  Considerable research interest has been attracted to noncollinear magnetic
structures for their intriguing physics and promising applications. In this
work, based on relativistic density functional theory, we reveal the
interesting magnetic order and relevant properties in monolayer RuF$_4$, which
can be exfoliated from its bulk phase. Although the spins on Ru ions are almost
antiferromagnetically aligned between nearest-neighbors, weak ferromagnetism is
generated because of the antisymmetric Dzyaloshinskii-Moriya interaction as
well as the single-ion anisotropy. A prominent magneto-optical Kerr effect can
be observed for this antiferromagnet, similar to those of regular strong
ferromagnets. In addition, a uniaxial strain can induce a ferroelastic
switching together with the in-plane rotation of spin direction, giving rise to
a strong intrinsic magnetoelasticity. Our work not only suggests an alternative
direction for two-dimensional magnetic materials, but also provides hints to
future devices based on antiferromagnetic magnetoelastic or magneto-optical
materials.
