Frustrated three-dimensional antiferromagnet ${\text{Li}}_2{\text{CuW}}_2{\text{O}}_8$: ${}^7\mathrm{Li}$ NMR and the effect of nonmagnetic dilution

We report a ${}^7\mathrm{Li}$ nuclear magnetic resonance (NMR) study of a frustrated three-dimensional spin-$\frac{1}{2}$ antiferromagnet ${\text{Li}}_2{\text{CuW}}_2{\text{O}}_8$ and also explore the effect of nonmagnetic dilution. The magnetic long-range ordering in the parent compound at $T_{\mathrm{N}}\simeq 3.9\mathrm{K}$ was detected from the drastic line broadening and a peak in the spin-lattice relaxation rate ($1/T_1$). The NMR spectrum above $T_{\mathrm{N}}$ broadens systematically, and its full width at half maximum (FWHM) tracks the static spin susceptibility. From the analysis of FWHM vs static susceptibility, the coupling between the Li nuclei and ${\text{Cu}}^{2+}$ ions was found to be purely dipolar in nature. The magnitude of the maximum exchange coupling constant is $J_{\max }/k_{\mathrm{B}}\simeq 13\mathrm{K}$. NMR spectra below $T_{\mathrm{N}}$ broaden abruptly and transform into a double-horn pattern reflecting the commensurate nature of the spin structure in the ordered state. Below $T_{\mathrm{N}}$, $1/T_1$ follows a $T^5$ behavior. The frustrated nature of the compound is confirmed by persistent magnetic correlations at high temperatures well above $T_{\mathrm{N}}$. The dilution of the spin lattice with nonmagnetic Zn atoms has dramatic influence on $T_N$ that decreases exponentially similar to quasi-one-dimensional antiferromagnets, even though ${\text{Li}}_2{\text{CuW}}_2{\text{O}}_8$ has only a weak one-dimensional anisotropy. Heat capacity of doped samples follows power law ($C_{\mathrm{p}}\propto T^{\alpha }$) below $T_{\mathrm{N}}$, and the exponent ($\alpha$) decreases from 3 in the parent compound to 1 in the 25% doped sample.

Figure 1

Triangular layer formed by ${\text{Cu}}^{2+}$ ions, columnar arrangement of spins, and the couplings of Li atoms to the magnetic spins are shown.

Figure 2

X-ray powder diffraction pattern (open circles) at room temperature for ${\text{Li}}_2{\text{CuW}}_2{\text{O}}_8$. The solid red line represents the calculated pattern using Le Bail fit, with the vertical bars showing the expected Bragg peaks, and the lower solid blue line representing the difference between the observed and calculated intensities.

Figure 3

${}^7\mathrm{Li}$ Fourier transform spectra measured at an applied field of $H=1.5109$ T and at different temperatures.

Figure 4

Temperature dependence of the full width at half maximum ($\mathrm{\Delta }\nu$) of the ${}^7\mathrm{Li}$ NMR spectra measured at an applied field of $H=1.5109$ T (left $y$ axis) and magnetic susceptibility ($\chi$) measured at $H=1$ T (right $y$ axis). Inset shows the $\mathrm{\Delta }\nu$ vs $\chi$ with temperature as an implicit parameter and the solid line is the fit by Eq. (3).

Figure 5

(a) Temperature dependence of the ${}^7\mathrm{Li}$ spin-lattice relaxation rate, $1/T_1$, for ${\text{Li}}_2{\text{CuW}}_2{\text{O}}_8$ at $H=1.5109$ T. The solid line and the dotted line correspond to $1/T_1\propto T^5$ and $1/T_1\propto T^2{e}^{-\mathrm{\Delta }/k_{\mathrm{B}}T}$ behaviors, respectively. The dashed line is the linear fit ($1/T_1\propto T$) in the $5.5\mathrm{K}\le T\le 16$ K range. The inset shows $1/T_1$ vs $-logH$ measured at $T=8$ K. (b) $1/\chi T_{1}T$ as a function of temperature.

Figure 6

$1/T_2$ as a function of temperature. Inset: spin-echo decays are plotted as a function of $\tau$ at two different temperatures. The solid line is the fit using Eq. (5).

Figure 7

Temperature-dependent field-sweep ${}^7\mathrm{Li}$ NMR spectra measured at 24.79 MHz below $T_{\mathrm{N}}$. The red solid line is the fit to the spectra at 3.43 K using the sum of two Gaussian functions.

Figure 8

Temperature dependence of the internal field $H_{\mathrm{int}}$ obtained from ${}^7\mathrm{Li}$ NMR spectra measured at 24.79 MHz in the ordered state. The solid line is the fit by Eq. (6) as described in the text. Inset: $H_{\mathrm{int}}$ vs $\tau$ and the solid line is the simulation of $0.053\times {\tau }^{0.35}$ taking $T_{\mathrm{N}}\simeq 3.51$ K.

Figure 9

$\chi \left(T\right)$ of Zn-doped ${\text{Li}}_2{\text{CuW}}_2{\text{O}}_8$ samples measured at ${\mu }_{0}H=1$ T. Inset: Curie-Weiss temperature ${\theta }_{\mathrm{CW}}$ as a function of doping concentration $x$ and the solid line is a linear fit.

Figure 10

$C_p/T$ of Zn-doped ${\text{Li}}_2{\text{CuW}}_2{\text{O}}_8$ samples measured in zero magnetic field. The downward arrows point to the Néel temperatures $T_N$. The solid lines are the fits by power law below $T_{\mathrm{N}}$.

Figure 11

${}^7\mathrm{Li} 1/T_1$ for ${\text{Li}}_2{\text{CuW}}_2{\text{O}}_8$ vs the reduced temperature ($\tau$). The solid line is a fit by the power law, 1/$T_1\propto {\tau }^{-\gamma }$ with $\gamma \simeq 0.1$ and a fixed $T_{\mathrm{N}}\simeq 3.6$ K.

Figure 12

Log $T_{\mathrm{N}}$ and $\alpha$ vs $x$ obtained from the $C_{\mathrm{p}}\left(T\right)$ analysis in Fig. 10 in the left and right $y$ axes, respectively. The solid lines are the linear fits. Inset: $T_{\mathrm{N}}/J^{\prime }$ vs $\overline{L}{J}^{\prime }$ where the average chain length $\overline{L}=1/x-1$ and $J_{1\mathrm{D}}=15$ K is compared with the theoretical results from Ref. [54].