Optical and magneto-optical properties of ferromagnetic monolayer CrBr3 : A first-principles GW and GW plus Bethe-Salpeter equation study

Abstract

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 (CrBr3). 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 dielectric function tensor that governs the optical and magnetooptical properties. In addition, we provide a detailed theoretical formalism for simulating magnetic circular dichroism, magneto-optical Kerr effect, and Faraday effect, demonstrating the approach with monolayer CrBr3. Due to reduced dielectric screening in 2D and localized nature of the Cr d orbitals, we find strong self-energy effects on the quasiparticle band structure of monolayer CrBr3 that give a 3.8 eV indirect band gap. Also, excitonic effects dominate the low-energy optical and magneto-optical responses in monolayer CrBr3 where a large exciton binding energy of 2.3 eV is found for the lowest bright exciton state with excitation energy at 1.5 eV. We further find that the magneto-optical signals demonstrate strong dependence on the excitation frequency and substrate refractive index. Our theoretical framework for modelling optical and magneto-optical effects could serve as a powerful theoretical tool for future study of optoelectronic and spintronics devices consisting of van der Waals 2D magnets.

Chirality-Dependent Valley Polarization in Magnetic van der Waals Heterostructures via Spin-Selective Charge Transfer

“…To further reveal the influence of different materials on valley polarization, their spin-projected band structures are extracted individually and plotted in Figure c–e. According to crystal field theory, since the Cr 3+ ions are located in an octahedral environment coordinated by six Br – ions in a CrBr 3 crystal, as shown in Figure c, the Cr-3d orbitals are split into three low-lying t 2g and two high-lying e g orbitals. , The e g orbitals constitute the majority-spin, and the spin direction is the same as the magnetization direction in CrBr 3 material . As for WS 2 , as shown in Figure d, its band structures at K and K′ valleys are almost the same as that of the individual WS 2 monolayer (see Figure S7 in the Supporting Information) because of its weak coupling with the CrBr 3 crystal .…”

“…According to crystal field theory, since the Cr 3+ ions are located in an octahedral environment coordinated by six Br − ions in a CrBr 3 crystal, as shown in Figure 4c, the Cr-3d orbitals are split into three lowlying t 2g and two high-lying e g orbitals. 37,38 The e g orbitals constitute the majority-spin, and the spin direction is the same as the magnetization direction in CrBr 3 material. 19 As for WS 2 , as shown in Figure 4d, its band structures at K and K′ valleys are almost the same as that of the individual WS 2 monolayer (see Figure S7 in the Supporting Information) because of its weak coupling with the CrBr 3 crystal.…”

Optically Addressing Exciton Spin and Pseudospin in Nanomaterials for Spintronics Applications

“…Grzeszczyk et al revealed such dramatic differences in the exciton-magnetization coupling between the two systems by analyzing the exciton wave functions in band-, orbital-, spin-basis and in real space. The authors also noted that a part of the essential conclusions were different if a nonself-consistent (single-shot) GW theory , was used instead of a fully self-consistent theory. A self-consistent, parameter free, many-body perturbative approach appears to be more important in the “Frenkel” limit where the electron and hole parts of the excitonic wave function get delocalized in the band-basis over several valence and conduction bands (Figure ) (which includes both p and d characters and contain spins of both kinds), in strong contrast to Wannier-Mott limit where a reasonable description of the electron and hole wave functions from the conduction band bottom and valence band top is sufficient to describe the excitons reliably.…”

“…Another recent study activates the dark excitons in CrCl 3 by forming heterostructures with WSe 2 . Moreover, additional studies − show that the direct or indirect nature of the electronic band gaps do change going from bulk to single layer. This can have important consequences in tuning the brightness of the excitons across different numbers of layers.…”

“…From bulk to monolayer, several TMDCs are reported to undergo a transition from an indirect bandgap to a direct bandgap semiconductor. ,− Owing to this low dimensionality, 2D materials have weak dielectric screening which in turn results in a strong Coulomb interaction. Consequently, these are excitonic systems with large binding energies and oscillator strength. ,, Excitons with the electron and hole in the same valley but opposite spin are bright excitons due to the conservation of spin and momentum.…”