Abstract
We study classical $J_1$-$J_2$ models with distinct spin degrees of freedom on a honeycomb lattice. For the XY and Heisenberg spins, the system develops a spiral spin liquid (SSL) that is a thermal cooperative paramagnetic regime with spins fluctuating around the spiral contours in the momentum space, and at low temperatures supports a vector spin-chirality order despite the absence of long-range magnetic order. In a strong contrast, for the Ising moments, the low-temperature spin correlation forms a reciprocal "kagom\'e" structure in the momentum space that resembles the SSL behaviors and persists for a range of exchange couplings. The unexpected emergence and persistence of the reciprocal "kagom\'e" are attributed to the stiffness of the Ising moments and the frustration. At higher temperatures when the thermal fluctuations is strong and the spin correlation is not fully melted, the reciprocal structures evolve from the "kagom\'e" towards the ones demanded by the soft spin limit. This contrasts strongly with the behaviors of the spiral contours in the SSL regime for the continuous spins. We suggest various experimentally relevant systems including van der Waals magnets such as the transition metal phosphorus trichalcogenides TMPX$_3$, Cr$_2$Ge$_2$Te$_6$, the rare-earth chalcohalides (like HoOF, ErOF and DyOF) and other isostructural systems to realize the SSL-like behaviors and/or the reciprocal kagom\'{e} structure.
Highlights
The recently developed van der Waals materials provide an excellent platform for the understanding of the two-dimensional physics and the potential application of various devices [1–5]
We have shown that the spiral spin liquid regime holds for both XY and Heisenberg spins in the frustrated regime at low but finite temperatures
For the Ising spin, a reciprocal kagome structure emerges in the low-temperature spin structure factors in the momentum space and persists for a range of exchanges in the frustrated regime, which resembles the spiral spin liquid regime
Summary
The recently developed van der Waals (vdW) materials provide an excellent platform for the understanding of the two-dimensional physics and the potential application of various devices [1–5]. III shows that this reciprocal kagome structure persists at low temperatures for a range of J2’s Apart from the finite-temperature phase transition due to the discrete nature of the local moments, the spin correlation supports the reciprocal kagome structure in the momentum space at the low temperatures. This is explained from the local-constraint point of view. We emphasize the Ising spin connection with the rare-earth chalcohalides (such as HoOF, ErOF, and DyOF) and make predictions based on our theoretical results
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