Codimension-Two Spiral Spin-Liquid in the Effective Honeycomb-Lattice Compound Cs${}_3$Fe${}_2$Cl${}_9$

A codimension-two spiral spin-liquid is a correlated paramagnetic state with one-dimensional ground state degeneracy hosted within a three-dimensional lattice. Here, via neutron scattering experiments and numerical simulations, we establish the existence of a codimension-two spiral spin-liquid in the effective honeycomb-lattice compound Cs${}_3$Fe${}_2$Cl${}_9$, which demonstrates a novel path to spiral spin-liquids by overcoming the long-standing impediment of weak further-neighbor interactions. In the long-range ordered regime, competing spiral and spin density wave orders emerge as a function of applied magnetic field, among which a possible order-by-disorder transition is identified.