Spin-orbit interactions and magnetic phase transitions

With the spin-orbit interaction (λ) as a tuning parameter, we show a non-trivial quantum phase transition that unambiguously links the ferromagnetic (F) and antiferromagnetic (AF) phases of the spin system wherein the Heisenberg isotropic exchange is positive. Using a spin-only exchange Hamiltonian that also faithfully accounts for the spin-orbit interactions and the double-time Green function formalism of quantum statistical mechanics, we obtain an implicit analytical expression for the average magnetization. As expected, the high temperature phase is paramagnetic (P). For λ=0, the spin system displays a P-F transition. If the spin-orbit interaction is not quenched (λ≠0), the susceptibility curves reveal a robust P-AF transition. The present λ-mediated F-AF phase transition arises due to the broken inversion symmetry in the effective spin-only Hamiltonian. This is physically distinct from the Néel-VanVleck-Anderson mechanism, which posits a negative Heisenberg isotropic exchange for the existence of the AF phase, and thus offers a new perspective on quantum magnetism and other analogous complex systems.