Optical and magneto-optical properties of ferromagnetic monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CrBr</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>: A first-principles <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math> plus Bethe-Salpeter equation study
Meng Wu, Zhenglu Li, Steven G. Louie
Abstract
The discovery of atomically thin two-dimensional (2D) magnetic semiconductors has triggered enormous research interest recently. In this paper, we use first-principles many-body perturbation theory to study a prototypical 2D ferromagnetic semiconductor, monolayer chromium tribromide (${\mathrm{CrBr}}_{3}$). 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-optical (MO) properties. In addition, we provide a detailed theoretical formalism for simulating magnetic circular dichroism, MO Kerr effect, and Faraday effect, demonstrating the approach with monolayer ${\mathrm{CrBr}}_{3}$. Due to reduced dielectric screening in 2D and the localized nature of the Cr $d$ orbitals, we find strong self-energy effects on the quasiparticle band structure of monolayer ${\mathrm{CrBr}}_{3}$ that give a 3.8 eV indirect bandgap. Also, excitonic effects dominate the low-energy optical and MO responses in monolayer ${\mathrm{CrBr}}_{3}$ 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 MO signals demonstrate strong dependence on the excitation frequency and substrate refractive index. Our theoretical framework for modeling optical and MO effects could serve as a powerful theoretical tool for future study of optoelectronic and spintronics devices consisting of van der Waals 2D magnets.