Why strong spin-orbit coupling does not destabilize the Dirac spin liquid in the Yb delafossites

Abstract

The Yb delafossites NaYbSe$_2$, KYbSe$_2$, CsYbSe$_2$ and NaYbO$_2$ are candidates for the U(1) Dirac spin liquid (DSL) of the triangular lattice. Strong spin-orbit coupling gives their exchange an XXZ anisotropy $Δ$ and bond-dependent couplings $J_{\pm\pm}$, $J_{z\pm}$ that lock the spin frame to the lattice. We show that, within a single layer of a stable Heisenberg DSL, these couplings generate no relevant Lorentz-scalar operator of their own. Inversion at the bond centers removes the Dzyaloshinskii-Moriya channel that gaps the kagome DSL, so the locked symmetry forbids a mass, density or current at any order and, assuming continuity, any new monopole term through charge three. Every Lorentz-scalar four-fermion operator induced by spin-orbit coupling shares an SU(4) multiplet, and hence its scaling dimension, with a Heisenberg-allowed one, and the nine non-scalar quartics without such a partner arise only at second order and are irrelevant at large $N$. The Heisenberg DSL itself allows a Lorentz-vector quartic of large-$N$ dimension 2.92, which a stable phase must also render irrelevant. Beyond a single layer, spin-orbit coupling opens an interlayer monopole channel in rhombohedral stacking. If the Heisenberg DSL is instead multicritical, an anisotropy as small as that of KYbSe$_2$ matters only below tens of mK. At the transition to 120$^\circ$ order the anisotropy is relevant, and exact diagonalization indicates that easy-plane anisotropy selects the chiral-Ising class. Existing KYbSe$_2$ neutron data below $J$ do not yet fix the K-point exponent, and gapless out-of-plane spin fluctuations at the K point would test the chiral-Ising selection.