A Unified Theory of Collective Magnon and Orbiton Excitations in Altermagnets

Altermagnetism has recently emerged as a distinct collinear magnetic phase exhibiting momentum-dependent spin-splitting despite vanishing net magnetization, as a consequence of inequivalent non-magnetic environments. Lately, it has been proposed that strong electronic correlations may yield spontaneous altermagnetism due to orbital ordering even for equivalent non-magnetic environments. While previous studies have largely focused on the electronic structure, a unified understanding of the collective excitations associated with these two different microscopic mechanisms stabilizing altermagnetism remains absent. Here, we develop an extended Kugel'-Khomskiĭ spin-orbital model on a decorated square lattice that simultaneously incorporates inequivalent non-magnetic environments and correlation-driven orbital ordering within a common theoretical framework. Employing a self-consistent mean-field spin-wave orbital-wave formalism, we demonstrate the emergence of mutually unhybridized but interdependent magnon and orbiton excitations exhibiting characteristic chiral-splitting. We show that the splitting originates from two distinct microscopic contributions: a lattice-dependent term arising from inequivalent non-magnetic environments and an orbital-order-induced exchange-anisotropy term that survives even for equivalent non-magnetic environments. The proposed framework therefore unifies the collective excitations associated with both types of altermagnetism. We further investigate the finite-temperature evolution of the coupled spin-orbital system, revealing the breakdown of spin-wave and orbital-wave approximations through spurious 1st-order transitions, while complementary classical Monte Carlo simulations recover the expected continuous 2nd-order behaviour. Our work establishes a unified microscopic framework for understanding collective magnon and orbiton excitations in altermagnets.