Long-range anisotropic Heisenberg ferromagnets and electrically tunable ordering

This is the authors' abstract. We don't add key points for this paper.

Recent realizations of intrinsic magnetic order in truly two-dimensional materials have opened new avenues in the fundamental knowledge and spintronic applications. Here we develop an anisotropic Heisenberg model with relativistic exchange interactions that are obtained from the first-principles calculations. We demonstrate the crucial importance of magnetic interactions beyond the first neighbor to qualitatively and quantitatively reproduce the experimental results. Once we ascertain the predictive capacity of the model for chromium trihalides and CrGeTe₃, we investigate the feasibility of tuning the magnetic ordering by electrical means in these materials. A remarkable fivefold increase in the ferromagnetic Curie temperature is predicted in monolayer CrI₃ within experimentally obtainable hole density. The elusive microscopic mechanism behind the doping-dependent Curie temperature is illustrated. Furthermore, in the present context, the effects of induced biaxial strain and chemical doping are also addressed. The results should trigger further experimental attention to test the present conclusions.