Ground State of the Kagomé-Like $S=1/2$ Antiferromagnet Volborthite ${\mathrm{Cu}}_3{\mathrm{V}}_2{\mathrm{O}}_7(\mathrm{OH}{)}_2·2{\mathrm{H}}_2\mathrm{O}$

The volborthite compound is one of the very few realizations of $S=1/2$ quantum spins on a highly frustrated kagomé-like lattice. Low-$T$ SQUID measurements reveal a broad magnetic transition below 2 K which is further confirmed by a peak in the ${}^{51}\mathrm{V}$ nuclear spin relaxation rate ($1/T_1$) at $1.4\mathrm{K}\pm 0.2\mathrm{K}$. Through ${}^{51}\mathrm{V}$ NMR, the ground state (GS) appears to be a mixture of different spin configurations, among which 20% corresponds to a well defined short-range order, possibly of the $\sqrt{3}\times \sqrt{3}$ type. While the freezing involves all the ${\mathrm{Cu}}^{2+}$ spins, only 40% of the copper moment is actually frozen which suggests that quantum fluctuations strongly renormalize the GS.

Figure 1

SQUID dc susceptibility in ${\mathrm{Cu}}_{3(1-x)}{\mathrm{Zn}}_{3x}{\mathrm{V}}_2{\mathrm{O}}_7(\mathrm{OH}{)}_2·2{\mathrm{H}}_2\mathrm{O}$ measured after two cooling protocols, with (open symbols) and without (full symbols) a 100 Oe applied field. Inset: comparison of $T_g$ vs $S=0$ impurity dilution rate in volborthite and SCGO bilayer compounds.

Figure 2

${}^{51}\mathrm{V}$ NMR spectra measured at 20.733 MHz as a function of the applied field. For clarity, the spectra have been normalized to their maximum value. The vertical arrow shows the position $H_0$ of the unshifted reference line.

Figure 3

Half widths of the NMR spectra measured at $1/2$ ($\mathrm{HW}1/2$, open symbols) and $1/5$ ($\mathrm{HW}1/5$, full symbols) of the maximum height. Inset: $T$ dependence of the ${}^{51}\mathrm{V}$ spin-lattice relaxation rate ($1/T_1$) measured at the maximum intensity of the spectra ($H=1.85\mathrm{T}$). Lines are guides for the eye.

Figure 4

${}^{51}\mathrm{V}$ NMR spectra measured for two different delays $\tau$ at $T=0.35\mathrm{K}$. Note the different scales in the top and bottom panel. The solid lines are fits to the data and result from the sum of three components (dashed, dashed-dotted, and dotted lines) as explained in the text. Inset: scheme of the proposed $\sqrt{3}\times \sqrt{3}$ local order responsible for the ordered component (dashed line). The vector at the center of the hexagon stands for the resulting frozen field at the vanadium site.