Spin liquid candidate materials often suffer from disorder, if they are free from undesirable magnetic long range order. Since NMR is a site-specific probe, one can in principle use the NMR spin-lattice relaxation rate 1/T₁ ~ ∑ Im χ(q,ω_n)/ω_n as the local probe of the disorder-induced spatial distribution of low-energy spin excitations, where Im χ(q,ω_n) is the imaginary part of the dynamical electron spin susceptibility at the resonant frequency ω_n. Nonetheless, NMR experts often deduce only the spatially averaged value of the distributed 1/T₁ by fitting the time evolution of the nuclear magnetization with an empirical stretched exponential form, M(t) = A - B * exp[-(t/T₁)^β]. But the stretched fit value of 1/T₁ does not necessarily reflect the intrinsic spin liquid behavior one is looking for, because 1/T₁ in the vicinity of defects may be dominated by the properties of defects, and the distribution of 1/T₁ often reaches as large as several orders of magnitude. In this talk, we will introduce the novel approach based on the inverse Laplace transform (ILT) T₁ analysis techniques [1,2]. By numerically inverting M(t) based on ILT, one can deduce the histogram of the spatially distributed values of 1/T₁ in the form of the density distribution function P(1/T₁), i.e. the histogram of 1/T₁. We demonstrate that the stretched fit 1/T₁ is merely a crude approximation of the center of gravity of P(1/T₁). From the multiple peaks observed in P(1/T₁), we discuss the nature of the spatial distribution of the low energy spin excitations in spin liquid candidate materials, such as Cu₂IrO₃ [3], Ag₃LiIr₂O₆ [4] and beyond [5].

[1] P.M. Singer et al., PRB 101 (2020) 174508, and references therein.
[2] A. Arsenault et al., PRB 101 (2020) 184505.
[3] S. K. Takahashi et al., PRX 9 (2019) 031407.
[4] J. Wang et al., to be published.
[5] J. Wang et al., to be published.