  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-neighbour to qualitatively and quantitatively reproduce the experimental
results. Once we ascertain the predictive capacity of the model for chromium
trihalides and CrGeTe$_3$, we investigate the feasibility of tuning the
magnetic ordering by electrical means in these materials. A remarkable
five-fold increase in the ferromagnetic Curie temperature is predicted in
monolayer CrI$_3$ within experimentally obtainable hole density. The elusive
microscopic mechanism behind the doping-dependent Curie temperature is
illustrated. Further, in the present context, the effects of biaxial strain and
chemical doping are also addressed. The results should trigger further
experimental attention to test the present conclusions.
