Two-dimensional (2D) magnetic materials offer a promising platform for nanoscale spintronics and for exploration of novel physical phenomena. Here, we predict a diverse range of magnetic orders in cobalt-based 2D single septuple layers CoXY, namely, CoBiTe, CoBiSeTe, CoBiSe, and CoSbTe. Notably, CoBiTe presents intrinsic non-collinear antiferromagnetism (AFM), while the others display collinear AFM. The emergence of AFM in all CoXY materials is attributed to the antiferromagnetic 90° Co-Te(Se)-Co superexchange coupling. The origin of non-collinear/collinear orders lies in competing Heisenberg exchange interactions within the Co triangular lattice. A pivotal factor governing the non-collinear order of CoBiTe is the vanishingly small ratio of exchange coupling between next-nearest neighbour Co and the nearest neighbour Co (/ ∼ 0.01). Furthermore, our investigation into strain effects on CoXY lattices demonstrates the tunability of the magnetic state of CoSbTe from collinear to non-collinear. Our prediction of the unique non-collinear AFM in 2D suggests the potential for observing extraordinary magnetic phenomena in 2D, including non-collinear scattering and magnetic domain walls.
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