Dynamic spin fluctuations at $T\to 0$ in a spin-$\frac{1}{2}$ ferromagnetic kagome lattice

We report magnetization, electron-spin resonance (ESR), and muon-spin relaxation ($\mu$SR) measurements on single crystals of the $S=1/2$ (${\mathrm{Cu}}^{+2}$) kagome compound Cu(1,3-benzendicarboxylate). The $\mu$SR is carried to temperatures as low as 45 mK. The spin-Hamiltonian parameters are determined from the analysis of the magnetization and ESR data. We find that this compound has anisotropic ferromagnetic interactions. Nevertheless, no spin freezing is observed even at temperatures two orders of magnitude lower than the coupling constants. In light of this finding, the relation between persistent spin dynamics and spin liquids on kagome lattices is reexamined.

Figure 1

Magnetization of Cu(1,3-bdc) at $T=2.4$ K, measured at two directions of the crystal: $\mathbf{H}\parallel \widehat{\mathbf{c}}$ (black filled symbols) and $\mathbf{H}\perp \widehat{\mathbf{c}}$ (red hollow symbols). The dash-dotted line indicates a spin-$1/2$ Brillouin function with $g=2.0023$. The solid line indicates a fit to a Brillouin function with an effective field [see Eq. (2)]. The dashed (dotted) curves show the Brillouin function with an effective field using two possible derived Hamiltonian parameters given in Table 1.

Figure 2

Representative ESR data for the two measured directions, $\mathbf{H}\parallel \widehat{\mathbf{c}}$ (red) and $\mathbf{H}\perp \widehat{\mathbf{c}}$ (black), taken at $T=295$ K. The inset displays the ESR raw signal. The main panel shows the integrated signal (absorption line). The dashed lines demonstrate the fit to a Lorentzian function.

Figure 3

(a) The raw $\mu$SR data with applied longitudinal field of 50 to 800 G; the solid lines demonstrate the fit to Eq. (11). (b) A semilogarithmic scale of the spins fluctuation rate $\nu$ obtained in Ref. [14] with the added points at 240 and 45 mK. Inset: The kagome unit cell (bold red) with its three sublattices (a, b, and c), the corresponding magnetic moment (${\mathbf{M}}^a$, ${\mathbf{M}}^b$, and ${\mathbf{M}}^c$), and angles ($\alpha$, $\beta$, $\gamma$).

Figure 4

The temperature dependence of the inverse susceptibility ${\chi }^{-1}\left(T\right)$, measured at two directions: $\mathbf{H}\parallel \widehat{\mathbf{c}}$ (filled symbols) and $\mathbf{H}\perp \widehat{\mathbf{c}}$ (hollow symbols); the solid lines are fits to a the inverse Curie-Weiss law. The inset shows the residuals from the fit at low temperatures.