Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI_{3}

Magnetic State Control of Non-van der Waals 2D Materials by Hydrogenation

Controlling the magnetic state of two-dimensional (2D) materials is crucial for spintronics. By employing data-mining and autonomous density functional theory calculations, we demonstrate the switching of magnetic properties of 2D non-van der Waals materials upon hydrogen passivation. The magnetic configurations are tuned to states with flipped and enhanced moments. For 2D CdTiO3─a diamagnetic compound in the pristine case─we observe an onset of ferromagnetism upon hydrogenation. Further investigation of the magnetization density of the pristine and passivated systems provides a detailed analysis of modified local spin symmetries and the emergence of ferromagnetism. Our results indicate that selective surface passivation is a powerful tool for tailoring magnetic properties of nanomaterials, such as non-vdW 2D compounds.

Chirality-selective topological magnon phase transition induced by interplay of anisotropic exchange interactions in honeycomb ferromagnet

A variety of distinct anisotropic exchange interactions commonly exist in one magnetic material due to complex crystal, magnetic and orbital symmetries. Here we investigate the effects of multiple anisotropic exchange interactions on topological magnon in a honeycomb ferromagnet, and find a chirality-selective topological magnon phase transition induced by a complicated interplay of Dzyaloshinsky-Moriya interaction and pseudo-dipolar interaction, accompanied by the bulk gap close and reopen with chiral inversion. Moreover, this novel topological phase transition involves band inversion at high symmetry pointsKandK', which can be regarded as a pseudo-orbital reversal, i.e. magnon valley degree of freedom, implying a new manipulation corresponding to a sign change of the magnon thermal Hall conductivity. Indeed, it can be realized in 4dor 5dcorrelated materials with both spin-orbit coupling and orbital localized states, such as iridates and ruthenates,etc.This novel regulation may have potential applications on magnon devices and topological magnonics.

Beyond Kitaev physics in strong spin-orbit coupled magnets

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.

Topological magnons driven by the Dzyaloshinskii-Moriya interaction in the centrosymmetric ferromagnet Mn5Ge3

The phase of the quantum-mechanical wave function can encode a topological structure with wide-ranging physical consequences, such as anomalous transport effects and the existence of edge states robust against perturbations. While this has been exhaustively demonstrated for electrons, properties associated with the elementary quasiparticles in magnetic materials are still underexplored. Here, we show theoretically and via inelastic neutron scattering experiments that the bulk ferromagnet Mn5Ge3 hosts gapped topological Dirac magnons. Although inversion symmetry prohibits a net Dzyaloshinskii-Moriya interaction in the unit cell, it is locally allowed and is responsible for the gap opening in the magnon spectrum. This gap is predicted and experimentally verified to close by rotating the magnetization away from the c-axis with an applied magnetic field. Hence, Mn5Ge3 realizes a gapped Dirac magnon material in three dimensions. Its tunability by chemical doping or by thin film nanostructuring defines an exciting new platform to explore and design topological magnons. More generally, our experimental route to verify and control the topological character of the magnons is applicable to bulk centrosymmetric hexagonal materials, which calls for systematic investigation.

Magnon-phonon coupling: from fundamental physics to applications

In recent decades, there are immense applications for bulk and few-layer magnetic insulators in biomedicine, data storage, and signal transfer. In these applications, the interaction between spin and lattice vibration has significant impacts on the device performance. In this article, we systematically review the fundamental physical aspects of magnon-phonon coupling in magnetic insulators. We first introduce the fundamental physics of magnons and magnon-phonon coupling in magnetic insulators and then discuss the influence of magnon-phonon coupling on the properties of magnons and phonons. Finally, a summary is presented, and we also discuss the possible open problems in this field. This article presents the advanced understanding of magnon-phonon coupling in magnetic insulators, which provides new opportunities for improving various possible applications.

Same effect of biquadratic exchange interaction and Heisenberg linear interaction in a spin spiral

Monolayer (ML) NiCl₂ exhibits a strong biquadratic exchange interaction between the first neighboring magnetic atoms (B₁), as demonstrated by the spin spiral model in J. Ni et al., Phys. Rev. Lett., 2021, 127, 247204. This interaction is crucial for stabilizing the ferromagnetic collinear order within the ML NiCl₂. However, they neither point out the role of B₁ nor discuss the dispersion relation from spin orbit coupling (SOC) in the spin spiral. As we have done in this work, these parameters might theoretically potentially be derived directly by fitting the calculated spin spiral dispersion relation. Here, we draw attention to the fact that B₁ is equivalent to half of J₃ in Heisenberg linear interactions and that the positive B₁ partially counteracts the negative J₃'s impact on the spin spiral to make the ML NiCl₂ ferromagnetic. The comparatively small J₃ + 1/2B₁ from the spin spiral led us to believe that J₃ could be substituted by B₁, yet it still exists and plays a crucial function in magnetic semiconductors or insulators. The dispersion relation, which we also obtain from SOC, displays weak antiferromagnetic behavior in the spin spiral.

Enhancing the Curie Temperature in Cr2Ge2Te6 via Charge Doping: A First-Principles Study

In this work, we explore the impacts of charge doping on the magnetism of a Cr₂Ge₂Te₆ monolayer using first-principles calculations. Our results reveal that doping with 0.3 electrons per unit cell can enhance the ferromagnetic exchange constant in a Cr₂Ge₂Te₆ monolayer from 6.874 meV to 10.202 meV, which is accompanied by an increase in the Curie temperature from ~85 K to ~123 K. The enhanced ratio of the Curie temperature is up to 44.96%, even higher than that caused by surface functionalization on monolayer Cr₂Ge₂Te₆, manifesting the effectiveness of charge doping by improving the magnetic stability of 2D magnets. This remarkable enhancement in the ferromagnetic exchange constant and Curie temperature can be attributed to the increase in the magnetic moment on the Te atom, enlarged Cr-Te-Cr bond angle, reduced Cr-Te distance, and the significant increase in super-exchange coupling between Cr and Te atoms. These results demonstrate that charge doping is a promising route to improve the magnetic stability of 2D magnets, which is beneficial to overcome the obstacles in the application of 2D magnets in spintronics.

Control of magnetic states and spin interactions in bilayer CrCl3 with strain and electric fields: an ab initio study

Using ab initio density functional theory, we demonstrated the possibility of controlling the magnetic ground-state properties of bilayer CrCl[Formula: see text] by means of mechanical strains and electric fields. In principle, we investigated the influence of these two fields on parameters describing the spin Hamiltonian of the system. The obtained results show that biaxial strains change the magnetic ground state between ferromagnetic and antiferromagnetic phases. The mechanical strain also affects the direction and amplitude of the magnetic anisotropy energy (MAE). Importantly, the direction and amplitude of the Dzyaloshinskii-Moriya vectors are also highly tunable under external strain and electric fields. The competition between nearest-neighbor exchange interactions, MAE, and Dzyaloshinskii-Moriya interactions can lead to the stabilization of various exotic spin textures and novel magnetic excitations. The high tunability of magnetic properties by external fields makes bilayer CrCl[Formula: see text] a promising candidate for application in the emerging field of two-dimensional quantum spintronics and magnonics.

Frequency Splitting of Chiral Phonons from Broken Time-Reversal Symmetry in CrI_{3}

Conventional approaches for lattice dynamics based on static interatomic forces do not fully account for the effects of time-reversal-symmetry breaking in magnetic systems. Recent approaches to rectify this involve incorporating the first-order change in forces with atomic velocities under the assumption of adiabatic separation of electronic and nuclear degrees of freedom. In this Letter, we develop a first-principles method to calculate this velocity-force coupling in extended solids and show via the example of ferromagnetic CrI_{3} that, due to the slow dynamics of the spins in the system, the assumption of adiabatic separation can result in large errors for splittings of zone-center chiral modes. We demonstrate that an accurate description of the lattice dynamics requires treating magnons and phonons on the same footing.

Atomically Unveiling an Atlas of Polytypes in Transition-Metal Trihalides

Transition-metal trihalides MX₃ (M = Cr, Ru; X = Cl, Br, and I) belong to a family of novel two-dimensional (2D) magnets that can exhibit topological magnons and electromagnetic properties, thus affording great promises in next-generation spintronic devices. Rich magnetic ground states observed in the MX₃ family are believed to be strongly correlated to the signature Kagome lattice and interlayer van der Waals coupling raised from distinct stacking orders. However, the intrinsic air instability of MX₃ makes their direct atomic-scale analysis challenging. Therefore, information on the stacking-registry-dependent magnetism for MX₃ remains elusive, which greatly hinders the engineering of desired phases. Here, we report a nondestructive transfer method and successfully realize an intact transfer of bilayer MX₃, as evidenced by scanning transmission electron microscopy (STEM). After surveying hundreds of MX₃ thin flakes, we provide a full spectrum of stacking orders in MX₃ with atomic precision and calculated their associated magnetic ground states, unveiled by combined STEM and density functional theory (DFT). In addition to well-documented phases, we discover a new monoclinic C2/c phase in the antiferromagnetic (AFM) structure widely existing in MX₃. Rich stacking polytypes, including C2/c, C2/m, R3̅, P3₁12, etc., provide rich and distinct magnetic ground states in MX₃. Besides, a high density of strain soliton boundaries is consistently found in all MX₃, combined with likely inverted structures, allowing AFM to ferromagnetic (FM) transitions in most MX₃. Therefore, our study sheds light on the structural basis of diverse magnetic orders in MX₃, paving the way for modulating magnetic couplings via stacking engineering.

Systematic DFT+U and Quantum Monte Carlo Benchmark of Magnetic Two-Dimensional (2D) CrX3 (X = I, Br, Cl, F)

The search for two-dimensional (2D) magnetic materials has attracted a great deal of attention because of the experimental synthesis of 2D CrI₃, which has a measured Curie temperature of 45 K. Often times, these monolayers have a higher degree of electron correlation and require more sophisticated methods beyond density functional theory (DFT). Diffusion Monte Carlo (DMC) is a correlated electronic structure method that has been demonstrated to be successful for calculating the electronic and magnetic properties of a wide variety of 2D and bulk systems, since it has a weaker dependence on the Hubbard parameter (U) and density functional. In this study, we designed a workflow that combines DFT +U and DMC in order to treat 2D correlated magnetic systems. We chose monolayer CrX₃ (X = I, Br, Cl, F), with a stronger focus on CrI₃ and CrBr₃, as a case study due to the fact that they have been experimentally realized and have a finite critical temperature. With this DFT+U and DMC workflow and the analytical method of Torelli and Olsen, we estimated a maximum value of 43.56 K for the T_c of CrI₃ and 20.78 K for the T_c of CrBr₃, in addition to analyzing the spin densities and magnetic properties with DMC and DFT+U. We expect that running this workflow for a well-known material class will aid in the future discovery and characterization of lesser known and more complex correlated 2D magnetic materials.

Large Photogalvanic Spin Current by Magnetic Resonance in Bilayer Cr Trihalides

Spin current is a key to realizing various phenomena and functionalities related to spintronics. Recently, the possibility of generating spin current through a photogalvanic effect of magnons was pointed out theoretically. However, neither a candidate material nor a general formula for calculating the photogalvanic spin current in materials is known so far. In this Letter, we develop a general formula for the photogalvanic spin current through a magnetic resonance process. This mechanism involves a one-magnon excitation process in contrast to the two-particle processes studied in earlier works. Using the formula, we show that GHz and THz waves create a large photogalvanic spin current in the antiferromagnetic phase of bilayer CrI_{3} and CrBr_{3}. The large spin current arises from an optical process involving two magnon bands, which is a contribution unknown to date. This spin current appears only in the antiferromagnetic ordered phase and is reversible by controlling the order parameter. These results open a route to material design for the photogalvanic effect of magnetic excitations.

Coherent helicity-dependent spin-phonon oscillations in the ferromagnetic van der Waals crystal CrI3

The discovery of two-dimensional systems hosting intrinsic magnetic order represents a seminal addition to the rich landscape of van der Waals materials. CrI₃ is an archetypal example, where the interdependence of structure and magnetism, along with strong light-matter interactions, provides a new platform to explore the optical control of magnetic and vibrational degrees of freedom at the nanoscale. However, the nature of magneto-structural coupling on its intrinsic ultrafast timescale remains a crucial open question. Here, we probe magnetic and vibrational dynamics in bulk CrI₃ using ultrafast optical spectroscopy, revealing spin-flip scattering-driven demagnetization and strong transient exchange-mediated interactions between lattice vibrations and spin oscillations. The latter yields a coherent spin-coupled phonon mode that is highly sensitive to the driving pulse's helicity in the magnetically ordered phase. Our results elucidate the nature of ultrafast spin-lattice coupling in CrI₃ and highlight its potential for applications requiring high-speed control of magnetism at the nanoscale.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

A combined first principles study of the structural, magnetic, and phonon properties of monolayer CrI3

The first magnetic 2D material discovered, monolayer (ML) CrI₃, is particularly fascinating due to its ground state ferromagnetism. However, because ML materials are difficult to probe experimentally, much remains unresolved about ML CrI₃'s structural, electronic, and magnetic properties. Here, we leverage Density Functional Theory (DFT) and high-accuracy Diffusion Monte Carlo (DMC) simulations to predict lattice parameters, magnetic moments, and spin-phonon and spin-lattice coupling of ML CrI₃. We exploit a recently developed surrogate Hessian DMC line search technique to determine CrI₃'s ML geometry with DMC accuracy, yielding lattice parameters in good agreement with recently published STM measurements-an accomplishment given the ∼10% variability in previous DFT-derived estimates depending upon the functional. Strikingly, we find that previous DFT predictions of ML CrI₃'s magnetic spin moments are correct on average across a unit cell but miss critical local spatial fluctuations in the spin density revealed by more accurate DMC. DMC predicts that magnetic moments in ML CrI₃ are 3.62 μ_B per chromium and -0.145 μ_B per iodine, both larger than previous DFT predictions. The large disparate moments together with the large spin-orbit coupling of CrI₃'s I-p orbital suggest a ligand superexchange-dominated magnetic anisotropy in ML CrI₃, corroborating recent observations of magnons in its 2D limit. We also find that ML CrI₃ exhibits a substantial spin-phonon coupling of ∼3.32 cm^-1. Our work, thus, establishes many of ML CrI₃'s key properties, while also continuing to demonstrate the pivotal role that DMC can assume in the study of magnetic and other 2D materials.

Giant Biquadratic Exchange in 2D Magnets and Its Role in Stabilizing Ferromagnetism of NiCl_{2} Monolayers

Two-dimensional (2D) van der Waals (vdW) magnets provide an ideal platform for exploring, on the fundamental side, new microscopic mechanisms and for developing, on the technological side, ultracompact spintronic applications. So far, bilinear spin Hamiltonians have been commonly adopted to investigate the magnetic properties of 2D magnets, neglecting higher order magnetic interactions. However, we here provide quantitative evidence of giant biquadratic exchange interactions in monolayer NiX_{2} (X=Cl, Br and I), by combining first-principles calculations and the newly developed machine learning method for constructing Hamiltonian. Interestingly, we show that the ferromagnetic ground state within NiCl_{2} single layers cannot be explained by means of the bilinear Heisenberg Hamiltonian; rather, the nearest-neighbor biquadratic interaction is found to be crucial. Furthermore, using a three-orbitals Hubbard model, we propose that the giant biquadratic exchange interaction originates from large hopping between unoccupied and occupied orbitals on neighboring magnetic ions. On a general framework, our work suggests biquadratic exchange interactions to be important in 2D magnets with edge-shared octahedra.

Anomalous Thermal Hall Effect in an Insulating van der Waals Magnet

Two-dimensional (2D) van der Waals (vdW) magnets have been a fertile playground for the discovery and exploration of physical phenomena and new physics. In this Letter, we report the observation of an anomalous thermal Hall effect (THE) with κ_{xy}∼1×10^{-2}  W K^{-1} m^{-1} in an insulating van der Waals ferromagnet VI_{3}. The thermal Hall signal persists in the absence of an external magnetic field and flips sign upon the switching of the magnetization. In combination with theoretical calculations, we show that VI_{3} exhibits a dual nature of the THE, i.e., dominated by topological magnons hosted by the ferromagnetic honeycomb lattice at higher temperatures and by phonons induced by the magnon-phonon coupling at lower temperatures. Our results not only position VI_{3} as the first ferromagnetic system to investigate both anomalous magnon and phonon THEs, but also render it as a potential platform for spintronics-magnonics applications.

Magnon-phonon hybridization in 2D antiferromagnet MnPSe3

Magnetic excitations in van der Waals (vdW) materials, especially in the two-dimensional (2D) limit, are an exciting research topic from both the fundamental and applied perspectives. Using temperature-dependent, magneto-Raman spectroscopy, we identify the hybridization of two-magnon excitations with two phonons in manganese phosphorus triselenide (MnPSe₃), a magnetic vdW material that hosts in-plane antiferromagnetism. Results from first-principles calculations of the phonon and magnon spectra further support our identification. The Raman spectra’s rich temperature dependence through the magnetic transition displays an avoided crossing behavior in the phonons’ frequency and a concurrent decrease in their lifetimes. We construct a model based on the interaction between a discrete level and a continuum that reproduces these observations. Our results imply a strong hybridization between each phonon and a two-magnon continuum. This work demonstrates that the magnon-phonon interactions can be observed directly in Raman scattering and provides deep insight into these interactions in 2D magnetic materials.

Unified Treatment of Magnons and Excitons in Monolayer CrI_{3} from Many-Body Perturbation Theory

We present first principles calculations of the two-particle excitation spectrum of CrI_{3} using many-body perturbation theory including spin-orbit coupling. Specifically, we solve the Bethe-Salpeter equation, which is equivalent to summing up all ladder diagrams with static screening, and it is shown that excitons as well as magnons can be extracted seamlessly from the calculations. The resulting optical absorption spectrum as well as the magnon dispersion agree very well with recent measurements, and we extract the amplitude for optical excitation of magnons resulting from spin-orbit interactions. Importantly, the results do not rely on any assumptions of the microscopic magnetic interactions such as Dzyaloshinskii-Moriya (DM), Kitaev, or biquadratic interactions, and we obtain a model independent estimate of the gap between acoustic and optical magnons of 0.3 meV. In addition, we resolve the magnon wave function in terms of band transitions and show that the magnon carries a spin that is significantly smaller than ℏ. This highlights the importance of terms that do not commute with S^{z} in any Heisenberg model description.

Monolayer CrCl_{3} as an Ideal Test Bed for the Universality Classes of 2D Magnetism

The monolayer halides CrX_{3} (X=Cl, Br, I) attract significant attention for realizing 2D magnets with genuine long-range order (LRO), challenging the Mermin-Wagner theorem. Here, we show that monolayer CrCl_{3} has the unique benefit of exhibiting tunable magnetic anisotropy upon applying a compressive strain. This opens the possibility to use CrCl_{3} for producing and studying both ferromagnetic and antiferromagnetic 2D Ising-type LRO as well as the Berezinskii-Kosterlitz-Thouless (BKT) regime of 2D magnetism with quasi-LRO. Using state-of-the-art density functional theory, we explain how realistic compressive strain could be used to tune the monolayer's magnetic properties so that it could exhibit any of these phases. Building on large-scale quantum Monte Carlo simulations, we compute the phase diagram of strained CrCl_{3}, as well as the magnon spectrum with spin-wave theory. Our results highlight the eminent suitability of monolayer CrCl_{3} to achieve very high BKT transition temperatures, around 50 K, due to their singular dependence on the weak easy-plane anisotropy of the material.

Spin stiffness of chromium-based van der Waals ferromagnets

Low temperature magnetization of CrI₃, CrSiTe₃and CrGeTe₃single crystals were systematically studied. Based on the temperature dependence of extrapolated spontaneous magnetization from magnetic isotherms measured at different temperatures, the spin stiffness constant (D) and spin excitation gap (Δ) were extracted according to Bloch's law. For spin stiffness,Dis estimated to be 27 ± 6 meV Ų, 20 ± 3 meV Ųand 38 ± 7 meV Ųfor CrI₃, CrSiTe₃and CrGeTe₃respectively. Spin excitation gaps determined via Bloch's formulation have larger error bars yielding 0.59 ± 0.34 meV (CrI₃), 0.37 ± 0.22 meV (CrSiTe₃) and 0.28 ± 0.19 meV (CrGeTe₃). Among all three studied compounds, larger spin stiffness value leads to higher ferromagnetic transition temperature.

Magnetoelectric Response of Antiferromagnetic CrI3 Bilayers

We predict that layer antiferromagnetic bilayers formed from van der Waals (vdW) materials with weak interlayer versus intralayer exchange coupling have strong magnetoelectric response that can be detected in dual-gated devices where internal displacement fields and carrier densities can be varied independently. We illustrate this strong temperature-dependent magnetoelectric response in bilayer CrI₃ at charge neutrality by calculating the gate voltage-dependent total magnetization through Monte Carlo simulations and mean-field solutions of the anisotropic Heisenberg model informed from density functional theory and experimental data and present a simple model for electrical control of magnetism by electrostatic doping.

Quantum Rescaling, Domain Metastability, and Hybrid Domain-Walls in 2D CrI3 Magnets

Higher-order exchange interactions and quantum effects are widely known to play an important role in describing the properties of low-dimensional magnetic compounds. Here, the recently discovered 2D van der Waals (vdW) CrI₃ is identified as a quantum non-Heisenberg material with properties far beyond an Ising magnet as initially assumed. It is found that biquadratic exchange interactions are essential to quantitatively describe the magnetism of CrI₃ but quantum rescaling corrections are required to reproduce its thermal properties. The quantum nature of the heat bath represented by discrete electron-spin and phonon-spin scattering processes induces the formation of spin fluctuations in the low-temperature regime. These fluctuations induce the formation of metastable magnetic domains evolving into a single macroscopic magnetization or even a monodomain over surface areas of a few micrometers. Such domains display hybrid characteristics of Néel and Bloch types with a narrow domain wall width in the range of 3-5 nm. Similar behavior is expected for the majority of 2D vdW magnets where higher-order exchange interactions are appreciable.

2D Polarized Materials: Ferromagnetic, Ferrovalley, Ferroelectric Materials, and Related Heterostructures

The emergence of 2D polarized materials, including ferromagnetic, ferrovalley, and ferroelectric materials, has demonstrated unique quantum behaviors at atomic scales. These polarization behaviors are tightly bonded to the new degrees of freedom (DOFs) for next generation information storage and processing, which have been dramatically developed in the past few years. Here, the basic 2D polarized materials system and related devices' application in spintronics, valleytronics, and electronics are reviewed. Specifically, the underlying physical mechanism accompanied with symmetry broken theory and the modulation process through heterostructure engineering are highlighted. These summarized works focusing on the 2D polarization would continue to enrich the cognition of 2D quantum system and promising practical applications.

Spectroscopic Determination of Key Energy Scales for the Base Hamiltonian of Chromium Trihalides

The van der Waals (vdW) chromium trihalides (CrX₃) exhibit field-tunable, two-dimensional magnetic orders that vary with the halogen species and the number of layers. Their magnetic ground states with proximity in energies are sensitive to the degree of ligand-metal (p-d) hybridization and relevant modulations in the Cr d-orbital interactions. We use soft X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS) spectroscopy at Cr L-edge along with the atomic multiplet simulations to determine the key energy scales such as the crystal field 10 Dq and interorbital Coulomb interactions under different ligand metal charge transfer (LMCT) in CrX₃ (X= Cl, Br, and I). Through this systematic study, we show that our approach compared to the literature has yielded a set of more reliably determined parameters for establishing a base Hamiltonian for CrX₃.

Colossal Magnetization and Giant Coercivity in Ion-Implanted (Nb and Co) MoS2 Crystals

Colossal saturation magnetization and giant coercivity are realized in MoS₂ single crystals doped with Nb and/or Co using an ion implantation method. Magnetic measurements have demonstrated that codoping with 2 at % Nb and 4 at % Co invoked a "giant" coercivity, as high as 9 kOe at 100 K. Doping solely with 5 at % Nb induces a "colossal" magnetization of 1800 emu/cm³ at 5 K, which is higher than that of metallic Co. The high magnetization is due to the formation of Nb-rich defect complexes, as confirmed by first-principles calculations. It is proposed that the high coercivity is due to the combined effects of strong directional exchange coupling induced by the Nb and Co doping and pinning effects from defects within the layered structure. This high magnetization mechanism is also applicable to 2D materials with bilayers or few layers of thickness, as indicated by first-principles calculations. Hence, this work opens a potential pathway for the development of 2D high-performance magnetic materials.

Imaging and control of critical fluctuations in two-dimensional magnets

Strong magnetization fluctuations are expected near the thermodynamic critical point of a continuous magnetic phase transition. Such critical fluctuations are highly correlated and in principle can occur at any time and length scales¹; they govern critical phenomena and potentially can drive new phases^2,3. Although critical phenomena in magnetic materials have been studied using neutron scattering, magnetic a.c. susceptibility and other techniques^4-6, direct real-time imaging of critical magnetization fluctuations remains elusive. Here we develop a fast and sensitive magneto-optical imaging microscope to achieve wide-field, real-time monitoring of critical magnetization fluctuations in single-layer ferromagnetic insulator CrBr₃. We track the critical phenomena directly from the fluctuation correlations and observe both slowing-down dynamics and enhanced correlation length. Through real-time feedback control of the critical fluctuations, we further achieve switching of magnetic states solely by electrostatic gating. The ability to directly image and control critical fluctuations in 2D magnets opens up exciting opportunities to explore critical phenomena and develop applications in nanoscale engines and information science.

Bosonic Bott Index and Disorder-Induced Topological Transitions of Magnons

We investigate the role of disorder on the various topological magnonic phases present in deformed honeycomb ferromagnets. To this end, we introduce a bosonic Bott index to characterize the topology of magnon spectra in finite, disordered systems. The consistency between the Bott index and Chern number is numerically established in the clean limit. We demonstrate that topologically protected magnon edge states are robust to moderate disorder and, as anticipated, localized in the strong regime. We predict a disorder-driven topological phase transition, a magnonic analog of the "topological Anderson insulator" in electronic systems, where the disorder is responsible for the emergence of the nontrivial topology. Combining the results for the Bott index and transport properties, we show that bulk-boundary correspondence holds for disordered topological magnons. Our results open the door for research on topological magnonics as well as other bosonic excitations in finite and disordered systems.

Predicted 2D ferromagnetic Janus VSeTe monolayer with high Curie temperature, large valley polarization and magnetic crystal anisotropy

The development of two-dimensional (2D) intrinsic ferromagnetic semiconductors is urgent in the spintronic field. Motivated by the recent experiments on the successful synthetization of monolayer (ML) Janus transition-metal dichalcogenides (MoSSe) and ferromagnetic (FM) VSe2, a highly stable ML Janus 2H-VSeTe is fabricated by density functional theory and confirmed by a global minimum search. The Janus VSeTe shows a large valley polarization of 158 meV as the space- and time-reversal symmetry is broken. The VSeTe shows FM order with Curie temperature (Tc) of 350 K and a sizable magnetocrystalline anisotropy (MCA) of -8.54 erg cm-2. The high Tc and large valley polarization suggest the 2D Janus VSeTe is a promising magnetic material for potential applications in electronics, spintronics, and valleytronics.

Short-Range Order in VI3

We present a detailed investigation of the crystal structure of VI₃, a two-dimensional van der Waals material of interest for studies of low-dimensional magnetism. As opposed to the average crystal structure that features R3̅ symmetry of the unit cell, our Raman scattering and X-ray atomic pair distribution function analysis supported by density functional theory calculations point to the coexistence of short-range ordered P3̅1c and long-range ordered R3̅ phases. The highest-intensity peak, A_1g³, exhibits a moderate asymmetry that might be traced back to the spin-phonon interactions, as in the case of CrI₃.

Engineering magnetic anisotropy and exchange couplings in double transition metal MXenes via surface defects

Two-dimensional (2D) materials have been experimentally proven to manifest almost all types of material properties observed in bulk materials. However, 2D magnetism was elusive until recently. In this work, we used an approach that synergistically uses density functional theory, and Monte Carlo methods to investigate the magnetic and electronic properties of magnetic double transition metal MXene alloys (Hf₂MnC₂O₂and Hf₂VC₂O₂) by exploiting realistic surface terminations via creating surface defects including oxygen vacancies and H adatoms. We found that introducing surface oxygen vacancies or hydrogen adatoms is able to modify the electronic structures, magnetic anisotropies, and exchange couplings. Depending on the defect concentration, a ferromagnetic half-metallic state can be realized for both Hf₂VC₂O₂and Hf₂MnC₂O₂. Bare Hf₂VC₂O₂exhibits easy-axis anisotropy, whereas bare Hf₂MnC₂O₂exhibits easy-plane anisotropy; however, defects can change the latter to easy-axis anisotropy, which is preferable for spintronics applications. The considered defects were found to modify the magnetic anisotropy by as much as 300%. Defects also produce an inhomogeneous pattern of exchange couplings, which can further enhance the Curie temperature. In particular, Hf₂MnC₂O₂H_0.22was predicted to have a Curie temperature of about 171 K due to a combination of easy-axis anisotropy and a connected network of enhanced exchange couplings. Our calculations suggest a route toward engineering exchange couplings and magnetic anisotropy to improve magnetic properties.

Valence band electronic structure of the van der Waals ferromagnetic insulators: VI[Formula: see text] and CrI[Formula: see text]

Ferromagnetic van der Waals (vdW) insulators are of great scientific interest for their promising applications in spintronics. It has been indicated that in the two materials within this class, CrI[Formula: see text] and VI[Formula: see text], the magnetic ground state, the band gap, and the Fermi level could be manipulated by varying the layer thickness, strain or doping. To understand how these factors impact the properties, a detailed understanding of the electronic structure would be required. However, the experimental studies of the electronic structure of these materials are still very sparse. Here, we present the detailed electronic structure of CrI[Formula: see text] and VI[Formula: see text] measured by angle-resolved photoemission spectroscopy (ARPES). Our results show a band-gap of the order of 1 eV, sharply contrasting some theoretical predictions such as Dirac half-metallicity and metallic phases, indicating that the intra-atomic interaction parameter (U) and spin-orbit coupling (SOC) were not properly accounted for in the calculations. We also find significant differences in the electronic properties of these two materials, in spite of similarities in their crystal structure. In CrI[Formula: see text], the valence band maximum is dominated by the I 5p, whereas in VI[Formula: see text] it is dominated by the V 3d derived states. Our results represent valuable input for further improvements in the theoretical modeling of these systems.

Magnetic Two-Dimensional Chromium Trihalides: A Theoretical Perspective

The discovery of ferromagnetic order in monolayer two-dimensional (2D) crystals has opened a new venue in the field of 2D materials. Two-dimensional magnets are not only interesting on their own, but their integration in van der Waals heterostructures allows for the observation of new and exotic effects in the ultrathin limit. The family of chromium trihalides, CrI₃, CrBr₃, and CrCl₃, is so far the most studied among magnetic 2D crystals. In this Mini Review, we provide a perspective of the state of the art of the theoretical understanding of magnetic 2D trihalides, most of which will also be relevant for other 2D magnets, such as vanadium trihalides. We discuss both the well-established facts, such as the origin of the magnetic moment and magnetic anisotropy, and address as well open issues such as the nature of the anisotropic spin couplings and the magnitude of the magnon gap. Recent theoretical predictions on Moiré magnets and magnetic skyrmions are also discussed. Finally, we give some prospects about the future interest of these materials and possible device applications.

Distinct magneto-Raman signatures of spin-flip phase transitions in CrI3

The discovery of 2-dimensional (2D) materials, such as CrI₃, that retain magnetic ordering at monolayer thickness has resulted in a surge of both pure and applied research in 2D magnetism. Here, we report a magneto-Raman spectroscopy study on multilayered CrI₃, focusing on two additional features in the spectra that appear below the magnetic ordering temperature and were previously assigned to high frequency magnons. Instead, we conclude these modes are actually zone-folded phonons. We observe a striking evolution of the Raman spectra with increasing magnetic field applied perpendicular to the atomic layers in which clear, sudden changes in intensities of the modes are attributed to the interlayer ordering changing from antiferromagnetic to ferromagnetic at a critical magnetic field. Our work highlights the sensitivity of the Raman modes to weak interlayer spin ordering in CrI₃.

Gate-tunable spin waves in antiferromagnetic atomic bilayers

Remarkable properties of two-dimensional (2D) layer magnetic materials, which include spin filtering in magnetic tunnel junctions and the gate control of magnetic states, were demonstrated recently^1-12. Whereas these studies focused on static properties, dynamic magnetic properties, such as excitation and control of spin waves, remain elusive. Here we investigate spin-wave dynamics in antiferromagnetic CrI₃ bilayers using an ultrafast optical pump/magneto-optical Kerr probe technique. Monolayer WSe₂ with a strong excitonic resonance was introduced on CrI₃ to enhance the optical excitation of spin waves. We identified subterahertz magnetic resonances under an in-plane magnetic field, from which the anisotropy and interlayer exchange fields were determined. We further showed tuning of the antiferromagnetic resonances by tens of gigahertz through electrostatic gating. Our results shed light on magnetic excitations and spin dynamics in 2D magnetic materials, and demonstrate their potential for applications in ultrafast data storage and processing.

Accessing new magnetic regimes by tuning the ligand spin-orbit coupling in van der Waals magnets

Van der Waals (VdW) materials have opened new directions in the study of low dimensional magnetism. A largely unexplored arena is the intrinsic tuning of VdW magnets toward new ground states. Chromium trihalides provided the first such example with a change of interlayer magnetic coupling emerging upon exfoliation. Here, we take a different approach to engineer previously unknown ground states, not by exfoliation, but by tuning the spin-orbit coupling (SOC) of the nonmagnetic ligand atoms (Cl, Br, I). We synthesize a three-halide series, CrCl3 - x - y Br x I y , and map their magnetic properties as a function of Cl, Br, and I content. The resulting triangular phase diagrams unveil a frustrated regime near CrCl3. First-principles calculations confirm that the frustration is driven by a competition between the chromium and halide SOCs. Furthermore, we reveal a field-induced change of interlayer coupling in the bulk of CrCl3 - x - y Br x I y crystals at the same field as in the exfoliation experiments.

Two-Dimensional van der Waals Nanoplatelets with Robust Ferromagnetism

We have synthesized unique colloidal nanoplatelets of the two-dimensional (2D) van der Waals ferromagnet CrI₃ and have characterized these nanoplatelets structurally, magnetically, and by magnetic circular dichroism spectroscopy. The CrI₃ nanoplatelets have lateral dimensions of ∼25 nm and thicknesses of only ∼4 nm, corresponding to just a few CrI₃ monolayers. Magnetic and magneto-optical measurements demonstrate robust 2D ferromagnetic ordering with Curie temperatures similar to bulk CrI₃, despite their small size. These data also show magnetization steps akin to those observed in micron-sized few-layer 2D sheets associated with concerted spin-reversal of individual CrI₃ layers within few-layer van der Waals stacks. Similar data have also been obtained for CrBr₃ and anion-alloyed Cr(I_1-xBr_x)₃ nanoplatelets. These results represent the first example of lateral nanostructures of 2D van der Waals ferromagnets of any composition. The demonstration of robust ferromagnetism at nanometer lateral dimensions opens new doors for miniaturization in spintronics devices based on van der Waals ferromagnets.

Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2

Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold promise for quantum computing and quantum information. Among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., RuCl_{3} and Na_{2}IrO_{3}, having an effective S=1/2 spin value. Here, via extensive first-principles-based simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as CrSiTe_{3}, that rather possess a S=3/2 spin value. Our study thus extends the playground of Kitaev physics and QSLs to 3d transition metal compounds.

Synthesis, structural, and electronic properties of Sr1−xCaxPdAs

.This work maps out the structural and electronic phase diagram of Sr_1-xCa_xPdAs, a unique family of layered intermetallic honeycomb phases in which the PdAs layers distort away from ideal hexagonal symmetry.