${}^7$Li NMR study of the ordering phenomena in the intrinsic two-component magnetoelectric material Li${}_2$ZrCuO${}_4$

We report an experimental and theoretical study of the low temperature ${}^7$Li nuclear magnetic resonance (NMR) spectra of oriented powder samples of $\gamma$-Li${}_2$ZrCuO${}_4$ ($\equiv$Li${}_2$CuZrO${}_4$) which comprises interpenetrating sublattices of frustrated quasi-one-dimensional $s=1/2$ quantum Heisenberg magnetic Cu${}^{2+}$ chains and frustrated quantum Ising electric sublattice of Li${}_{\mathrm{I}}$ ions. Incommensurate spin order occurring in this compound at $T_{\mathrm{N}}\backsimeq 6$ K gives rise to a drastic change of the ${}^7$Li NMR spectrum. We show that the peculiar NMR line shapes are determined by the specific, sample dependent, distribution of the Li${}_{\mathrm{I}}$ ions in the glassy ordered electric sublattice. The analysis of the NMR data in the framework of a spin-spiral model gives evidence for a remarkable interaction between magnetic and electric degrees of freedom in $\gamma$-Li${}_2$ZrCuO${}_4$, which suggests it as a promising model compound for fundamental studies of complex magnetoelectric phenomena and illustrates well their richness.

Figure 1

Interpenetrating spin-1/2 magnetic and pseudospin-1/2 electric sublattices in Li${}_2$ZrCuO${}_4$ associated with Cu${}^{2+}$ spins in the CuO${}_2$ chains and with half-occupied Li${}_{\mathrm{I}}$ split position, respectively. Arrows show schematically a possible spiral spin order in the CuO${}_2$ chains.

Figure 2

Comparison of low-temperature ${}^7$Li NMR spectra of the Li${}_2$ZrCuO${}_4$  sample studied in the present work (left panel) and those from Ref. 8 (right panel). Thick solid lines: Results of the model fitting with different Li${}_{\mathrm{I}}$-distribution functions, $f_1$ (left panel) and $f_3$ (right panel), respectively (see the text). Thin solid lines: Partial contribution of the ${}^7$Li${}_{\mathrm{II}}$ NMR signal. Dashed lines in the left panel show the ${}^7$Li NMR spectra at 10 K. (a) and (c) Low-$T$ ${}^7$Li NMR spectra obtained for $\mathbf{H}$ $\parallel$ $\mathbf{a}$. (b) and (d) Low-$T$${}^7$Li NMR spectra obtained for $\mathbf{H}$ $\perp$ $\mathbf{a}$.

Figure 3

Simulation of the ${}^7$Li${}_{\mathrm{I}}$ NMR line shape with $A^{\left(0\right)}=0.06$ T, $A^{\left(1\right)}=black0.18$ T, and different distribution of Li${}_{\mathrm{I}}$ centers: (a) $black\sigma =0$,$\pm$1; (b)–(d) $f\left(black\sigma \right)=f_{1,2,3}\left(z\right)$, Eq. (4), respectively.