Symmetry-breaking induced transition among net-zero-magnetization magnets

Net-zero-magnetization magnets have garnered intensive research attention due to their ultradense and ultrafast potential. In terms of the symmetric classification of connecting magnetic atoms with opposite spin polarization, the net-zero-magnetization magnets mainly include $PT$-antiferromagnet (the joint symmetry ($PT$) of space inversion symmetry ($P$) and time-reversal symmetry ($T$)), altermagnet and fully-compensated ferrimagnet. Studying transitions among net-zero-magnetization magnets is essentially the research on symmetry breaking, which can also clearly reveal the transformation of spin-splitting symmetry. Symmetry breaking can be achieved through methods such as Janus engineering, isovalent alloying, and external electric field. Here, we start from a parent $PT$-antiferromagnet that simultaneously possesses both $P$ and rotational/mirror symmetries to induce altermagnet and fully-compensated ferrimagnet. Based on first-principles calculations, the proposed transitions can be verified in $PT$-antiferromagnet $\mathrm{CrC_2S_6}$ monolayer. By Janus engineering and isovalent alloying, $\mathrm{CrC_2S_6}$ can change into altermagnetic $\mathrm{CrC_2S_3Se_3}$ and fully-compensated ferrimagnetic $\mathrm{CrMoC_2S_6}$. The $\mathrm{CrC_2S_3Se_3}$ can also become fully-compensated ferrimagnetic $\mathrm{CrMoC_2S_3Se_3}$ by isovalent alloying. Our work provides a clear and intuitive example to explain the transitions among net-zero-magnetization magnets, which can inspire more research on net-zero-magnetization magnets.