  A recent theoretical study reported large effects of perpendicular electric
fields on the atomic structure of a monolayer CrI3, which could be related to
the microscopic origin of the technologically promising and experimentally
observed electrical switching of magnetization in bilayer CrI3. However, those
theoretical results are not in line with a previous theoretical finding of only
slight changes under a strong electric field in CrI3. Given the important
consequences that the presence of large structural distortions in an electric
field might have, we investigated the effects of external electric fields on
the CrI3 monolayer using density functional theory for a wide range of field
strengths. Conclusively, we find that the structural response of CrI3 to the
applied perpendicular electric field is extremely small due to a very efficient
electronic screening of the electric field within the monolayer. Therefore it
cannot be the origin of the observed electrical switching of magnetization in
the bilayer CrI3. Furthermore, we find that the very small linear dependence of
the structural changes on the electric field persists up to a field value of
0.45 V/Angstrom, while the Cr magnetic moment remains constant for the same
strengths of electric field.
