fully explain this observed macroscopic effect.

Nanometre-scale probing of spin waves using single-electron spins.

Pushing the frontiers of condensed-matter magnetism requires the development of tools that provide real-space, few-nanometre-scale probing of correlated-electron magnetic excitations under ambient conditions. Here we present a practical approach to meet this challenge, using magnetometry based on single nitrogen-vacancy centres in diamond. We focus on spin-wave excitations in a ferromagnetic microdisc, and demonstrate local, quantitative and phase-sensitive detection of the spin-wave magnetic field at ∼50 nm from the disc. We map the magnetic-field dependence of spin-wave excitations by detecting the associated local reduction in the disc's longitudinal magnetization. In addition, we characterize the spin–noise spectrum by nitrogen-vacancy spin relaxometry, finding excellent agreement with a general analytical description of the stray fields produced by spin–spin correlations in a 2D magnetic system. These complementary measurement modalities pave the way towards imaging the local excitations of systems such as ferromagnets and antiferromagnets, skyrmions, atomically assembled quantum magnets, and spin ice.