Spin Noise Spectroscopy of Herbertsmithite ZnCu₃(OH)₆Cl₂

An emerging concept for identifying various types of spin liquid states, which are often altogether designated by the absence of order, is through their characteristic spin noise. This spin noise approach has been successfully demonstrated in the classical spin ice material Dy₂Ti₂O₇ [1,2] and the spiral spin liquid material Ca₁₀Cr₇O₂₈ [3]. Here we report the spin noise spectroscopy study of Herbertsmithite ZnCu₃(OH)₆Cl₂ [4], an iconic quantum spin liquid candidate with S = 1/2 Cu²⁺ kagome layers whose exact spin ground state has remained controversial. While much effort has focused on the kagome layer, here we exploit spin dynamics of the interlayer Cu²⁺ “witness-spins” which, interacting primarily via the kagome layer, evidence its quantum dynamics.

To do so, we have developed a mK SQUID-based spin noise spectrometer with fT/√Hz-sensitivity and µs-time resolution to measure the magnetization noise M(t, T) in ZnCu₃(OH)₆Cl₂. Below 400 mK, intense witness-spin fluctuations emerge over frequencies ranging 0.1 Hz < f < 1 kHz with a scale-invariant power spectral density S_M(ω,T)∝1/ω^α(T). We find a sharp transition at T* = 260 mK, indicated by a peak in both the noise variance and the µT-DC susceptibility. Below T*, the noise spectrum stabilizes as nearly 1/ω and the spin state enters an ultra-slow “aging” regime over at least 10⁵ s. We theoretically explore spinon RKKY interactions between the witness-spins for consistency with all these phenomena.



[1] R. Dusad et al. Nature 571, 234 (2019)

[2] J. C. Dasini et al. arXiv:2408.00460 (2024)

[3] H. Takahashi & C.-C. Hsu et al. arXiv:2405.02075 (2024)

[4] H. Takahashi & J. Murphy et al. submitted (2024)