Rethinking $\alpha$-RuCl$_3$

We argue that several empirical constraints strongly restrict parameters of the effective microscopic spin model describing $\alpha$-RuCl$_3$. In particular, such constraints dictate a substantial \emph{positive} off-diagonal anisotropic coupling, $\Gamma^\prime\!>\!0$, not anticipated previously. The renormalization by quantum fluctuations allows to reconcile larger values of the advocated bare parameters with their earlier assessments and provides a consistent description of the field evolution of spin excitations in the paramagnetic phase. We assert that large anisotropic terms inevitably result in strong anharmonic coupling of magnons, necessarily leading to broad features in their spectra due to decays, in accord with the observations in $\alpha$-RuCl$_3$. Using duality transformations, we explain the origin of the pseudo-Goldstone mode that is ubiquitous to the studied parameter space and is present in $\alpha$-RuCl$_3$. Our analysis offers a description of $\alpha$-RuCl$_3$ as an easy-plane ferromagnet with antiferromagnetic further-neighbor and strong off-diagonal couplings, which is in a fluctuating zigzag ground state proximate to an incommensurate phase that is continuously connected to a ferromagnetic one.