Bilayer CrI3 Research Articles

Robust Electric-Field Control of Colossal Exchange Bias in CrI3 Homotrilayer.

Controlling exchange bias (EB) by electric fields is crucial for next-generation magnetic random access memories and spintronics with ultralow energy consumption and ultrahigh speed. Multiferroic heterostructures have been traditionally used to electrically control EB and interfacial ferromagnetism through weak/indirect coupling between ferromagnetic and ferroelectric films. However, three major bottlenecks (lattice mismatch, interface defects, and weak/indirect coupling in multiferroic heterostructures) remain, resulting in only a few tens of milli-tesla EB field. Here, this study reports a robust electric-field control recipe to dynamically tailor the EB effect in a pure CrI3 homotrilayer on a ferroelectric Y-doped HfO2 (HYO) substrate, and demonstrate a colossal and tunable EB field (HE) from -0.15 to +0.33 T, giving rise to an EB modulation of 0.48 T. The charge doping due to ferroelectric HYO film divides a homo-configuration of CrI3 homotrilayer into one antiferromagnetic (AFM) bilayer CrI3 and one ferromagnetic (FM) monolayer CrI3, favoring direct exchange coupling. The synergies of charge doping and electric field induce a transition of magnetic orders from AFM to FM phase in bilayer CrI3, which is also supported by first-principles calculations, leading to the robust electric control of colossal EB effect. The results therefore open numerous opportunities for exploring 2D spintronics, memories, and braininspired in-memory computing.

Magnetic bilayer qubits: A bipartite quantum system

An exfoliated monolayer CrI3 possessing the ferromagnetic (FM) nature of out-of-plane Ising spin-up (or spin-down) electrons can be considered as a qubit with a quantum state of |ѱ>=|↑>=|0> (or |ѱ>=|↓>=|1>) due to the theory of the Bloch sphere. Therefore, here a bipartite quantum system of the antiferromagnetic (AFM) and FM bilayer CrI3 is proposed for four fundamental two-qubit (2Q) quantum states (≡|ѱѱ>) of |↑↓>=|01>, |↓↑>=|10>, |↑↑>=|00> and |↓↓>=|11>, respectively. Energy-resolved magnetic circular dichroism (MCD) spectropolarimetry was used to detect d-d transitions of the FM and AFM bilayer CrI3 for the four fundamental quantum states. The obtained MCD spectra of the d-d transitions with spin-frustration and spin-parallelism possess quantum signals of the four fundamental 2Q quantum states at θB = 0, where θB is the angle between the magnetic field and the surface normal. Hence, the bilayer CrI3 is a potential candidate for use in quatum computer.

Deep learning methods for Hamiltonian parameter estimation and magnetic domain image generation in twisted van der Waals magnets

The application of twist engineering in van der Waals magnets has opened new frontiers in the field of two-dimensional magnetism, yielding distinctive magnetic domain structures. Despite the introduction of numerous theoretical methods, limitations persist in terms of accuracy or efficiency due to the complex nature of the magnetic Hamiltonians pertinent to these systems. In this study, we introduce a deep-learning approach to tackle these challenges. Utilizing customized, fully connected networks, we develop two deep-neural-network kernels that facilitate efficient and reliable analysis of twisted van der Waals magnets. Our regression model is adept at estimating the magnetic Hamiltonian parameters of twisted bilayer CrI3 from its magnetic domain images generated through atomistic spin simulations. The ‘generative model’ excels in producing precise magnetic domain images from the provided magnetic parameters. The trained networks for these models undergo thorough validation, including statistical error analysis and assessment of robustness against noisy injections. These advancements not only extend the applicability of deep-learning methods to twisted van der Waals magnets but also streamline future investigations into these captivating yet poorly understood systems.

Coexistence of Ferromagnetism and Ferroelectricity in Cu-Intercalated Bilayer CrI3.

Design of two-dimensional (2D) multiferroic materials with two or more ferroic orders in one structure is highly desired in view of the development of next-generation electronic devices. Unfortunately, experimental or theoretical discovery of 2D intrinsic multiferroic materials is rare. Using first-principles calculation methods, we report the realization of multiferroics that couple ferromagnetism and ferroelectricity by intercalating Cu atoms in bilayer CrI3, Cux@bi-CrI3 (x = 0.03, 0.06, and 0.25). Our results show that the intercalation of Cu atoms leads to the inversion symmetry breaking of bilayer CrI3 and produces intercalation density-dependent out-of-plane electric polarization, around 18.84-90.31 pC·cm-2. Moreover, the switch barriers of Cux@bi-CrI3 in both polarization states are small, ranging from 0.31 to 0.69 eV. Furthermore, the magnetoelectric coupling properties of Cux@bi-CrI3 can be modulated via varying the metal ion intercalation density, and half-metal to semiconductor transition can be occurred by decreasing the intercalation density of metal ions. Our work paves a practical path for 2D magnetoelectron coupling devices.

Delving into the anisotropic interlayer exchange in bilayer CrI3

Bilayer CrI3 attracted much attention due to stacking-induced switching between the layered ferromagnetic and antiferromagnetic order. This discovery brought under the spotlight the interlayer Cr–Cr exchange interaction, which despite being much weaker than the intralayer exchange, plays an important role in shaping the magnetic properties of bilayer CrI3. In this work we delve into the anisotropic part of the interlayer exchange with the aim to separate the contributions from the Dzyaloshinskii–Moriya (DMI) and the Kitaev interactions (KI). We leverage the density functional theory calculations with spin Hamiltonian modeling and develop an energy mapping procedure to assess these anisotropic interactions with accuracy. After inspecting the rhombohedral and monoclinic stacking sequences of bilayer CrI3, we reveal a considerable DMI and a weak interlayer KI between the sublattices of a monoclinic bilayer. We explain the dependence of DMI and KI on the interlayer distance, stacking sequence, and the spin–orbit coupling strength, and we suggest the dominant superexchange processes at play. In addition, we demonstrate that the single-ion anisotropy in bilayer CrI3 is highly stacking-dependent, increasing by 50% from monoclinic to rhombohedral bilayer. Remarkably, our findings prove that iodines are highly efficient in mediating the DMI across the van der Waals gap, much owing to spatially extended 5p orbitals which feature strong spin–orbit coupling. Our study gives promise that the interlayer chiral control of spin textures, demonstrated in thin metallic films where the DMI is with a much longer range, can be achieved with similar efficiency in semiconducting two-dimensional van der Waals magnets.

Magnetization Process in Bilayer Honeycomb Spin Lattice

The magnetization process of the AA-stacked bilayer honeycomb spin lattice in the out-of-plane applied field is examined in the framework of the Ising model and mean field approximation. Competition between different kinds (antiferromagnetic: AF, or ferromagnetic: FM) of intra-layer and inter-layer spin exchange couplings could lead to the first order magnetization process, characterized by sharp jumps in magnetization curves occurring in critical external fields (spin-flop and spin- flip fields). There is only the spin-flip field at very low temperature and its magnitude depends not only on the intra-layer frustration level but also exchange coupling between spin layers. During the magnetization process, the initial AF bilayer honeycomb spin lattice may undergo ferrimagnetic or week-ferromagnetic states before reaching full ferromagnetic saturation state by the spin-flip field. The results of this work can be applied for an explanation of the spin-flip phenomenon registered in the AF bilayer CrI3.

Photoinduced Ultrafast Phase Transition in Bilayer CrI3.

In two-dimensional magnets, the ultrafast photoexcited method represents a low-power and high-speed method of switching magnetic states. Bilayer CrI3 (BLC) is an ideal platform for studying ultrafast photoinduced magnetic phase transitions due to its stacking-dependent magnetic properties. Here, by using time-dependent density functional theory, we explore the photoexcitation phase transition in BLC from the R- to M-stacked phase. This process is found to be induced by electron-phonon interactions. The activated Ag and Bg phonon modes in the xy direction drive the horizontal relative displacements between the layers. The activated Ag mode in the z direction leads to a transition potential reduction. Furthermore, this phase transition can invert the sign of the interlayer spin interaction, indicating a photoinduced transition from ferromagnet to antiferromagnet. This investigation has profound implications for magnetic phase engineering strategies.

Electrically tunable lateral spin-valve transistor based on bilayer CrI3

The recent discovery of two-dimensional (2D) magnetic materials has opened new frontiers for the design of nanoscale spintronic devices. Among 2D nano-magnets, bilayer CrI3 outstands for its antiferromagnetic interlayer coupling and its electrically-mediated magnetic state control. Here, leveraging on CrI3 magnetic and electrical properties, we propose a lateral spin-valve transistor based on bilayer CrI3, where the spin transport is fully controlled via an external electric field. The proposed proof-of-concept device, working in the ballistic regime, is able to both filter (>99%) and select ON/OFF the spin current up to a ratio of ≈102, using a double split-gate architecture. Our results obtained exploiting a multiscale approach ranging from first-principles to out-of-equilibrium transport calculations, open unexplored paths towards the exploitation of bilayer CrI3 or related 2D nano-magnets, as a promising platform for future electrically tunable, compact, and scalable spintronic devices.

General Theory for Bilayer Stacking Ferroelectricity.

Two-dimensional (2D) ferroelectrics, which are rare in nature, enable high-density nonvolatile memory with low energy consumption. Here, we propose a theory of bilayer stacking ferroelectricity (BSF), in which two stacked layers of the same 2D material, with different rotation and translation, exhibit ferroelectricity. By performing systematic group theory analysis, we find all the possible BSF in all 80 layer groups (LGs) and discover the rules about the creation and annihilation of symmetries in the bilayer. Our general theory can not only explain all the previous findings (including sliding ferroelectricity), but also provide a new perspective. Interestingly, the direction of the electric polarization of the bilayer could be totally different from that of the single layer. In particular, the bilayer could become ferroelectric after properly stacking two centrosymmetric nonpolar monolayers. By means of first-principles simulations, we predict that the ferroelectricity and thus multiferroicity can be introduced to the prototypical 2D ferromagnetic centrosymmetric material CrI_{3} by stacking. Furthermore, we find that the out-of-plane electric polarization in bilayer CrI_{3} is interlocked with the in-plane electric polarization, suggesting that the out-of-plane polarization can be manipulated in a deterministic way through the application of an in-plane electric field. The present BSF theory lays a solid foundation for designing a large number of bilayer ferroelectrics and thus colorful platforms for fundamental studies and applications.

Two-Dimensional Intercalating Multiferroics with Strong Magnetoelectric Coupling.

Intrinsic two-dimensional (2D) multiferroics that couple ferromagnetism and ferroelectricity are rare. Here, we present an approach to achieve 2D multiferroics using powerful intercalation technology. In this approach, metal atoms such as Cu or Ag atoms are intercalated in bilayer CrI3 to form Cu(CrI3)4 or Ag(CrI3)4. The intercalant leads to the inversion symmetry breaking and produces a large out-of-plane electric polarization with a low transition barrier and a small reversal electric field, exhibiting excellent 2D ferroelectric properties. In addition, due to charge transfer between the intercalated atoms and bilayer CrI3, the interlayer coupling transits from antiferromagnetic to ferromagnetic, and the intralayer ferromagnetic coupling is also enhanced. Furthermore, the built-in electric polarization causes a distinct surface magnetization difference, generating a strong magnetoelectric coupling with a coefficient larger than that of Fe, Co, and Ni thin films. Our work paves a practical path for 2D multiferroics, which may have crucial applications in spintronics.

Magnetic Skyrmion Lattices in a Novel 2D‐Twisted Bilayer Magnet

AbstractMagnetic skyrmions are topologically protected spin swirling vertices, which are promising in device applications due to their particle‐like nature and excellent controlability. Magnetic skyrmions are extensively studied in a variety of materials and proposed to exist in the extreme 2D limit, i.e., in twisted bilayer CrI3 (TBCI). Unfortunately, the magnetic states of TBCIs with small twist angles are disorderly distributed ferromagnetic and antiferromagnetic (AFM) domains in recent experiments, and thus the method to get rid of disorders in TBCIs is highly desirable. Here, intralayer exchange interactions up to the third nearest neighbors without empirical parameters and very accurate interlayer exchange interactions are used to study the magnetic states of TBCIs. The functions of interlayer exchange interactions obtained using first‐principles calculations and stored in symmetry‐adapted artificial neural networks are proposed. Based on these, the subsequent Landau–Lifshitz–Gillbert equation calculations explain the disorderly distributed FM‐AFM domains in TBCIs with small twist angles and predict the orderly distributed skyrmions in TBCIs with large twist angles. This novel twisted 2D bilayer magnet can be used to design memory devices, monochromatic spin wave generators and many kinds of skyrmion lattices.

Understanding External Pressure Effects and Interlayer Orbital Exchange Pathways in the Two-Dimensional Magnet─Chromium Triiodide

Recent experiments have shown that exfoliated few-layer CrI3, a prototypical van der Waals magnet, undergoes a phase transition from the high-temperature monoclinic structure to the low-temperature rhombohedral structure under pressure. To understand how the magnetism of CrI3 responds to these structural changes, we perform ab initio density functional theory simulations on bilayer CrI3. We simulate the interlayer lateral shift-dependent potential energy surface of bilayer CrI3 to examine the stability and magnetism as a function of external pressure. Using the hybrid PBE0 functional, we are able to give qualitatively correct exchange coupling energies, without using an on-site Coulomb interaction correction. Thus, we avoid using tunable parameters. The results show that under external pressure, the monoclinic crystal structure is destabilized in comparison with the rhombohedral structure, in agreement with the observed phase transition in few-layer CrI3 devices under pressure. We also look into the microscopic origins of the interlayer exchange coupling. We identify the competing orbital pathways that favor ferromagnetic and antiferromagnetic kinetic exchange, respectively, which are consistent with previous reports. This study opens a new direction of using hybrid functionals with Gaussian orbitals and a cluster-based approach for obtaining Heisenberg J values to accurately simulate the magnetic properties of 2D materials.

Antiferromagnetic-configuration–dependent high harmonic generation in bilayer CrI3

Bilayer CrI3 accommodates both interlayer antiferromagnetic (AFM) and intralayer ferromagnetic couplings. Different alignments of intralayer ferromagnetic orders would lead to almost degenerate AFM configurations, which are insensitive to conventional techniques such as VSM and magneto-optical Kerr effect. Here, we demonstrate high harmonic generation (HHG) as a feasible means to detect the AFM configurations in bilayer CrI3 with AB and stacking orders. When the intralayer magnetic moments are aligned along the z-axis, the AB stacked bilayer CrI3 cancels the 3n-order harmonics under the circularly polarized laser field. However, the stacked bilayer contains both even and odd harmonic. The 3n-order harmonics are recovered as the intralayer magnetic moments of AB bilayer are in-plane aligned. For an in-plane linearly polarized laser field, the stacking bilayer with the magnetic moments along the x-axis contains both the even and odd harmonics in each component. However, when the magnetic moments are along the y-axis, the perpendicular component of HHG cancels out for the linearly polarized laser field along the x-axis. More interestingly, when the linearly polarized laser field is along the y-axis, the parallel component includes only the odd harmonics while the perpendicular component contains only the even harmonics. Our study provides HHG as a potential tool to detect AFM configurations.

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.

Interlayer Hopping Kinetics of Vacancies in CrI3 Layers Leading to Monolayer/Bilayer Heterostructures

Abstract2D magnets, especially their multilayer structures exhibit promising applications in magnetic sensing and data storage due to magnetoresistance effect. Defects have significant influence on the performance of devices and are widely investigated for typical 2D magnets. However, the defects in multilayer structures are rarely studied. Here, based on density functional theory, an interesting synergy of the interlayer migration of I and Cr vacancies in bilayer CrI3 is found. Cr vacancies attract I vacancies in adjacent layers and greatly reduce the intermigration barrier of I. On the other hand, I vacancies also facilitate the interlayer migration of Cr vacancies. A monolayer/bilayer heterostructure is expected to form after annealing at about 500 K due to the fast hopping of vacancies between layers and the strong driving force for vacancies clustering. The interlayer hopping and merge of vacancies help eliminate defect states in bilayer CrI3. These results provide an atomic‐scale understanding of vacancy migration between CrI3 layers, which is important for defect engineering and applications of bilayer and multilayer CrI3.

Magnetic domain wall dynamics under external electric field in bilayer CrI3

Motivated by manipulating the magnetic order of bilayer CrI$_3$, we carry out microscopic calculations to find the magnetic order and various magnetic domains of the system in the presence of an electric field. Making use of density functional simulations, a spin model Hamiltonian is introduced consisting of isotropic exchange couplings, Dzyaloshinskii-Moriya (DM) interaction, and on-site magnetic anisotropy. The spin dynamics of two well-known states of bilayer CrI$_3$, low temperature (LT) and high temperature (HT) phases, are obtained by solving the Landau-Lifshitz-Gilbert equation. We show that the magnetic texture is stacking-dependent in bilayer CrI$_3$ and stable magnetic domains can appear in the HT stack which are tunable by external electric and magnetic fields. Therefore, we suggest that the HT phase represents a promising candidate for data storage in the modern generation of spintronic devices working on magnetic domain engineering.

Strain Tunable Electronic Band Structure and Magnetic Anisotropy of CrI3 Bilayer

Bilayer (BL) CrI3 attracts major attention among two dimensional (2D) materials due to the exhibition of unique interlayer antiferromagnetic ordering in contrast to other atomically thin films exhibiting long-range ferromagnetic ordering. It is believed that the high temperature monoclinic AB′ stacking plays the key role to induce unusual antiferromagnetic interlayer coupling in BL CrI3. The magnetic states of this system can be effectively controlled by external perturbations like magnetic field, electric field, carrier doping, strain etc. So, it is expected that strain effects can show a distinct behavior in the magnetic transition in BL CrI3. Here, we have studied the electronic and magnetic properties of BL CrI3 under in-plane biaxial and out-of-plane vertical strain from compression to stretch through density functional theory calculations. A compressive biaxial strain around −2.5 can induce a transition from AFM to FM magnetic ground state which continues upto −6 strain. Beyond this point, a second transition from FM to AFM1 state occurs. Detailed analysis of electronic structure indicates a strain induced direct to indirect band gap transition. Magnetic anisotropy energy (MAE) calculations show an out-of-plane easy axis for pristine CrI3 BL and this feature remains unchanged in the entire range of applied strain. It is also found that most of the perpendicular magnetic anisotropy contribution comes from the iodine atoms. Large MAE found in BL CrI3 may find useful applications in high density data storage devices.

Domain Wall Formation and Magnon Localization in Twisted Chromium Trihalides

The rise of twistronics revolutionizes the field of condensed matter physics, and more specifically the future applications of 2D materials. At small twist angles, the microscopic world becomes strongly correlated, and unexpected physical phenomena such as superconductivity emerge. For magnetic layers, stacking plays a crucial role in the magnetic exchange coupling between the layers leading to nontrivial spin configurations and flat spin‐wave dispersion when twisted. Herein, a short overview of the most recent theoretical and experimental works reporting the effect of twist angles on 2D magnets is given. In addition, the effect of the twist angle and the local antiferromagnetic interlayer exchange coupling on the formation of antiferromagnetic domains in chromium trihalides is discussed. Finally, some preliminary results on the effect of the stacking and the twist angle on the spin‐wave dispersion of bilayer CrI3 are shown.

Atomic Intercalation Induced Spin-Flip Transition in Bilayer CrI3.

The recent discovery of 2D magnets has induced various intriguing phenomena due to the modulated spin polarization by other degrees of freedoms such as phonons, interlayer stacking, and doping. The mechanism of the modulated spin-polarization, however, is not clear. In this work, we demonstrate theoretically and computationally that interlayer magnetic coupling of the CrI3 bilayer can be well controlled by intercalation and carrier doping. Interlayer atomic intercalation and carrier doping have been proven to induce an antiferromagnetic (AFM) to ferromagnetic (FM) phase transition in the spin-polarization of the CrI3 bilayer. Our results revealed that the AFM to FM transition induced by atom intercalation was a result of enhanced superexchange interaction between Cr atoms of neighboring layers. FM coupling induced by O intercalation mainly originates from the improved superexchange interaction mediated by Cr 3d-O 2p coupling. FM coupling induced by Li intercalation was found to be much stronger than that by O intercalation, which was attributed to the much stronger superexchange by electron doping than by hole doping. This comprehensive spin exchange mechanism was further confirmed by our results of the carrier doping effect on the interlayer magnetic coupling. Our work provides a deep understanding of the underlying spin exchange mechanism in 2D magnetic materials.

Intriguing magnetoelectric effect in two-dimensional ferromagnetic/perovskite oxide ferroelectric heterostructure

Two-dimensional (2D) magnets have broad application prospects in the spintronics, but how to effectively control them with a small electric field is still an issue. Here we propose that 2D magnets can be efficiently controlled in a multiferroic heterostructure composed of 2D magnetic material and perovskite oxide ferroelectric (POF) whose dielectric polarization is easily flipped under a small electric field. We illustrate the feasibility of such strategy in the bilayer CrI3/BiFeO3(001) heterostructure by using the first-principles calculations. Different from the traditional POF multiferroic heterostructures which have strong interface interactions, we find that the interface interaction between CrI3 and BiFeO3(001) is van der Waals type. Whereas, the heterostructure has particular strong magnetoelectric coupling where the bilayer CrI3 can be efficiently switched between ferromagnetic and antiferromagnetic types by the polarized states P↑ and P↓ of BiFeO3(001). We also discover the competing effect between electron doping and the additional electric field on the interlayer exchange coupling interaction of CrI3, which is responsible to the magnetic phase transition. Our results provide a avenue for the tuning of 2D magnets with a small electric field.