$\mu \mathrm{SR}$ insight into the impurity problem in quantum kagome antiferromagnets

Impurities, which are unavoidable in real materials, may play an important role in the magnetism of frustrated spin systems with a spin-liquid ground state. We address the impurity issue in quantum kagome antiferromagnets by investigating ${\mathrm{ZnCu}}_3{\left(\mathrm{OH}\right)}_6{\mathrm{SO}}_4$ (Zn-brochantite) by means of muon spin spectroscopy. We show that muons dominantly couple to impurities, originating from Cu-Zn intersite disorder, and that the impurity spins are highly correlated with the kagome spins, allowing us to probe the host kagome physics via a Kondo-like effect. The low-temperature plateau in the impurity susceptibility suggests that the kagome spin-liquid ground state is gapless. The corresponding spin fluctuations exhibit an unconventional spectral density and a nontrivial field dependence.

Figure 1

The ${\mu }^{+}$ polarization in Zn-brochantite in a TF of 0.3 T in the laboratory frame of reference (LFR; upper panel) and in the rotating frame of reference (RFR; lower panel), the latter rotating with the Larmor frequency $\nu$ and thus displaying the envelope of the oscillations in the LFR. Symbols show the measurements and solid lines depict the fits, which are further explained in the text.

Figure 2

The $T$ dependence of the Knight shift $K$ and the transverse relaxation rate ${\lambda }_{\mathrm{T}}$ in Zn-brochantite in a TF of 0.3 T. The data for the longitudinal relaxation rate ${\lambda }_{\mathrm{L}}$ in a magnetic field of 8 mT are reproduced from Ref. [37]. The lower inset displays the linear scaling of the mean precession frequency with the bulk susceptibility [12] at low susceptibility values (high $T$'s). The extrapolation line yields ${\nu }_0=40.713$ MHz. The upper inset shows the $T$ dependence of the stretching exponent in the TF experiment.

Figure 3

The scaling of the Knight shift $K$ and the transverse muon relaxation rate ${\lambda }_{\mathrm{T}}$ with the bulk susceptibility $\chi$ in Zn-brochantite. The solid lines give the coupling $A_{\mathrm{k}}\left(A_{\mathrm{i}}\right)$ between the muons and the kagome (impurity) moments. The NMR Knight-shift data $K_{\mathrm{NMR}}$ are reproduced from Ref. [37].

Figure 4

The scaling of the inverse longitudinal muon relaxation rate with the applied LF in Zn-brochantite at 110 mK. Two power-law regimes are indicated by solid lines. The inset shows the corresponding polarization curves (symbols) and stretched-exponential fits (solid lines).