Spin-orbit-induced quantum chiral phases

The scalar spin chirality (SSC), whose nonzero value $\langle {\bf S}_i \cdot ({\bf S}_j \times {\bf S}_k) \rangle \neq 0$ implies the breaking of time-reversal and certain point-group symmetries in the ground state, is a key quantity characterizing chiral magnetism in both classical and quantum settings. The classical SSC is manifested, for instance, in skyrmion crystal phase, while the quantum SSC is still highly sought after in various frustrated spin-1/2 models. An interesting possibility that has not been explored so far is the case in which SSC is symmetry-wise allowed, yet remains zero classically due to the collinear or coplanar arrangement of spins, but is generated by virtue of quantum fluctuation. We demonstrate the existence of precisely such a phase in a spin-1/2 triangular-lattice model with XXZ interaction, spin-orbit-induced exchange interactions, and an external magnetic field. Using iDMRG, we thoroughly map out the phase diagram of the model and identify several phases with coexisting magnetic order and SSC. The nonzero SSC arises despite the classical magnetic order being collinear or coplanar. We provide detailed magnon analysis to ascribe its origin to quantum fluctuations around classical magnetic order. The estimate of SSC from magnon analysis agrees with iDMRG results quantitatively. We map out the magnon spectrum and its Berry curvature, culminating in the prediction of finite thermal Hall conductivity in these phases with SSC.