High-temperature spin relaxation process in ${\text{Dy}}_2{\text{Ti}}_2{\text{O}}_7$ probed by ${}^{47}\text{T}\text{i-NQR}$

We have performed nuclear quadrupole resonance (NQR) experiments on ${}^{47}\text{T}\text{i}$ nuclei in ${\text{Dy}}_2{\text{Ti}}_2{\text{O}}_7$ in the temperature range of 70–300 K in order to investigate the dynamics of $4f$ electrons with strong Ising anisotropy. A significant change in the NQR frequency with temperature was attributed to the variation of the quadrupole moment of $\text{Dy}4f$ electrons. A quantitative account was given by the mean-field analysis of the quadrupole-quadrupole (Q-Q) interaction in the presence of the crystalline-electric-field splitting. The magnitude and the temperature dependence of the nuclear spin-lattice relaxation rate were analyzed, including both the spin-spin and the Q-Q interactions. The results indicate that these two types of interaction contribute almost equally to the fluctuation of Dy magnetic moments.

Figure 1

(Color online) (a) The crystal structure of ${\text{Dy}}_2{\text{Ti}}_2{\text{O}}_7$ viewed perpendicular to the [111] direction. A magnetic field applied along [111] generates two spectroscopically inequivalent Ti sites; ${\text{Ti}}^1$ on the triangular plane and ${\text{Ti}}^2$ on the kagome plane of the Ti pyrochlore sublattice. (b) ${}^{47}\text{T}\text{i-NMR}$ field-swept spectra at 9.7 MHz for the two field orientations. The one-in, three-out configuration is selected for $H\parallel \left[111\right]$, whereas the two-in, two-out configuration remains stable for $H\parallel \left[001\right]$. The arrows indicate the calculated resonance positions as described in the text. For $H\parallel \left[001\right]$, the two resonance lines in low field region were not observed probably because of too short $T_2$.

Figure 2

(Color online) ${}^{47}\text{T}\text{i-NQR}$ spectra at 150 and 240 K. The NQR frequencies depend strongly on temperature.

Figure 3

(Color online) The peak frequency (lower panel) and the full width at half maximum (upper panel) of the ${}^{47}\text{T}\text{i-NQR}$ resonance lines for the transitions $I_z=\pm 1/2\leftrightarrow \pm 3/2$ $\left({\nu }_Q\right)$ and $I_z=\pm 3/2\leftrightarrow \pm 5/2$ $\left(2{\nu }_Q\right)$. The dotted and double dashed lines in the lower panel show the calculated results considering the temperature dependence of the quadrupole moment $⟨C_0^2⟩$ without and with the electric quadrupole-quadrupole interaction, respectively.

Figure 4

(Color online) CEF level scheme of ${\text{Dy}}_2{\text{Ti}}_2{\text{O}}_7$ inferred from the CEF parameters of ${\text{Ho}}_2{\text{Ti}}_2{\text{O}}_7$ (Ref. 16). The arrows represent the major process for the spin-flip relaxations between the ground-state doublet.

Figure 5

(Color online) Temperature dependences of the spin-lattice relaxation rate $1/T_1$ and the spin-spin relaxation rates $1/T_2$ measured for the $I_z=\pm 1/2\leftrightarrow \pm 3/2$ $\left({\nu }_Q\right)$ and $I_z=\pm 3/2\leftrightarrow \pm 5/2$ $\left(2{\nu }_Q\right)$ transitions. The $1/T_1$ was measured at $2{\nu }_Q$. The three straight lines indicate the $T^{-3}$ dependence. One is the fit to the data of $1/T_1$ and others are multiplied by 4.6 and 7.6 (see text).

Figure 6

(Color online) Spin relaxation time $\tau$ as a function of temperature extracted from the ${}^{47}\text{T}\text{i-NQR}$ relaxation rate $1/T_1$ using Eq. (11) with the amplitude of the moment fluctuation $⟨J^2⟩$ shown in the inset. The results of the nuclear forward scattering (Ref. 23) is shown for comparisons. The Arrhenius fit gives the activation energy $E_a$ of $409\pm 10\text{K}$. The calculated results of $\tau$ based on the CEF scheme is shown for three cases, taking account of only the spin-spin interaction, only the quadrupole-quadrupole interaction, or both interactions together. The results for the first two cases coincide almost completely.