Spiral-spin-liquid behaviors and persistent reciprocal kagomé structure in frustrated van der Waals magnets and beyond

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.

• The paper demonstrates spiral-spin-liquid behavior emerging in classical J1-J2 models across XY, Heisenberg, and Ising spin systems.
• It employs Monte Carlo simulations to reveal temperature-dependent phase transitions and establishes vector spin-chirality order under specific coupling ratios.
• The findings offer insights for experimental realizations in vdW magnets, highlighting potential routes for spintronic and quantum information applications.

Spiral-Spin-Liquid Behaviors in Frustrated Van Der Waals Magnets

The study of spiral-spin-liquid (SSL) behaviors, particularly within the context of frustrated antiferromagnetic systems, represents a challenging and intricate area of condensed matter physics. The paper "Spiral-spin-liquid behaviors and persistent reciprocal kagome structure in frustrated van der Waals magnets and beyond" by Huang, Liu, and Chen provides valuable insights into the interplay of frustration, spin anisotropy, and dimensionality on magnetic ordering and correlations. Utilizing classical $J_1$-$J_2$ spin models on a honeycomb lattice, the authors analyze various spin types—Ising, XY, and Heisenberg—to understand the emergence of unique magnetic phases and correlation patterns.

Key Findings and Numerical Results

The researchers explore the $J_1$-$J_2$ model, identifying distinct regimes of SSL behavior across different spin types and lattice structures. For XY and Heisenberg spins, SSL emerges as a thermally induced cooperative paramagnetic regime characterized by spiral contours in the momentum space—manifesting despite the lack of long-range magnetic order. Remarkably, this phase supports a vector spin-chirality order at lower temperatures when the exchange coupling $J_2$ exceeds a certain threshold relative to $J_1$. The authors substantiate these findings using classical Monte Carlo simulations to decipher the complex temperature dependencies of specific heat and chiral order parameters.

In the case of Ising spins, a reciprocal "kagome" structure surprisingly appears in the spin correlation at low temperatures, even in the absence of explicit non-collinear spin spirals. This persistence over a range of $J_2$ couplings underscores the significance of Ising stiffness and interaction frustration on the magnetic correlation landscape. The emergent behavior deviates significantly from conventional expectations, highlighting the intricacies inherent in discrete spin systems under frustration.

Quantitatively, the paper presents detailed phase diagrams illustrating transitions and crossovers for each spin type, governed largely by the ratio $\gamma = J_2/J_1$. The critical points and resultant spin states are evaluated through both analytical methods and numerical simulations, ensuring robustness in the reported phase evolution.

Implications and Future Directions

The insights gained from this study have profound implications for both theoretical understanding and experimental exploration of frustrated magnetism. The elucidation of SSL regimes provides a basis for interpreting spin liquid behavior in both 2D materials and potential 3D extensions. This study further suggests that the incorporation of external stimuli, such as hydrostatic pressure, might provoke crossovers between identified spin states, facilitating experimental verification in diverse magnetic systems.

The authors also propose that materials like transition-metal phosphorus trichalcogenides and rare-earth chalcohalides serve as promising candidates for realizing these identified magnetic regimes. The exploration of these materials, particularly under varying anisotropic interactions, may yield novel device applications relevant to spintronics and quantum information technologies.

In summary, this paper sheds light on the nuanced effects of spin geometry, anisotropy, and lattice structure under the umbrella of frustrated magnetism. It paves the way for future studies to explore quantum spin liquids beyond conventional Heisenberg models, especially leveraging advancements in material synthesis and experimental techniques to substantiate theoretical predictions.