Dilute RKKY model for NMR line broadening in the hidden-order state ofURu2Si2

Abstract

A well-known analytic model for Lorentzian broadening of metallic NMR lines by dilute localized magnetic centers embedded in a lattice has been applied to the case of the twofold-symmetry magnetism in ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$ reported by R. Okazaki et al. [Science 331, 439 (2011)]. The observed Lorentzian spectra are accounted for with a simple formula giving the $^{29}\mathrm{Si}$ NMR linewidth in terms of the susceptibility of the magnetic-broadening centers and a Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling parameter. The concentration of such centers is estimated as $c\ensuremath{\sim}0.01$. A numerical simulation of these effects confirms Lorentzian broadening with no measurable NMR shift and a width in reasonable agreement with the analytical model. The simulation shows further that domain effects on these spectra are largely absent. A four-site extended model of the broadening centers gives an estimate of the twofold susceptibility within a factor of 2 of the torque value of the susceptibility. Hypothetical superlattice effects are shown to be easily smoothed over by convolution with background Lorentzian broadening.