Session L53: 2D Semiconductors: Magnetism

Stacking dependent 2D magnetism

In van der Waals layered materials, the symmetries and functionalities could be controlled by modifying the stacking order through rotation and translation between the layers. Whereas most previous work has focused on the electronic and optical properties associated with the van der Waals stacking, the recent discovery of magnetism in 2D materials, achieved through both mechanical exfoliation and molecular beam epitaxy (MBE), provides an exciting opportunity to explore the effects of stacking order on a material's magnetic properties. In this talk, I will present two of our recent studies in this direction. 1) By discovering a giant nonreciprocal second harmonic generation from layered antiferromagnetism in mechanically exfoliated bilayer CrI3, we revealed the underlying C2h symmetry, and thus monoclinic stacking order in bilayer CrI3, providing crucial structural information for the microscopic origin of layered antiferromagnetism. 2) By using the molecular beam epitaxy to grow monolayer and bilayer CrBr3 and in situ characterization with a spin-polarized scanning tunneling microscopy and spectroscopy, we observed that while individual CrBr3 monolayer is ferromagnetic, the interlayer coupling in bilayer depends strongly on the stacking structure and can be either ferromagnetic or antiferromagnetic. Thus, the direct correlation between stacking order and interlayer magnetism pave the way for manipulating 2D magnetism.   

Electronic properties of magnetically ordered topological semimetals.

Magentic topological semimetals are new and exciting field of research. In this talks we will present ARPES studies of several magentically ordered topological systems, where magentic ordering allows to tune and control the topological features leading to observation of novel groundstates.   

Probing magnetic orders and stacking patterns in bilayer CrI3 by theoretical Raman scattering

Chromium triiodide (CrI₃), a 2D van der Waals magnet, has been extensively studied due to its fascinating properties. Within each layer spins are ferromagnetically coupled with strong out-of-plane anisotropy, but between layers the spin ordering can be manipulated between ferromagnetic (FM) and antiferromagnetic (AFM) ordering by numerous ways, such as stacking pattern and applied electric/magnetic field. For bilayer CrI₃, the interlayer spin ordering is closely connected to the stacking configuration, such as the common hombohedral and monoclinic patterns. Using density functional theory, I carried out a systematic study on a variety of possible stacking patterns in bilayer CrI₃, where for each stacking both interlayer FM and AFM spin orders were considered. The calculations found that different stacking patterns and magnetic orderings lead to different symmetries and interlayer coupling strengths, which can alter Raman optical selection rules, phonon frequencies, and Raman intensities. This highlights the intricate interactions between stackings, spins, and phonons in 2D magnets. I will present a Raman spectra map of bilayer CrI₃ with different stacking patterns and spin orderings under both linearly and circularly polarized light for guiding experimental identification.   

Imaging domains and defects in the stacking of few-layer and twisted CrI3

Different lateral shifts of the stacked monolayers in CrI3 lead to different magnetic ground states, with a rhombohedral-symmetry stacking resulting in ferromagnetic layer ordering, and a monoclinic-symmetry stacking leading to antiferromagnetic layer ordering. Here we explore the structural arrangements found as the CrI3 thickness is systematically reduced to the monolayer limit using 4D-STEM electron diffraction and atomic resolution imaging. We find that CrI3 flakes from bilayer to 50 nanometer thickness remain in a monoclinic stacking when cooled to 95 K. However, the monoclinic group allows for multiple variants -- arising from 120 degree stacking rotations both in-layer and between neighboring CrI3 layers -- and we observe a rich assortment of stacking orders and domains, as well as moirés. We show that these stacking rotations can change as a function of temperature. The observed vertical superposition of monoclinic variants in few-layer to bulk CrI3 flakes may present as an overall three-fold symmetry to macroscopic-averaged measurement, but can be recognized by atomic resolution imaging.   

Raman spectroscopy studies of spin-lattice coupling in bilayer CrI3

CrI₃ has been shown to be a layered antiferromagnet in its few-layer form. Upon the application of a moderate out-of-plane magnetic field, the layered antiferromagnetic state can be switched to a fully spin-polarized state. Among the few-layer CrI₃ system, bilayer CrI₃ is of particular interest because the coupling between its crystal structure and magnetic ordering can give rise to unique magneto-optical effects such as magnetic circular dichroism, nonreciprocal second harmonic generation, and deviation of Raman selection rules. In this talk, we will present Raman spectroscopic evidence of spin-lattice coupling in bilayer CrI₃. We will show that spin-lattice coupling in bilayer CrI₃ manifests itself in both first-order and higher-order Raman modes. The results of temperature and magnetic field dependence measurements will be discussed.   

Topological spin waves in 2D CrI3: an itinerant fermion description

We present a theory of spin waves in ferromagnetic CrI₃ monolayers based on the calculation of the renormalized spin susceptibility, computed using an extended multi-orbital Hubbard model obtained from first-principles calculations. Our theory includes the multi-orbital nature of Cr and I atoms, as well as their spin orbit coupling and yield the spin waves as poles from the spin suceptibility tensor. For monolayers, theory reproduces the spin wave dispersion measured with inelastic neutron scattering, with a gap at the Dirac point compatible with a topological origin. We have computed the spin waves for a ribbon and find in-gap chiral edge states that provide further back-up to this scenaro. Importantly, our approach goes does not require to define spin Hamiltonian, and can be applied to a wide class of magnetic 2D materials.   

Magneto-optical properties of CrI3, CrBr3 and CrCl3 monolayers: chemical trends and excitonic effects

Chromium trihalides (CrI₃, CrBr₃ and CrCl₃) are a prominent family of isostructural insulating layered materials in which ferromagnetic order has been observed down to the monolayer. Here we provide a comprehensive computational study of the magneto-optical properties useful to probe ferromagnetic order of monolayers, magnetic circular dichroism and magneto-optic Kerr effect. We combine density functional theory calculations and many-body perturbation theory. We solve the Bethe-Salpeter to obtain the excitonic states and to calculate the optical absorption and Kerr angle spectra. We compare the magneto-optical response of the chromium trihalides series. We find strong excitonic effects on the optical response. Moreover, the Kerr angle spectrum is governed by the spin-orbit coupling of the ligand atoms (I, Br or Cl) and is a fingerprint of the degree of magnetic anisotropy of these compounds.   

Evidence of the polaronic character of excitons in a two-dimensional ferromagnet

Studies of exciton dynamics in two-dimensional (2D) transition metal dichalcogenide (TMDC) semiconductors have led to discoveries of a variety of fascinating properties for optoelectronic applications. It has been known that exciton dynamics can be strongly affected by lattice vibrations through electron-phonon (e-ph) coupling. The recently discovered 2D ferromagnetic semiconductor, CrI₃, provides a new platform to explore exciton physics beyond the well-studied 2D TMDC semiconductors because of its localized orbitals, intrinsic long-range ferromagnetic order, and strong e-ph coupling. Here we use linear absorption spectroscopy to identify the exciton resonance transitions in bilayer CrI₃. We further use resonant micro-Raman spectroscopy to explore the electron-phonon coupling in bilayer CrI₃. Temperature and magnetic field dependence of e-ph coupling in bilayer CrI₃ will be discussed.   

Switching 2D Magnetic States via Pressure Tuning of Layer Stacking

The physical properties of two-dimensional van der Waals crystals can be sensitive to the interlayer coupling. For 2D magnets, theory suggests that the interlayer exchange coupling strongly depends on layer separation, while the stacking arrangement can even change the sign of the interlayer magnetic exchange, thus drastically modifying the ground state. Here, we demonstrate pressure tuning of magnetic order in the 2D magnet CrI₃. We probe the magnetic states using tunneling and scanning magnetic circular dichroism microscopy measurements. We find that the critical field for the spin-flip transition can be more than doubled by hydrostatic pressure. In bilayer CrI₃, pressure induces a transition from layered antiferromagnetic to ferromagnetic phases. In trilayer CrI₃, pressure can create coexisting domains of three phases, one ferromagnetic and two antiferromagnetic. The observed changes in magnetic order can be explained by changes in the stacking arrangement. Such coupling between stacking order and magnetism provides ample opportunities for designer magnetic phases and functionalities.   

Uncovering two-dimensional intrinsic ferromagnetism from host antiferromagnet via super-exchange interaction modulation

Two-dimensional ferromagnetic semiconductors have been gaining great attention as they incorporate low-dimensionality, ferromagnetism and semiconductivity, which are promising for next-generation multifunctional spintronics. Here, we report an effective strategy to design ferromagnetic single crystals based on our previous extended super-exchange theory for polyvalent anion materials, e.g. CrOCl. We reveal that the magnetic order of one specific super-exchange cation-anion-cation path in CrOCl prototype is directly related to all anions' valence state. Choosing suitable anions (A₁=VIIA, A₂=VA element) in sites, all super-exchange paths are tuned into strongly ferromagnetic, leading to designed materials are intrinsic ferromagnets companied with high Curie temperatures. On the basis of the explored strategy and first-principles calculations, two stable monolayers CrIP and CrIAs are predicted to be ferromagnetic half-metal and semiconductor, respectively. The Curie temperature, estimated by Monte Carlo simulation using Heisenberg model, is as high as 1050 K and 655 K.   

Exotic magnetism in 2D Ni-based halides

Driven by the increasing enthusiasm towards long-range magnetic order in two-dimensional materials (2D) (such as CrI3 and CrGeTe3), we carry out simulations based on density functional theory (DFT) for halides, focusing in particular on Ni-(VII)2 (VII = Cl, Br, I) monolayers. In addition to standard analysis of structural and electronic properties, we put special emphasis on the magnetic properties, in terms of magnetic moments, Heisenberg exchange coupling (including anisotropic and off-diagonal terms in the exchange tensor) and magnetic anisotropy energy. Moreover, starting from DFT results and mapping total energies on model spin Hamiltonians, we perform Monte-Carlo simulations to investigate the ground-state magnetic ordering and trends at finite temperatures and upon magnetic fields. Our predictions suggest a particularly rich phase diagram for Ni iodide and bromide monolayers, with exotic non-collinear spin configurations and complex topological transitions.