Figure 1

(a) The Cr atoms in SCGO form a lattice of kagome bilayers separated from each other by a layer of isolated dimers consisting of pairs of Cr atoms. Each kagome bilayer is a corner-sharing arrangement of tetrahedra and triangles made up of two kagome lattices coupled to each other through “apical” sites shared between up-pointing and down-pointing tetrahedra. Links between near-neighbor sites in each bilayer represent a Heisenberg exchange coupling $J=80\mathrm{K}$ between neighboring ${\mathrm{Cr}}^{3+}$ spins, while links in the isolated dimer layer represent a Heisenberg exchange coupling $J^{\prime }=216\mathrm{K}$ between the two ${\mathrm{Cr}}^{3+}$ ions that constitute each pair. Two vacancies in a triangle [(green) circles] leave behind an orphan spin. (b) The 12 ${\mathrm{Cr}}^{3+}$ sites (black) that are hyperfine coupled to a given Ga ($4f$) site (red) in the SCGO lattice.Reuse & Permissions

Figure 2

(a) In the spin-liquid regime, the orphan spin in field $h$ develops magnetization (symbols) that matches $B_S(h/2,T)$, the magnetization of a spin $S$ in field $h/2$ (full line). The dotted curve is the magnetization for an isolated spin $S$ in field $h$. (b) The orphan induced spin texture shown along two cuts on the lattice. Numerical data are shown as points with error bars and the effective theory result as lines. The spin texture shown at the top (bottom) of the main plot is along the cut shown on the left (right) of the orphan spin (arrow) in the inset. The orphan spin is denoted by an arrow in the inset. (c) The impurity magnetization (defined in text) of a single orphan-texture complex (symbols) compared with $B_{S/2}(h,T)$ (solid curve), the magnetization curve of a classical spin $S/2$ in the spin-liquid regime. Note the much faster convergence of numerical data to $B_{S/2}(h,T)$ in the linear (small $hS/T$) part of the magnetization curve. Inset: The corresponding impurity susceptibility (defined in text) matches the susceptibility of a free classical spin $S/2$ up to temperatures $T\sim 0.1J{S}^2$.Reuse & Permissions

Figure 3

(a) ${}^{71}\mathrm{Ga}(4f)$ “field-scan” NMR lines predicted [10] within the minimal disorder model of uncorrelated dilution at vacancy density $x=0.2$. (b) Experimental results of Ref. 7 for field-scan ${}^{71}\mathrm{Ga}(4f)$ NMR lines (dots) at dilution $x=0.19$ compared to theoretical predictions of the minimal disorder model (with $y$ axis rescaled and $x$ axis offset appropriately for easy comparison of linewidths and shapes of all curves) at vacancy density $x=0.2$ (dashed curves) and $x=0.3$ (full curves). Only the low-field side of the experimental line is compared with theory, as the high-field side is known to be contaminated by the presence of a satellite peak arising from nonstoichiometric (impurity) ${}^{71}\mathrm{Ga}$ nuclei located at three different Cr sites in the SCGO lattice [7]. (c) Temperature and $x$ dependence of the width $\Delta H$ of the theoretically predicted field-scan ${}^{71}\mathrm{Ga}(4f)$ NMR lines, normalized by a reference field $H_{\mathrm{ref}}=3.12\mathrm{T}$. Solid curves in the main plot are fits of $\Delta H$ to $\mathcal{A}(x)/T$ over the experimentally relevant temperature range, and inset shows the approximately linear $x$ dependence of the corresponding best-fit values of $\mathcal{A}(x)$.Reuse & Permissions