Two-dimensional (2D) chromium tellurides have attracted considerable research interest for their high Curie temperatures. Their magnetic properties have been found diverse in various experiments, the understanding of which however remains limited. In this work, we report that the magnetic ordering of ultrathin chromium tellurides is structure dependent and can be tuned by external strain. Based on first-principles calculations and Monte Carlo simulations, we show long-range stable magnetism with high and low Curie temperature, and short-range magnetism in 2D Cr5Te8, CrTe2, and Cr2Te3 layers, respectively. We further find that ferromagnetic-to-antiferromagnetic transition can be realized by 2% compressive strain for CrTe2 and 2% tensile strain for Cr2Te3, and their magnetic easy axis is tuned from out-of-plane to in-plane by the medium tensile and compressive strain. This strain dependent magnetic coupling is found to be related to Cr-Cr direct exchange and the change of magnetic anisotropy is understood by the atom and orbital resolved magnetic anisotropy energy and second order perturbation theory. Our results reveal the important roles of the structure and strain in determining the magnetic ordering in 2D chromium telluride, shedding light on understanding of the diverse magnetic properties observed in experiments.
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