Two-dimensional CoSe structures: Intrinsic magnetism, strain-tunable anisotropic valleys, magnetic Weyl point, and antiferromagnetic metal state

The interplay between magnetism, band topology, and electronic correlation in low dimensions has been a fascinating subject of research. Here, we propose two-dimensional (2D) material systems which demonstrate such an interesting interplay. Based on first-principles calculations and structural search algorithms, we identify three lowest energy 2D CoSe structures, termed as the $α$-, $β$-, and $γ$-CoSe. {We show that $α$- and $β$-CoSe are two rare examples of 2D antiferromagnetic metals, which are related to their Fermi surfaces nesting features, and meanwhile, $γ$-CoSe is a ferromagnetic metal. They possess a range of interesting physical properties, including anisotropic valleys connected by crystalline symmetries, strain-tunable valley polarization, strain-induced metal-semiconductor and/or magnetic phase transitions, as well as topological band features such as the magnetic Weyl point and the magnetic Weyl loop. Remarkably, all the topological features here are robust against spin-orbit coupling.} Some experimental aspects of our predictions have been discussed.