  Magnetic skyrmions are nano-scale spin structures that are promising for
ultra-dense memory and logic devices. Recent progresses in two-dimensional
magnets encourage the idea to realize skyrmionic states in freestanding
monolayers. However, monolayers such as CrI3 lack Dzyaloshinskii-Moriya
interactions (DMI) and thus do not naturally exhibit skyrmions but rather a
ferromagnetic state. Here we propose the fabrication of Cr(I,X)3 Janus
monolayers, in which the Cr atoms are covalently bonded to the underlying I
ions and top-layer Br or Cl atoms. By performing first-principles calculations
and Monte-Carlo simulations, we identify strong enough DMI, which leads to not
only helical cycloid phases, but also to intrinsic skyrmionic states in
Cr(I,Br)3 and magnetic-field-induced skyrmions in Cr(I,Cl)3.
