Recently, great effort has been devoted to the search for two-dimensional (2D) ferromagnetic materials with inherent strong Dzyaloshinskii--Moriya interaction (DMI). Here, through a first-principles approach, we systematically investigate the effect of biaxial strain on the DMI, the Heisenberg exchange interaction, and the magnetic anisotropy energy (MAE) of Janus Cr$_{ 2}$X$_{ 3}$Y$_{ 3}$ (X, Y = Cl, Br, I, X $\neq$ Y) monolayers. Both DMI and MAE can be significantly enhanced by tensile strain, while a reversal of the chirality of DMI in Cr$_{ 2}$Cl$_{ 3}$Br$_{ 3}$ and a switch of MAE from off-plane to in-plane in Cr$_{ 2}$I$_{ 3}$Cl$_{ 3}$ are induced by a compressive strain of $2\%$. Microscopically, DMI and MAE are associated mainly with the large spin--orbit coupling of the heavy nonmagnetic halogen atoms rather than that of the magnetic Cr atoms. In particular, the peculiar magnetic transition of Cr$_{ 2}$I$_{ 3}$Cl$_{ 3}$ is explained by competition between direct exchange and superexchange interactions. Micromagnetic simulations show that a small external magnetic field of 65~mT stabilizes a skyrmion with a diameter of 9.8~nm in the Cr$_2$I$_3$Cl$_3$ monolayer. Our results will provide guidance for further research on DMI and skyrmions in 2D Janus materials, as well as a basis for the potential applications in spintronic devices.
Categories: cond-mat.mtrl-sci