External-field-induced altermagnetism in experimentally synthesized monolayer CrX₃ (X=Cl, Br and I)

Net-zero-magnetization magnets are attracting significant research interest, driven by their potential for ultrahigh density and ultrafast performance. Among these materials, the altermagnets possess alternating spin-splitting band structures and exhibit a range of phenomena previously thought to be exclusive to ferromagnets, including the anomalous Hall and Nernst effects, non-relativistic spin-polarized currents, and the magneto-optical Kerr effect. Bulk altermagnets have been experimentally identified, while two-dimensional (2D) altermagnets remain experimentally unexplored. Here, we take experimentally synthesized 2D ferromagnetic $\mathrm{CrX_3}$ (X=Cl, Br and I) as the parent material and achieve altermagnetism through external field. First, we achieve the transition from ferromagnetism to antiferromagnetism through biaxial strain. Subsequently, we break the space inversion symmetry while preserving the mirror symmetry via an electric field, thereby inducing altermagnetism. Moreover, through the application of Janus engineering to construct $\mathrm{CrX_{1.5}Y_{1.5}}$ (X$\neq$Y=Cl, Br and I), the phase transition from ferromagnetism to antiferromagnetism induced by strain alone is sufficient to trigger the emergence of altermagnetism. All six monolayers possess the symmetry of $i$-wave spin-splitting. The computational results suggest that $\mathrm{CrCl_3}$ can be readily tuned to exhibit altermagnetism through external field in experiment, thanks to its low strain threshold for magnetic phase transition. Our work provides experimentally viable materials and methods for realizing altermagnetism, which can advance the development of 2D altermagnetism.