Deriving Quantum Spin Model for a Zigzag-Chain Ytterbium Magnet with Anisotropic Exchange Interactions

Abstract

We derive a quantum spin Hamiltonian of the spin-1/2 zigzag chain realized in a rare earth ytterbium-based magnetic insulator, YbCuS₂. This material undergoes a transition at 0.95 K to an incommensurate magnetic phase with small moments, which does not conform to the prediction of nonmagnetic singlet ground state of the spin-1/2 Heisenberg model. We take account of octahedral crystal field effect, atomic spin–orbit coupling, and strong Coulomb interactions on Yb ions, and perform a fourth-order perturbation theory to evaluate the superexchange coupling constants. A small but finite anisotropic exchange coupling called Γ-term appears similarly to the case reported previously in other triangular-based magnets. By varying several material parameters, we figure out two important factors to enhance the Γ-term. One is the splitting of excited f-states with two holes, which efficiently selects the perturbation terms associated with the lowest excited state having large total angular momentum, and accordingly with high spatial anisotropy. The other is the tilting of octahedra or distortion of S–Yb–S bond angle, which breaks the symmetry of the Slater–Koster overlap. These effects are systematically analyzed by focusing on the anisotropy of exchange interactions between two spins using the local axis frame, which reduces the complexity of dealing with the bulk Hamiltonian described in a global axis frame.