Identifying novel materials exhibiting quantum phases is arguably the most important and enduring, perhaps timely too, regarding the emergence of quantum information science in condensed matter physics, characterized by their dependence on quantum fluctuations and entanglement. A sought-after example of such phases is the quantum spin liquid (QSL), distinguished by its lack of magnetic order and the presence of extensive spin entanglement [1]. Among the myriad theoretical models, the Kitaev model is a new addition and promising avenue for realizing QSL in a few real materials [2]. This is primarily attributed to its analytical solvability and the relative simplicity of conditions theoretically required for its materialization.

          The original Kitaev model is based on the honeycomb network of spins with bond-dependent anisotropic interactions [2]. However, if and how Kitaev physics manifests in geometrically frustrated systems, such as the triangular lattice [3], is much less explored. Interestingly, recent theoretical studies suggest that bond-dependent anisotropy can stabilize the more exotic magnetic phases with the triangular lattice.

           This paper reports a frustrated triangular lattice with bond-dependent anisotropy in the cobalt-based van der Waals magnet CoI₂. By employing the Luttinger–Tisza method [4], we proposed two potential minimal models to elucidate the magnetic structure of CoI₂: one incorporating a Kitaev term (J₁-J_±±-J₃ model) and the other excluding it (J₁-J₂-J₃ model). Inelastic neutron scattering measurements conducted during the paramagnetic phase validated the suitability of the minimal model with bond-dependent anisotropy in explaining the characteristics of CoI₂. The spin-wave spectrum observed during the ordered phase exhibited large linewidth broadening across different momentum values, indicating magnon decay. To further investigate this decay process, we performed an analysis using the density of states for two-magnon.

           This study's outcomes have illuminated the intricate and diverse realm of spin dynamics within a cobalt Kitaev triangular lattice, specifically demonstrated in the case of the non-collinear antiferromagnet CoI₂. The underlying bond-dependent exchange anisotropy shapes the non-collinear magnetic order observed in CoI₂. Furthermore, our investigation has unveiled significant magnon decay, effectively managed to be selectively evaded across an extensive momentum spectrum. These phenomena find their roots in potent magnon-magnon interactions spurred by the interplay of bond-dependent anisotropy and non-collinear magnetic order [5,6]. Consequently, our findings are paramount in advancing our grasp of the intricate interrelationship between bond-dependent anisotropy and non-collinear magnetic order in quantum magnets.

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References:

[1] Balents, L. Spin liquids in frustrated magnets. Nature 464, 199-208 (2010)

[2] Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. -New York 321, 2-111 (2006)

[3] Maksimov, P., Zhu, Z., White, S. R. & Chernyshev, A. L. Anisotropic-exchange magnets on a triangular lattice: spin waves, accidental degeneracies, and dual spin liquids. Phys. Rev. X 9, 021017 (2019)

[4] Litvin, D. B. The Luttinger-Tsiza method. Physica 77, 205-219 (1974)

[5] Chernyshev, A. L. & Zhitomirsky, M. E. Spin waves in a triangular lattice antiferromagnet: decays, spectrum renormalization, and singularities. Phys. Rev. B 79, 144416 (2009)

[6] Winter, S. M. et al. Breakdown of magnons in a strongly spin-orbital coupled magnet. Nat. Commun. 8, 1152 (2017)