Curvature-induced magnetization in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>CrI</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> bilayer: Flexomagnetic effect enhancement in van der Waals antiferromagnets

The bilayer of ${\mathrm{CrI}}_{3}$ is a prototypical van der Waals (vdW) 2D antiferromagnetic material with magnetoelectric effect. It is not generally known, however, that for symmetry reasons the flexomagnetic effect, i.e., the strain gradient-induced magnetization, is also possible in this system. In the present paper, based on the first-principle calculations, we estimate the flexomagnetic effect to be $200\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}\ifmmode\cdot\else\textperiodcentered\fi{}\AA{}$, which is two orders of magnitude higher than it was predicted for the referent antiperovskite flexomagnetic material ${\mathrm{Mn}}_{3}\mathrm{GaN}$. The two major factors of flexomagnetic effect enhancement related to the peculiarities of antiferromagnetic structure of vdW magnets are revealed: the strain-dependent ferromagnetic coupling in each layer, and large interlayer distance separating antiferromagnetically coupled ions. Since 2D systems are naturally prone to mechanical deformation, the emerging field of flexomagnetism is of special interest for application in vdW spintronics, and straintronics in particular.