NMR and NQR study of the tetrahedral frustrated quantum spin system ${\text{Cu}}_2{\text{Te}}_2{\text{O}}_5{\text{Br}}_2$ in its paramagnetic phase

The quantum antiferromagnet ${\text{Cu}}_2{\text{Te}}_2{\text{O}}_5{\text{Br}}_2$ was investigated by NMR and nuclear quadrupole resonance (NQR). The ${}^{125}\text{T}\text{e}$ NMR investigation showed that there is a magnetic transition around 10.5 K at 9 T, in agreement with previous studies. From the divergence of the spin-lattice relaxation rate, we ruled out the possibility that the transition could be governed by a one-dimensional divergence of the spin-spin correlation function. The observed anisotropy of the ${}^{125}\text{T}\text{e}$ shift was shown to be due to a spin polarization of the $5s^2$ “E” doublet of the $\left[{\text{TeO}}_3\text{E}\right]$ tetrahedra, highlighting the importance of tellurium in the exchange paths. In the paramagnetic state, Br NQR and NMR measurements led to the determination of the Br hyperfine coupling and the electric field gradient tensor, and to the spin polarization of $\text{Br}p$ orbitals. The results demonstrate the crucial role of bromine in the interaction paths between Cu spins.

Figure 1

Schematic views of the ${\text{Cu}}_2{\text{Te}}_2{\text{O}}_5{\text{Br}}_2$ structure along the [001] axis (a) and the $\left[\overline{1}10\right]$ axis (b). Copper atoms (small spheres) are interconnected to emphasize the tetrahedral configuration. Tellurium atoms (not represented) are placed inside the sketched “${\text{O}}_3\text{E}$” tetrahedra, E representing the $5s^2$ lone pair of the Te atom (Ref. 1).

Figure 2

Temperature dependence of the shift of the four inequivalent ${}^{125}\text{T}\text{e}$ nuclear spins measured in a field of 9 T almost parallel to [110] superimposed to the SQUID susceptibility measurements (line). The existence of four NMR lines is due to a slight misorientation of the field out of the $ab$ plane.

Figure 3

(Color online) Linear relationship between the shift of the four inequivalent ${}^{125}\text{T}\text{e}$ nuclear spins measured in a field of 9 T almost parallel to [110] and the SQUID susceptibility. The calculation of the slopes lead to the determination of the hyperfine field.

Figure 4

Crystal orientation dependence of the ${}^{125}\text{T}\text{e}$ hyperfine field measured at 15 K and 9.4 T. The crystal was aligned to obtain only two resonance peaks in the $ab$ plane (with this orientation, the filled diamonds and the filled triangles in Figs. 2, 3 would be indistinguishable from the open diamonds and the open triangles, respectively). Inset: dipolar field calculated for a Te orbital pointing toward the center of the Br-Br axis.

Figure 5

Schematic view of the ${\text{Cu}}_2{\text{Te}}_2{\text{O}}_5{\text{Br}}_2$ structure along the [100] axis. Oxygen atoms (smallest spheres) are displayed and dashed lines show the exchange paths proposed by Ref. 9.

Figure 6

Temperature dependence of the ${}^{125}\text{T}\text{e}$ spin-lattice relaxation rate measured at 9 T on the lowest-frequency resonance (filled diamonds in Figs. 2, 3).

Figure 7

Br NQR spectrum measured at 15 K. The intensities have been divided by the square of the frequency. Note that the slight splitting observed on both lines is due to the presence of a residual nonzero ${\mathit{B}}_{\mathbf{0}}$ field in the superconducting coil.

Figure 8

(a) Sketch of the energy levels of Br nuclei. The solid arrows are the $\Delta m=1$ transitions and the dotted ones the $\Delta m>1$ transitions. (b) Definition of angles $\Theta$, $\Phi$, $\Omega$, and $\Psi$. The $X$, $Y$, and $Z$ axes correspond to the principal axes of the EFG and Knight shift tensors.

Figure 9

NMR Spectra for $B_0=14\text{T}$ along [110]. The intensities have been divided by the square of the frequency. Each line has been identified. The two sharp lines, one around 158 MHz and the other around 169 MHz indicate the position of the ${}^{63}\text{C}\text{u}$ and ${}^{65}\text{C}\text{u}$ resonance of the copper NMR coil and have been used to determine the exact value of $B_0$. At low frequencies (150–180 MHz) we can find the eight central lines. For ${\text{Br}}_i$ and ${\text{Br}}_{ii}$ these lines are overlapping since shift and quadrupolar frequency are small in this orientation of the field and the misorientation is not sufficient to separate them. At high frequencies (200–210 MHz), we observe only the four high-frequency satellites of ${\text{Br}}_i$ and ${\text{Br}}_{ii}$. Low frequency satellites are expected below 100 MHz and Br and ${\text{Br}}_{iii}$ high-frequency satellites are expected around 240 MHz. Note that since the field direction is close to the principal axis of the EFG tensor, the contribution of the quadrupolar term to the resonance frequency is nearly maximum).

Figure 10

(Color online) Br hyperfine shift vs magnetic susceptibility with $T$ as an implicit parameter. NMR shifts were measured on ${}^{79}\text{B}\text{r}$ at 9 T between 12 and 50 K. Black dots correspond to $K_{zz}$, parallel to the Cu-Br bond, and open circles to $K_{xx}=K_{yy}$.

Figure 11

(Color online) Computed Br transition frequencies and intensities as a function of the external magnetic field amplitude $\left|{\mathit{B}}_0\right|$ for ${\mathit{B}}_0$ oriented along [110]. The 48 possible transitions for the two Br isotopes and the four inequivalent sites are drawn. The intensities are represented on a color scale in arbitrary units: the lighter the color, the weaker the intensity. The experimental points corresponding to observed transitions are denoted by horizontal tips for spectra recorded at constant field and variable frequencies and by vertical tips for spectra recorded at fixed frequency sweeping the magnetic field.