NMR study of lineshifts and relaxation rates of the one-dimensional antiferromagnet ${\mathrm{LiCuVO}}_4$

NMR measurements were performed on single-crystalline samples of the one-dimensional Heisenberg antiferromagnet (1D HAF) ${\mathrm{LiCuVO}}_4$. We investigated ${}^7\mathrm{Li}$ and ${}^{51}\mathrm{V}$ NMR spectra, deduced the respective lineshifts $K\left(T\right)$, spin-lattice relaxation rates $1∕T_1$, and spin-spin relaxation rates $1∕T_2$ and $1∕T_{2G}$. The results are compared to theoretical predictions for the relaxation rates $1∕T_1\left(T\right)$ and $1∕T_{2G}\left(T\right)$ deduced from the dynamic susceptibility $\chi (\mathbf{q},\omega )$ of a 1D HAF spin chain as proposed by Sachdev [Phys. Rev. B 50, 13006 (1994)]. We document a correspondence between the anisotropic relaxation rates derived from electron paramagnetic resonance linewidth $\mathrm{\Delta }H\left(T\right)$ and nuclear magnetic resonance $1∕T_1\left(T\right)$, respectively, the former being well described in the framework of symmetric anisotropic exchange interactions for ${\mathrm{LiCuVO}}_4$ by Krug von Nidda et al. [Phys. Rev. B 65, 134445 (2002)].

Figure 1

Temperature dependence of the NMR spectra of single-crystalline ${\mathrm{LiCuVO}}_4$ for ${}^7\mathrm{Li}$ and ${}^{51}\mathrm{V}$ on the left and right columns, respectively, at $93.2\mathrm{MHz}$. Solid and dotted lines depict an orientation of the crystal with $H\Vert b$ and $H\perp b$, respectively.

Figure 2

Left column: NMR lineshifts $K\left(T\right)$ vs $T$ in single-crystalline ${\mathrm{LiCuVO}}_4$ for ${}^7\mathrm{Li}$ (A), (B) and ${}^{51}\mathrm{V}$ NMR (C), measured for different orientations of the crystal with respect to $H$. Right column: plots of $K\left(T\right)$ vs $\chi \left(T\right)$ with $T$ as implicit parameter for ${}^7\mathrm{Li}$ (D), (E) and ${}^{51}\mathrm{V}$ (F) yielding the hyperfine coupling constants $A_{\Vert }$ and $A_{\perp }$.

Figure 3

Temperature dependence of the spin-lattice relaxation obtained from magnetic resonance experiments: The spin-lattice relaxation rates $1∕T_1$ for ${}^7\mathrm{Li}$ NMR (A) and ${}^{51}\mathrm{V}$ NMR (B) were measured for $H\Vert b$ (46.6 and $93.2\mathrm{MHz}$ depicted as solid circles and open triangles, respectively) and $H\perp b$ ($93.2\mathrm{MHz}$ open diamonds). The lines in (A) and (B) are drawn to guide the eye. For comparison the EPR linewidth $\mathrm{\Delta }{H}_{\mathrm{EPR}}\left(T\right)$ as measured for all three orientations of the single crystal is displayed in (C). Arrows indicate the qualitative correspondence in the orientational anisotropy for the NMR rates as well as the EPR linewidth regarding the ratio of the obtained values for orientations $H\Vert b$ and $H\perp b$.

Figure 4

Decay of the transverse magnetization $M_{xy}\left(2\tau \right)$ in the powder sample at $78\mathrm{K}$ shown for ${}^7\mathrm{Li}$ (upper frame) and ${}^{51}\mathrm{V}$ (lower frame) in the representation $M_{xy}\left(2\tau \right)$ vs ${\tau }_{AB}^2$ and ${\tau }_{AB}$, respectively; for details see text. The insets show the decay of $M_{xy}\left(2\tau \right)$ of single-crystalline ${\mathrm{LiCuVO}}_4$ for different orientations of the crystal with respect to $H$.

Figure 5

Temperature dependence of $1∕T_{2\mathrm{G}}\left(T\right)$ for ${}^7\mathrm{Li}$ displayed for comparison with Sachdev’s model (Ref. 5); see text for details.