Electronic Responses in Solid Oxygen with Coexisting Structural and Magnetic Orders

Solid oxygen provides a unique platform for studying the interplay between structural and magnetic degrees of freedom, as each O$_2$ molecule possesses an $S=1$ spin and weak intermolecular van der Waals interactions allow substantial structural flexibility. In addition, because of its small intermolecular hopping integrals, this system is known to be a strongly correlated electron system with a multiorbital nature. In this study, we examine electronic states and magnetic and dielectric responses using a multiorbital Hubbard model with Peierls-type electron-lattice coupling. This model provides a minimal description of the interplay between structural and magnetic degrees of freedom in solid oxygen. We apply the Hartree-Fock approximation to obtain the ground-state phase diagram. Antiferromagnetic order appears when the onsite Coulomb interaction is strong, whereas three nonmagnetic bond-ordered states emerge when it is weak. At intermediate interaction strengths, antiferromagnetic order coexists with each of the three bond orders. These three coexistence phases all break time-reversal symmetry; one preserves spatial inversion symmetry, whereas the other two also break it. The two inversion-breaking phases exhibit linear magnetoelectric responses, whereas the inversion-symmetric phase exhibits altermagnetic spin splitting and a piezomagnetic response. These responses may provide experimental signatures of coexisting magnetic and structural orders in high-pressure solid oxygen suggested by recent experiments.