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Description
Traditional NMR data analysis techniques, such as the stretched exponential fit, are used to determine the sample-averaged nuclear spin-lattice relaxation rate $1/T_1$. However, they face difficulty when dealing with heterogeneous materials with NMR signals coming from distinct local environments, especially those with large, overlapping distributions of their Knight shifts and $1/T_1$.
To overcome this, we perform inverse Laplace transform (ILT) to obtain the histogram $P(1/T_1)$ of the $1/T_1$ distribution from the nuclear spin recovery curve $M(t)$. We apply this technique to $^{63}$Cu and $^{79}$Br NQR data of kagome lattice materials herbertsmithite (ZnCu$_{3}$(OD)$_{6}$Cl$_2$) and Zn-barlowite (ZnCu$_{3}$(OD)$_{6}$FBr) as well as $^{19}$F NMR data of the latter.
From the $^{63}$Cu data, we were able to use ILT to observe the gradual emergence of spin singlets with spatially varying excitation gaps below $\sim$30~K in both materials. We also performed ILT across the $^{19}$F NMR spectrum to obtain 3-dimensional ILT-resolved NMR lineshapes, which allowed us to separate the signals coming from two distinct, overlapping sites.
[1] J. Wang et al., Nat. Phys. 17, 1109–1113 (2021)
[2] J. Wang, W Yuan et al., Phys. Rev. Lett. (in press)
