Effects of Magnetic Fields and Orbital Angular Momentum on Excitonic Condensation in Two-Orbital Hubbard Model

We investigate magnetic-field effects on a two-orbital Hubbard model that describes multiple spin states. The exploration of spin-state degrees of freedom in perovskite-type cobalt oxides is motivated by their unique characteristic, where low-spin, intermediate-spin, and high-spin states have a significant impact on their magnetic properties. This feature results from the interplay between the Hund coupling and crystalline field effects. Recent studies have suggested that this interplay leads to quantum mechanical hybridization of these spin states, interpreted as excitonic condensation. To understand the influence of magnetic fields on excitonic condensation in multi-orbital systems, it is essential to consider both spin and orbital contributions to the magnetic properties. In this study, we investigate field-induced phenomena in the two-orbital Hubbard model, focusing on the role of orbital angular momentum. We conduct a comprehensive analysis of this model on a square lattice using the Hartree-Fock approximation. First, we examine the case without contributions from the orbital moment. In this case, an applied magnetic field induces two excitonic phases: one exhibits a staggered-type spin-state order, interpreted as an excitonic supersolid state, while the other does not. When considering the spin-orbit coupling, the latter phase displays a ferrimagnetic spin alignment attributed to spin anisotropy. Furthermore, our analysis demonstrates that incorporating the contribution of the orbital magnetic moment to the Zeeman term significantly modifies the structure of the overall phase diagram. Notably, the orbital magnetization destabilizes the excitonic phase, unlike scenarios excluding this contribution. We also discuss the relevance of our findings to real materials, such as cobalt oxides.