Remarkable features of spontaneous altermagnetic Mott insulator state

Altermagnetism has gained a lot of attention in the last few years because of its possible applications in spintronics and magnonics. All of the altermagnets realized in the experiments so far are assisted by the crystallographic environment around the magnetic atoms. Here, we present a comprehensive stability analysis of spontaneous altermagnetism driven by the coexistence of staggered magnetic and orbital order, within an unrestricted Hartree-Fock framework. Furthermore, we derive and discuss the Kugel-Khomskii type spin–orbital model for these materials and employ the Density Matrix Renormalization Group (DMRG) method on cylindrical geometries to confirm the emergence of the altermagnetic phase. We also examine possible phase transitions from the altermagnetic state to neighboring antiferromagnetic and antiferro-orbital phases via thermal fluctuations, which can be observed in experiments. In addition, we discuss the origin of chiral magnon splitting in spontaneous altermagnets. Finally, we propose a novel mechanism to realize a hybrid mode of chiral magnons and orbitons in the presence of a small in-plane magnetic field, which has potential applications in quantum magnonics.