High-field NMR of the quasi-one-dimensional antiferromagnet LiCuVO${}_4$

We report on NMR studies of the quasi-one-dimensional (1D) frustrated $S=1/2$ chain cuprate LiCuVO${}_4$ in magnetic fields $H$ up to ${\mu }_{0}H=30$ T ($\approx$70$\%$ of the saturation field $H_{\mathrm{sat}}$). NMR spectra in fields higher than $H_{c2}$ (${\mu }_0{H}_{c2}\approx 7.5$ T) and temperatures $T<T_N$ can be described within the model of a spin-modulated phase in which the magnetic moments are aligned parallel to the applied field $H$ and their values alternate sinusoidally along the magnetic chains. Based on theoretical concepts about frustrated 1D $S=1/2$ chains, the field dependence of the modulation strength of the magnetic structure is deduced from our experiments. Relaxation time $T_2$ measurements of the ${}^{51}$V nuclei show that $T_2$ depends on the particular position of the probing ${}^{51}$V nucleus with respect to the magnetic copper moments within the 1D chains: the largest $T_2$ value is observed for the vanadium nuclei which are right next to the magnetic Cu${}^{2+}$ ion with the largest ordered magnetic moment. This observation is in agreement with the expectation for the spin-modulated magnetic structure. The $(H,T)$ magnetic phase diagram of LiCuVO${}_4$ is discussed.

Figure 1

(a) Scheme of the Cu${}^{2+}$ moments in the crystal structure of LiCuVO${}_4$. Copper ions are marked by open circles with arrows at each site, which constitute the spin-modulated structure for $H>H_{c2}$, $\mathbf{H}\parallel \mathbf{c}$, and $T<T_N$. The red arrows $J_N,J_{\mathrm{NN}}$, and $J_a$ denote the main exchange integrals (Ref. 14). Additionally, the positions of Li (orange) and V (green) ions are exemplarily depicted by one ion each. (b) Projection of the magnetic structure of two ab planes for $H<H_{c2}$ and $\mathbf{H}\parallel \mathbf{c}$.

Figure 2

Field dependence of the incommensurate wave vector $k_{ic}$ for applied magnetic fields $\mathbf{H}\parallel \mathbf{c}$ in LiCuVO${}_4$. The open symbols are data from neutron diffraction of different authors: $\diamond$, Ref. 12; $\square$, Ref. 23; and $▵$ and $\circ$, Ref. 24. The solid line represents values obtained from magnetization measurements (Ref. 20) in the framework of the 1D model using Eq. (3).

Figure 3

Time dependence of the integral amplitude $M_{x,y}\left(2\tau \right)$ of the spin-echo signal (symbols) for $\mathbf{H}\parallel \mathbf{c}$, ${\mu }_{0}H=29.55$ T, $\nu =336$ MHz at $T=1$ K. Solid line: result of fitting with Eq. (4).

Figure 4

${}^{51}$V NMR spectra at $T=1.7$ and 0.38 K for $\mathbf{H}\parallel \mathbf{c}$ (upper and lower panel, respectively). Residual signals from metallic copper within the experimental setup are marked with arrows.

Figure 5

${}^7$Li NMR spectrum (black squares) at 1.7 K ($T<T_N$) for $\nu =336$ MHz and $\mathbf{H}\parallel \mathbf{c}$. The solid lines represent simulations of the NMR spectrum: the lower curve was computed using the assumption of short-range order in the c direction, and the upper curve was computed for disorder in the c direction.

Figure 6

Temperature dependence of ${}^{51}$V NMR spectra obtained at $\nu =$ (a) 245, (b) 291, and (c) 336 MHz for $\mathbf{H}\parallel \mathbf{c}$. Residual signals from metallic copper and aluminum within the experimental setup are marked with arrows.

Figure 7

${}^{51}$V NMR spectra and field dependences of the spin-spin relaxation time $T_2$ measured at frequencies (a) 164.6 MHz, (b) 210.5 MHz, (c) 291 MHz, and (d) 336 MHz for $\mathbf{H}\parallel \mathbf{c}$ in LiCuVO${}_4$ (solid squares). Spectra were measured at $T=0.38$ K and $T_2$ values at $T=1$ K, respectively. Open circles correspond to the expected NMR spectra after a so-called $T_2$ correction (see text).

Figure 8

${}^{51}$V and ${}^7$Li NMR spectra in the paramagnetic phase ($T=4$ K) for $\nu =336$ MHz and $\mathbf{H}\parallel \mathbf{c}$. The solid lines show the NMR spectra simulations with hyperfine constants of the contact interaction given in the text.

Figure 9

Upper frame: ${}^{51}$V NMR spectrum in the high-field phase for $T=0.38$ K $\ll T_N$, $\nu =245$ MHz, and $\mathbf{H}\parallel \mathbf{c}$ (solid squares). The solid lines show simulations of the NMR spectrum utilizing the model of the spin-modulated phase [see Eq. (2)] with long-range order (line i), short-range order (line ii), and disorder (line iii) in the c direction, respectively. Lower frame: Ordered magnetic moments along the chain are shown schematically.

Figure 10

Upper panel: Field dependence of the magnetization ${\mu }_m$ and modulation strength ${\mu }_1$ of the spin-modulated phase [see Eq. (2)]. The data ${\mu }_m\left(H\right)$ (triangles) are taken from Ref. 20. The values ${\mu }_1\left(H\right)$ (circles and squares) are obtained from fitting NMR spectra. Lower panel: Field dependence of the extremal values of magnetic moments in the spin-modulated structure as ${\mu }_m\pm {\mu }_1$. For both panels, solid symbols denote the fitting results modeling long- and short-range order in the c direction. The model ii is the most realistic one. The open circles and squares denote the fitting results modeling a disorder in the c direction. Square and circle symbols distinguish different temperatures of 1.7 and 0.38 K for $\mathbf{H}\parallel \mathbf{c}$.

Figure 11

$(H,T)$ phase diagram of LiCuVO${}_4$ for $\mathbf{H}\parallel \mathbf{c}$. The dashed lines are drawn to guide the eye. Additional data are collected from Refs. 12, 29, 13, and 30.