Spiral Spin Liquid Regardless of Spin Component on a Honeycomb Lattice

Spiral spin liquid is a special family of classical spin liquids and its degenerate manifolds of spin spirals are spiral surfaces or spiral lines in momentum space. In this work, we study the antiferromagnetic Ising, XY, and Heisenberg models with an additional second-neighbor antiferromagnetic exchange on a honeycomb lattice. We find they all develop spiral spin liquid in a certain parameter region where degenerate manifolds form closed contours in momentum space. We also propose several related materials which are expected to hold this exotic state.