Because of unusual properties and fascinating prospects for next-generation device applications, two-dimensional (2D) materials have attracted enormous attention since graphene was discovered in 2004. Among the 2D materials beyond graphene, group-IIIA metal-monochalcogenide (MX) monolayers (MLs), are receiving increasing interests because their excellent applications on electronics and optoelectronics. Recently, ferromagnetism and half-metallicity have been predicted in hole-doped GaS and GaSe MLs, which promise exciting potentials for semiconductor spintronics. Detection and measurement of spontaneous magnetization in these 2D materials will be essential for their spintronic applications. The magneto-optical (MO) effects not only are a powerful probe of magnetism in 2D materials but also have valuable applications in high-density data-storage technology. Furthermore, anomalous Hall effect is not only an ideal transport probe of itinerant magnetism but also of considerable current interest because of its topological nature. Here we perform a systematic first-principles density functional study on the MO Kerr and Faraday effects as well as such important magnetic and transport properties as magneto-crystalline anisotropy energy (MAE) and anomalous Hall conductivity (AHC) of all hole-doped MX (M = Ga, In; X = S, Se, Te) MLs. In this paper, we report the following important findings: (a) gate-tunable MO effects in MX MLs in a broad range of hole concentration; (b) large Kerr and Faraday rotation angles with Kerr angles comparable to well-known MO 3d-transition-metal multilayers and Faraday angles being among the largest ones reported; (c) tunable MAE and large AHC, making MX MLs suitable for magnetic memory devices current-driven via spin-transfer torque and also promising materials for magnetic field nanosensors with high sensitivity. Superior MO characteristics, together with the other interesting properties, would make MX MLs an excellent family of 2D materials for semiconductor MO and spintronic nanodevices.
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