Spiral Spin Liquid State in the Corrugated Honeycomb Lattice of CaMn$_2$P$_2$

Abstract: CaMn$2$P$_2$ exemplifies the realization of a frustrated $J_1$-$J_2$-$J_3$ Heisenberg model of a corrugated honeycomb magnetic lattice. Previous studies show that below the N\'eel temperature ($T{\rm N}$), the system forms a cycloidal $6\times 6$ $ab$-plane magnetic unit cell that conforms with various magnetic space groups. Here, we present single-crystal neutron-diffraction studies across expansive reciprocal-space volumes, confirming the cycloidal magnetic structure while uncovering further distinctive features. We find evidence for three magnetic domains, the analysis of which narrows the possible magnetic model structures. At $T_{\rm N}$, the insulator exhibits a sharp phase transition, above which the spin structure transforms into a spiral spin liquid state, evident via a continuous ring of scattering with degenerate wavevectors corresponding to a collection of short-range spiral spin configurations. These degenerate states emerge as thermal fluctuations effectively reduce the $J_3$ interaction. The integration of experimental, theoretical, and real-space simulation results reveals the intricate balance of exchange interactions ($J_1$-$J_2$-$J_3$) that stabilizes the ground-state magnetic structure and drives the emergence of a sought-after $U$(1)-symmetric spiral spin-liquid state with easy-plane anisotropy above the transition temperature.