Power-law dynamics in the spin-liquid kagome lattices SrCr8Ga4O19 and ZnCu3(OH)6Cl2

TL;DR

This paper investigates the low-energy magnetic dynamics in kagome lattice spin-liquid materials SrCr8Ga4O19 and ZnCu3(OH)6Cl2 using muSR and neutron scattering, revealing a power-law spectral behavior at microelectronvolt energies.

Contribution

It demonstrates a scaling law for magnetic correlations at microelectronvolt energies and compares it with higher-energy neutron data, suggesting different spin-dynamics mechanisms.

Findings

Spectral-weight function F(ω) scales as 1/|ω|^{1 - x} at microelectronvolt energies.

Inelastic neutron scattering data align with conventional behavior at millielectronvolt energies.

Proposes new experiments and theoretical work to understand spin-dynamics mechanisms.

Abstract

We consider the polarization function P^{exp}_Z(t) measured by the muon-spin relaxation (muSR) technique for the SrCr8Ga4O19 and ZnCu3(OH)6Cl2 spin-liquid systems. We show the functional form of P^{exp}_Z(t) to imply that, in the temperature range of order 0.1 K, the spectral-weight function F(\omega) of the magnetic correlations scales with 1/|\omega|^{1 -x} (0 < x < 1) in the energy range of one microelectronvolt, i.e. \hbar \omega ~ 1 \mu eV. We derive the parameters involved in F(\omega) from fits to available experimental data. Inelastic neutron scattering data probing F(\omega) in the millielectronvolt energy range are consistent with a more conventional behavior. These differences could be due to a variety of spin-dynamics mechanisms, i.e. intrinsic to the kagome layer or related to the magnetic defects that have been evidenced in these compounds, acting at different energies. New muSR measurements are proposed and theoretical developments are suggested to pinpoint the mechanisms at play.