Spin Noise Spectroscopy of Herbertsmithite ZnCu3(OH)6Cl2: Spinon Mediation of Witness-Spin Dynamics and Ground State

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 a classical spin ice material Dy2Ti2O7 [1] and a spiral spin liquid material Ca10Cr7O28 [2]. Here we extend the technique to herbertsmithite ZnCu3(OH)6Cl2, an iconic quantum spin liquid candidate with S = 1/2 Cu2+ kagome layers that are separated by nonmagnetic Zn2+ layers [3]. Some S = 1/2 Cu2+ randomly substitute Zn2+ to contribute weakly interacting quasi-free spins that are usually regarded as “impurities”. We reconceptualize them as “witness-spins” through which one can probe a conjectured quantum spin liquid state on the kagome layer.
By developing a millikelvin SQUID-based spin noise spectrometer with fT/√Hz-sensitivity and μs-time resolution, we detect magnetization noise M(t,T) of the witness-spins in ZnCu3(OH)6Cl2 which fluctuates intensively at pT-order [4]. A scale-invariant noise power spectral density S_M (ω,T)∝〖1/ω〗^α(T) and noise variance σ_M^2 (T) indicate a sharp transition at T^*∼260 mK. We introduce a model of spinon-mediated witness-spin interactions which, despite having only one free parameter, is consistent with the full range of experimental observations. Thus, the witness-spin noise phenomenology evidences spinon-mediated witness-spin dynamics in ZnCu3(OH)6Cl2.

[1] R. Dusad et al. Magnetic monopole noise. Nature 571, 234 (2019).
[2] H. Takahashi & C.-C. Hsu et al. Spiral spin liquid noise. Proc. Natl. Acad. Sci. U.S.A. 122, e2422498122 (2025).
[3] M. R. Norman, Colloquium: Herbertsmithite and the search for the quantum spin liquid. Rev. Mod. Phys. 88, 041002 (2016).
[4] H. Takahashi, J. Murphy, M. Wood-Thanan et al. Spinon Mediation of Witness-Spin Dynamics and Ground State in Herbertsmithite. Submitted, in prep for arXiv (2025)