Dynamical spin correlations of the kagome antiferromagnet

Abstract

Temperature-dependent dynamical spin correlations, which can be readily accessed via a variety of experimental techniques, hold the potential of offering a unique fingerprint of quantum spin liquids and other intriguing dynamical states. In this work we present an in-depth study of the temperature-dependent dynamical spin structure factor $S(\mathbf{q},\omega )$ of the antiferromagnetic (AFM) Heisenberg spin-1/2 model on the kagome lattice with additional Dzyaloshinskii--Moriya (DM) interactions. Using the finite-temperature Lanczos method on lattices with up to $N=30$ sites we find that even without DM interactions, chiral low-energy spin fluctuations of the $120^{\circ }$ AFM order parameter dominate the dynamical response. This leads to a nontrivial frequency dependence of $S(\mathbf{q},\omega )$ and the appearance of a pronounced low-frequency mode at the M point of the extended Brillouin zone. Adding an out-of-plane DM interactions $D^z$ gives rise to an anisotropic dynamical response, a softening of in-plane spin fluctuations, and, ultimately, the onset of a coplanar AFM ground-state order at $D^z>0.1J$. Our results are in very good agreement with existing inelastic neutron scattering and temperature-dependent NMR spin-lattice relaxation rate ($1/T_1$) data on the paradigmatic kagome AFM herbertsmithite, where the effect of its small $D^z$ on the dynamical spin correlations is shown to be rather small, as well as with $1/T_1$ data on the novel kagome AFM YCu${}_3$(OH)${}_6$Cl${}_3$, where its substantial $D^z\approx 0.25J$ interaction is found to strongly affect the spin dynamics.

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Cited by in corpus (12)

• Possible Dirac quantum spin liquid in a kagome quantum antiferromagnet YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_x$(OH)${}_{1-x}$]
• Experimental signatures of quantum and topological states in frustrated magnetism
• Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice
• Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice
• The observation of quantum fluctuations in a kagome Heisenberg antiferromagnet
• Finite-temperature properties of the easy-axis Heisenberg model on frustrated lattices
• Structures of magnetic excitations in the spin-1/2 kagome-lattice antiferromagnets Cs${}_2$Cu${}_3$SnF${}_{12}$ and Rb${}_2$Cu${}_3$SnF${}_{12}$
• Signatures of the finite-temperature mirror symmetry breaking in the $S$=1/2 Shastry-Sutherland model
• Chemo-Structural Disorder in the kagomé spin $S$ = 1/2 systems ZnCu${}_3$(OH)${}_6$Cl${}_2$ and YCu${}_3$(OH)${}_6$Br${}_2$[Br${}_x$(OH)${}_{1-x}$]
• Is Herbertsmithite far from an ideal antiferromagnet? Ab-initio answer including in-plane Dzyaloshinskii-Moriya interactions and coupling with extra-plane impurities
• Exerting chemical pressure on the kagome lattice as frustration control in the kapellasite family $A$Cu${}_3$(OH)${}_{6+x}$(Cl,Br)${}_{3-x}$
• Dynamical Spectral Function of the Kagome Quantum Spin Liquid