Creating and detecting ferro- and antiferromagnetic order in 2D materials by proximity effects

We propose an efficient way of detecting the magnetic state of bilayer CrI$_3$ via proximity effect, which can be generalized to other two-dimensional van der Waals magnets. In addition, we discuss the optical magnetization switching in CrI$_3$. First-principles calculations, together with a minimal tight binding Hamiltonian, reveal proximity exchange splittings of few meV in transition-metal dichalcogenides (TMDC) MoSe$_2$ and WSe$_2$ on mono- and bilayer magnetic insulator CrI$_3$ substrates. The magnitudes of proximity exchange and band offsets can be tuned by applying realistic transverse electric fields across the heterostructures. Most strikingly, the proximity exchange originates only from the ferromagnetic (FM) CrI$_3$ layer closest to the TMDC, as we find by comparison of mono- and bilayer CrI$_3$ substrates. Even though the bilayer CrI$_3$ can be in an antiferromagnetic (AFM) state with zero net magnetization, one can read out the magnetic state (FM or AFM) via proximity coupled two-dimensional materials, not necessarily TMDCs, on both sides of the bilayer CrI$_3$.