  Realizing sizeable Dzyaloshinskii-Moriya interaction (DMI) in intrinsic
two-dimensional (2D) magnets without any manipulation will greatly enrich
potential application of spintronics devices. The simplest and most desirable
situation should be 2D magnets with intrinsic DMI and intrinsic chiral spin
textures. Here, we propose to realize DMI by designing periodic ripple
structures with different curvatures in low-dimensional magnets and demonstrate
the concept in both one-dimensional (1D) CrBr2 and two-dimensional (2D) MnSe2
magnets by using first-principles calculations. We find that DMIs in curved
CrBr2 and MnSe2 can be efficiently controlled by varying the size of curvature
c, where c is defined as the ratio between the height h and the length l of
curved structure. Moreover, we unveil that the dependence of first-principles
calculated DMI on size of curvature c can be well described by the three-site
Fert-L\'evy model. At last, we uncover that field-free magnetic skyrmions can
be realized in curved MnSe2 by using atomistic spin model simulations based on
first-principles calculated magnetic parameters. The work will open a new
avenue for inducing DMI and chiral spin textures in simple 2D magnets via
curvature.
