Nuclear relaxation rates in the herbertsmithite kagome antiferromagnets ZnCu3(OH)6Cl2

Abstract

Local spectral functions and Nuclear Magnetic Relaxation (NMR) rates, 1/T1, for the spin-half Heisenberg antiferromagnet on the Kagome Lattice are calculated using Moriyas Gaussian approximation, as well as through an extrapolation of multiple frequency moments. The temperature dependence of the calculated rates is compared with the oxygen 1/T1 NMR data in Herbertsmithite. We find that the Gaussian approximation for 1/T1 shows behavior qualitatively similar to experiments with a sharp drop in rates at low temperatures, consistent with a spin-gapped behavior. However, this approximation significantly underestimates the magnitude of 1/T1 even at room temperature. Rates obtained from extrapolation of multiple frequency moments give very good agreement with the room temperature NMR data with J = 195 ± 20K and hyperfine couplings determined independently from other measurements. The use of multiple frequency moments also leads to additional low frequency weight in the local structure factors. The convergence of our calculations with higher frequency moments breaks down at low temperatures suggesting the existence of longer range dynamic correlations in the system despite the very short-range static correlations.

Quantum magnetism in minerals

“…The absence of magnetic order at ambient pressures stimulated a considerable experimental effort and raised intense theoretical discussions regarding the true ground state of herbertsmithite -whether it is gapped or gapless [324], and whether the singlet valence bonds form a solid (valence bond solid, VBS) [325,326] or fluctuate (resonating valence bonds, RVB) [327,328]. For a long time, inadvertent magnetic disorder has hindered the detection of a spin gap at low temperatures until it was finally observed in recent NMR measurements, evidenced by a sharp drop in the nuclear magnetic relaxation rate, 1/T 1 , and in the 17 O NMR frequency shift [329,330]. The resulting value of the spin gap, ∆ ≈ 10 K, favours theories promoting a Z 2 (topological) quantum spin-liquid ground state with a spin-gap of order 0.1J [331][332][333][334][335][336][337][338][339], supplanting alternative scenarios like valence-bond solids or gapless (algebraic) spin liquids [325,[340][341][342][343][344][345][346][347][348][349][350][351][352][353].…”

Dynamical spin correlations of the kagome antiferromagnet

“…The spectra are not featureless, as they exhibit two distinct frequency maxima, which seem quite robust. These were already tentatively observed via the numerical linked cluster method [29] by assuming an ad hoc Lorentzian line shape. Our FTLM calculations, on the other hand, do not require any a priori assumptions on the line shape.…”

“…The static (equal-time) spin correlation function S αα (q) has also been studied both at T = 0 [17] and at finite temperatures [27,28]. However, dynamical spin properties * andrej.zorko@ijs.si of the KLHM, in particular the dynamical spin structure factor (DSF) S αα (q, ω), are theoretically poorly understood even though the temperature-dependent DSF is potentially a unique fingerprint of SL states, and is experimentally directly accessible via inelastic neutronscattering (INS) and nuclear magnetic resonance (NMR) relaxation [29]. Because of its fundamental importance various analytical concepts and methods [30][31][32], as well as numerical approaches [28,33], have been employed to study it, though they have mostly led to inconclusive results.…”

Extend of the $\mathbb{Z}_2$-spin liquid phase on the Kagomé-lattice

“…However, while experimental findings provide increasing evidence for the presence of the spin-liquid phase 4,5 , theoretical predictions for the relevant anti-ferromagnetic spin- 1 2 Heisenberg model remain inconclusive as there are various competing states present in the low-energy regime of this model. The candidate phases of matter include the already mentioned spin liquids (gapped [6][7][8][9] and gapless [10][11][12][13][14] ) as well more conventionally phase such as Valence-Bond Solids (VBS) with unit cells of six 15 , twelve 16 , eighteen 17 or thirty-six sites [17][18][19] .…”