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Stabilizing the spiral order with spin-orbit coupling in an anisotropic triangular antiferromagnet

We study the effects of spin-orbit coupling (SOC) on the large-U Hubbard model on anisotropic triangular lattice at half-filling using the Schwinger-boson method. We find that the SOC will in general lead to a zero temperature condensation of the Schwinger bosons with a single condensation momentum. As a consequence, the spin-spin correlation vanishes along the z-axis but develops in the $x$-$y$ plane, with the ordering wave vector being dramatically dependent on the SOC. Moreover, the phase boundary of the magnetic ordered state extends to the region of large spatial anisotropy with increased condensation density, demonstrating that the spiral order is always stabilized by the SOC.