Effect of electron spin-spin interaction on level crossings and spin flips in a spin-triplet system

We study level crossings and spin flips in a system consisting of a spin-1 (an electron spin triplet) coupled to a nuclear spin of arbitrary size $K$, in the presence of a uniform magnetic field and the electron spin-spin interaction within the triplet. Through an analytical diagonalization based on the $\mathrm{SU}(3)$ Lie algebra, we find that the electron spin-spin interaction not only removes the curious degeneracy which appears in the absence of the interaction, but also produces some level anticrossings (LACs) for strong interactions. The real-time dynamics of the system shows that periodic spin flips occur at the LACs for arbitrary $K$, which might provide an option for nuclear or electron spin polarization.