We present a density functional theory (DFT) based study of a two-dimensional phase of chromium bismuthate (CrBi), previously unknown material with exceptional magnetic and magnetooptical characteristics. Monolayer CrBi is a ferromagnetic metal with strong spin-orbit coupling induced by the heavy bismuth atoms, resulting in a strongly anisotropic Ising-type magnetic ordering with the Curie temperature estimated to be higher than 300 K. The electronic structure of the system is topologically nontrivial, giving rise to a nonzero Berry curvature in the ground magnetic state, leading to the anomalous Hall effect with the conductivity plateau of $\sim$1.5 $e^2/h$ at the Fermi level. Remarkably, the Hall conductivity and the magnetooptical constant are found to be strongly dependent on the direction of magnetization. Besides, monolayer CrBi demonstrates the polar magnetooptical Kerr effect in the visible and near-ultraviolet spectral ranges with the maximum rotation angles of up to 10 mrad. Our findinds suggest that monolayer CrBi is a promising system for practical applications in magnetooptical and spintronic devices.
We build a microscopic model to study the intra- and inter-layer superexchange due to electrons hopping in chromium trihalides ($\mathrm{CrX}_3$, X= Cl, Br, and I). In evaluating the superexchange, we identify the relevant intermediate excitations in the hopping. In our study, we find that the intermediate hole-pairs excitations in the $p$-orbitals on X ion play a crucial role in mediating various types of exchange interactions. In particular, the inter-layer antiferromagnetic exchange may be realized by the hole-pair-mediated superexchange. Interestingly, we also find that these virtual hoppi…
Topological crystalline insulator (TCI) is a recently-discovered topological phase of matter. It possesses multiple Dirac surface states, which are protected by the crystal symmetry. This is in contrast to the time reversal symmetry that is operative in the well-known topological insulators. In the presence of a Zeeman field and/or strain, the multiple Dirac surface states are gapped. The high-Chern-number quantum anomalous Hall (QAH) state is predicted to emerge if the chemical potential resides in all the Zeeman gaps. Here, we use molecular beam epitaxy to grow 12 double layer (DL) pure and …
We calculate the Curie temperature of layered ferromagnets, chromium tri-iodide (CrI3), chromium tri-bromide (CrBr3), chromium germanium tri-telluride (CrGeTe3), and the Neel temperature of a layered anti-ferromagnet iron di-chloride (FeCl2), using first-principles density functional theory calculations and Monte-Carlo simulations. We develop a computational method to model the magnetic interactions in layered magnetic materials and calculate their critical temperature. We provide a unified method to obtain the magnetic exchange parameters (J) for an effective Heisenberg Hamiltonian from first…
The discovery of ferromagnetic order in monolayer 2D crystals has opened a new venue in the field of two dimensional (2D) materials. 2D 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, CrI$_3$, CrBr$_3$ and CrCl$_3$, 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 rel…
As a 2D ferromagnetic semiconductor with magnetic ordering, atomically thin chromium triiodide is the latest addition to the family of two-dimensional (2D) materials. However, realistic exploration of CrI3-based devices and heterostructures is challenging, due to its extreme instability under ambient conditions. Here we present Raman characterization of CrI3, and demonstrate that the main degradation pathway of CrI3 is the photocatalytic substitution of iodine by water. While simple encapsulation by Al2O3, PMMA and hexagonal BN (hBN) only leads to modest reduction in degradation rate, minimizi…
Two-dimensional materials have been gaining great attention as they displayed a broad series of electronic properties that ranging from superconductivity to topology. Among them, those which possess magnetism are most desirable, enabling us to manipulate charge and spin simultaneously. Here, based on first-principles calculation, we demonstrate monolayer chromium iodide arsenide (CrIAs), an undiscovered stable two-dimensional material, is an intrinsic ferromagnetic semiconductor with out-of-plane spin magnetization. The indirect bandgaps are predicted to be 0.32 eV for majority spin and 3.31 e…
Recent realizations of intrinsic magnetic order in truly two-dimensional materials have opened new avenues in the fundamental knowledge and spintronic applications. Here we develop an anisotropic Heisenberg model with relativistic exchange interactions that are obtained from the first-principles calculations. We demonstrate the crucial importance of magnetic interactions beyond the first-neighbour to qualitatively and quantitatively reproduce the experimental results. Once we ascertain the predictive capacity of the model for chromium trihalides and CrGeTe$_3$, we investigate the feasibility o…
The study of atomically thin ferromagnetic crystals has led to the discovery of unusual magnetic behaviour and provided insight into the magnetic properties of bulk materials. However, the experimental techniques that have been used to explore ferromagnetism in such materials cannot probe the magnetic field directly. Here, we show that ballistic Hall micromagnetometry can be used to measure the magnetization of individual two-dimensional ferromagnets. Our devices are made by van der Waals assembly in such a way that the investigated ferromagnetic crystal is placed on top of a multi-terminal Ha…
Recent observation of intrinsic ferromagnetism in two-dimensional (2D) CrI$_3$ is associated with the large magnetic anisotropy due to strong spin-orbit coupling (SOC) of I. Magnetic anisotropy energy (MAE) defines the stability of magnetization in a specific direction with respect to the crystal lattice and is an important parameter for nanoscale applications. In this work we apply the density functional theory to study the strain dependence of MAE in 2D monolayer chromium trihalides CrX$_3$ (with X = Cl, Br, and I). Detailed calculations of their energetics, atomic structures and electronic …
Observation of Orbit-Orbit Torques: Highly Efficient Torques on Orbital Moments Induced by Orbital Currents
School of Materials Science and Engineering, Beihang University（北京航空航天大学材料科学与工程学院）；State Key Laboratory of Tropic Ocean Engineering Materials and Materials Evaluation, Beihang University（北京航空航天大学热带海洋工程材料与材料评估国家重点实验室）
We report on first-principle calculations on magnetic proximity effect in a van der Waals heterostructure formed by a graphene monolayer induced by its interaction with a two-dimensional (2D) ferromagnet (chromium tribromide, CrBr3). We observe that the magnetic proximity effect arising from the spin-dependent interlayer coupling depends sensitively on the interlayer electronic configuration. The proximity effect results in spin polarization of graphene orbital by up to 63.6 %, together with a miniband splitting band gap of about 73.4 meV and 8% enhancement in magnetic moment (3.47$μ$B/cell) i…
The superconducting and magnetic properties of the (Fe/Cr/Fe)/V/Fe layered system with variable thickness of the chromium layer have been experimentally and theoretically studied. The magnetic properties of the system have been studied by the ferromagnetic resonance method, and the superconducting transition temperature has been measured from the jump in the magnetic susceptibility. A wide variety of magnetic states are observed in the system; in particular, the structure of small domains can arise in the iron layer placed between vanadium and chromium. It has been shown experimentally that th…
The recently reported magnetic ordering in insulating two-dimensional (2D) materials, such as chromium triiodide (CrI$_3$) and chromium tribromide (CrBr$_3$), opens new possibilities for the fabrication of magneto-electronic devices based on 2D systems. Inevitably, the magnetization and spin dynamics in 2D magnets are strongly linked to Joule heating. Therefore, understanding the coupling between spin, charge and heat, i.e. spin caloritronic effects, is crucial. However, spin caloritronics in 2D ferromagnets remains mostly unexplored, due to their instability in air. Here we develop a fabricat…
Multiferroic materials with coupled ferroelectric and ferromagnetic properties are important for multifunctional devices due to their potential ability of controlling magnetism via electric field, and vice versa. The recent discoveries of two-dimensional ferromagnetic and ferroelectric materials have ignited tremendous research interest and aroused hope to search for two-dimensional multiferroics. However, intrinsic two-dimensional multiferroic materials and, particularly, those with strong magnetoelectric couplings are still rare to date. In this paper, using first-principles simulations, we …
The discovery of atomically thin two-dimensional (2D) magnetic semiconductors has triggered enormous research interest recently. In this work, we use first-principles many-body perturbation theory to study a prototypical 2D ferromagnetic semiconductor, monolayer chromium tribromide (CrBr$_3$). With broken time-reversal symmetry, spin-orbit coupling, and excitonic effects included through the full-spinor $GW$ and $GW$ plus Bethe-Salpeter equation ($GW$-BSE) methods, we compute the frequency-dependent layer polarizability tensor and dielectric function tensor that govern the optical and magneto-…
The ability to imprint a given material property to another through proximity effect in layered two-dimensional materials has opened the way to the creation of designer materials. Here, we use molecular-beam epitaxy (MBE) for a direct synthesis of a superconductor-magnet hybrid heterostructure by combining superconducting niobium diselenide (NbSe$_2$) with the monolayer ferromagnetic chromium tribromide (CrBr$_3$). Using different characterization techniques and density-functional theory (DFT) calculations, we have confirmed that the CrBr$_3$ monolayer retains its ferromagnetic ordering with a…
Current-induced spin-orbit torque on the surface of a transition metal dichalcogenide connected to a two-dimensional ferromagnet CrI$_3$: Effects of twisting and gating
Shahid Chamran University of Ahvaz（阿瓦士沙希德·恰姆兰大学）；Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）；Zhejiang Normal University（浙江师范大学）
Chromium triiodide, CrI$_3$, is emerging as a promising magnetic two-dimensional semiconductor where spins are ferromagnetically aligned within a single layer. Potential applications in spintronics arise from an antiferromagnetic ordering between adjacent layers that gives rise to spin filtering and a large magnetoresistance in tunnelling devices. This key feature appears only in thin multilayers and it is not inherited from bulk crystals, where instead neighbouring layers share the same ferromagnetic spin orientation. This discrepancy between bulk and thin samples is unexpected, as magnetic o…
We apply the density-functional theory to study various phases (including non-magnetic (NM), anti-ferromagnetic (AFM), and ferromagnetic (FM)) in monolayer magnetic chromium triiodide (CrI$_3$), a recently fabricated 2D magnetic material. It is found that: (1) the introduction of magnetism in monolayer CrI$_3$ gives rise to metal-to-semiconductor transition; (2) the electronic band topologies as well as the nature of direct and indirect band gaps in either AFM or FM phases exhibit delicate dependence on the magnetic ordering and spin-orbit coupling; and (3)the phonon modes involving Cr atoms a…
Exfoliated chromium triiodide (CrI$_3$) is a layered van der Waals (vdW) magnetic insulator that consists of ferromagnetic layers coupled through antiferromagnetic interlayer exchange. The resulting permutations of magnetic configurations combined with the underlying crystal symmetry produces tunable magneto-optical phenomena that is unique to the two-dimensional (2D) limit. Here, we report the direct observation of 2D magnons through magneto-Raman spectroscopy with optical selection rules that are strictly determined by the honeycomb lattice and magnetic states of atomically thin CrI$_3$. In …
Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators
量子反常霍尔绝缘体是一种二维绝缘态，在没有外加磁场的情况下，表现出与量子霍尔态相似的性质。它们具有量子化的霍尔电导$σ^H=Ce^2/h$，其中整数$C$被称为陈数，并且表示无间隙边缘模式的数量。最近的实验表明，掺铬薄膜（Bi，Sb）$_2$ Te $_3$是一种QAH绝缘体，具有陈数$C=\pm1$。在这里，我们从理论上预测，薄膜拓扑晶体绝缘体（TCI）可以托管各种QAH相，当掺杂铁磁有序掺杂剂。$\pm4$之间的任何陈氏数原则上可以作为（a）取决于磁掺杂浓度的感应塞曼场，（b）固有的或由压电材料通过邻近效应感应的结构变形，以及（c）薄膜的厚度之间的相互作用的结果而达到。在TCI中发现的可调陈氏数在超低功耗信息处理应用中具有重要的潜力。
The designer approach has become a new paradigm in accessing novel quantum phases of matter. Moreover, the realization of exotic states such as topological insulators, superconductors and quantum spin liquids often poses challenging or even contradictory demands for any single material. For example, it is presently unclear if topological superconductivity, which has been suggested as a key ingredient for topological quantum computing, exists at all in any naturally occurring material . This problem can be circumvented by using designer heterostructures combining different materials, where the …
Noncollinear spin textures in low-dimensional magnetic systems have been studied for decades because of their extraordinary properties and promising applications derived from the chirality and topological nature. However, material realizations of topological spin states are still limited. Employing first-principles and Monte Carlo simulations, we propose that monolayer chromium trichloride (CrCl3) can be a promising candidate for observing the vortex/antivortex type of topological defects, so-called merons. The numbers of vortices and antivortices are found to be the same, maintaining an overa…
Atomically thin chromium triiodide (CrI3) has recently been identified as a layered antiferromagnetic insulator, in which adjacent ferromagnetic monolayers are antiferromagnetically coupled. This unusual magnetic structure naturally comprises a series of anti-aligned spin filters which can be utilized to make spin-filter magnetic tunnel junctions with very large tunneling magnetoresistance (TMR). Here we report voltage control of TMR formed by four-layer CrI3 sandwiched by monolayer graphene contacts in a dual-gated structure. By varying the gate voltages at fixed magnetic field, the device ca…
Resulting from strong magnetic anisotropy two-dimensional ferromagnetism was recently shown to be stabilized in chromium triiodide, CrI$_3$, in the monolayer limit. While its properties remain largely unexplored, it provides a unique material-specific platform to unveil its electromagnetic properties associated with coupling of modes. Indeed, trigonal symmetry in the presence of out-of-plane magnetization results in a non-trivial structure of the conductivity tensor, including the off-diagonal terms. In this paper, we study the surface electromagnetic waves localized in a CrI$_3$-based structu…
The coupling between spin and charge degrees of freedom in a crystal imparts strong optical signatures on scattered electromagnetic waves. This has led to magneto-optical effects with a host of applications, from the sensitive detection of local magnetic order to optical modulation and data storage technologies. Here, we demonstrate a new magneto-optical effect, namely, the tuning of inelastically scattered light through symmetry control in atomically thin chromium triiodide (CrI$_3$). In monolayers, we found an extraordinarily large magneto-optical Raman effect from an A$_{1g}$ phonon mode du…
