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We study classical $J_1$-$J_2$ models with distinct spin degrees of freedomon a honeycomb lattice. For the XY and Heisenberg spins, the system develops aspiral spin liquid (SSL) that is a thermal cooperative paramagnetic regime withspins fluctuating around the spiral contours in the momentum space, and at lowtemperatures supports a vector spin-chirality order despite the absence oflong-range magnetic order. In a strong contrast, for the Ising moments, thelow-temperature spin correlation forms a reciprocal "kagom\'e" structure in themomentum space that resembles the SSL behaviors and persists for a range ofexchange couplings. The unexpected emergence and persistence of the reciprocal"kagom\'e" are attributed to the stiffness of the Ising moments and thefrustration. At higher temperatures when the thermal fluctuations is strong andthe spin correlation is not fully melted, the reciprocal structures evolve fromthe "kagom\'e" towards the ones demanded by the soft spin limit. This contrastsstrongly with the behaviors of the spiral contours in the SSL regime for thecontinuous spins. We suggest various experimentally relevant systems includingvan der Waals magnets such as the transition metal phosphorus trichalcogenidesTMPX$_3$, Cr$_2$Ge$_2$Te$_6$, the rare-earth chalcohalides (like HoOF, ErOF andDyOF) and other isostructural systems to realize the SSL-like behaviors and/orthe reciprocal kagom\'{e} structure.

Spiral-spin-liquid behaviors and persistent reciprocal kagom\'{e} structure in frustrated van der Waals magnets and beyond