Anisotropy-driven magnetic phase transitions in SU(4)-symmetric Fermi gas in three-dimensional optical lattices

We study an SU(4)-symmetric ultracold fermionic mixture in a cubic optical lattice with a variable tunneling amplitude along one particular crystallographic axis in the crossover region from the two- to three-dimensional spatial geometry. To theoretically analyze the emerging magnetic phases and physical observables, we describe the system within the framework of the Fermi–Hubbard model and apply dynamical mean-field theory. We show that in two limiting cases of anisotropy, there are two phases with different antiferromagnetic orderings in the zero temperature limit and we determine a region of their coexistence. We also study the stability regions of different magnetically ordered states and density profiles of the gas in the harmonic optical trap.