Spin order accompanying loop-current order in cuprate superconductors

The theory of the long-range order of orbital current loops in the pseudogap phase is generalized to include the effects of spin-orbit scattering. It is shown by symmetry arguments as well as by microscopic calculation that a specific in-plane spin order must necessarily accompany the loop-current order. The microscopic theory also allows an estimate of the magnitude of the ordered spin moment. Exchange coupling between the generated spins further modifies the in-plane direction of the spin moments. The structure and form factor for the spin and orbital moments combined with the induced spin order are consistent with the direction of moments deduced from polarization analysis in a recent neutron-scattering experiment.