  Motivated by manipulating the magnetic order of bilayer CrI$_3$, we carry out
microscopic calculations to find the magnetic order and various magnetic
domains of the system in the presence of an electric field. Making use of
density functional simulations, a spin model Hamiltonian is introduced
consisting of isotropic exchange couplings, Dzyaloshinskii-Moriya (DM)
interaction, and on-site magnetic anisotropy. The spin dynamics of two
well-known states of bilayer CrI$_3$, low temperature (LT) and high temperature
(HT) phases, are obtained by solving the Landau-Lifshitz-Gilbert equation. We
show that the magnetic texture is stacking-dependent in bilayer CrI$_3$ and
stable magnetic domains can appear in the HT stack which are tunable by
external electric and magnetic fields. Therefore, we suggest that the HT phase
represents a promising candidate for data storage in the modern generation of
spintronic devices working on magnetic domain engineering.
