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.

References in corpus (14)

• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
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• Coexistence of magnetic order and persistent spin dynamics in a quantum kagome antiferromagnet with no intersite mixing
• Local study of the insulating quantum kagome antiferromagnets YCu3(OH)6OxCl3-x (x=0,1/3)
• Finite-temperature crossover phenomenon in the $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice
• Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures
• Structure factor of low-energy spin excitations in a S=1/2 kagome antiferromagnet
• Nuclear relaxation rates in the Herbertsmithite Kagome antiferromagnets ZnCu3(OH)6Cl2

Cited by in corpus (4)

• Experimental signatures of quantum and topological states in frustrated magnetism
• The observation of quantum fluctuations in a kagome Heisenberg antiferromagnet
• 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)${}_{1-x}$]