Probing spin dynamics and quantum relaxation in $\mathrm{Li}{\mathrm{Y}}_{0.998}{\mathrm{Ho}}_{0.002}{\mathrm{F}}_4$ via ${}^{19}\mathrm{F}$ NMR

We report measurements of ${}^{19}\mathrm{F}$ nuclear spin-lattice relaxation $1∕T_1$ as a function of temperature and external magnetic field in a $\mathrm{Li}{\mathrm{Y}}_{0.998}{\mathrm{Ho}}_{0.002}{\mathrm{F}}_4$ single crystal, a single-ion magnet exhibiting interesting quantum effects. The ${}^{19}\mathrm{F}$ $1∕T_1$ is found to depend on the coupling with the diluted rare-earth (RE) moments, making it an effective probe of the rare-earth spin dynamics. The results for $1∕T_1$ show a behavior similar to that observed in molecular nanomagnets, a result which we attribute to the discreteness of the energy levels in both cases. At intermediate temperatures the lifetime broadening of the crystal field split RE magnetic levels follows a $T^3$ power law. At low temperature the field dependence of $1∕T_1$ shows peaks in correspondence to the critical magnetic fields for energy level crossings (LC). A key result of this study is that the broadening of the levels at LC is found to become extremely small at low temperatures, about $1.7\mathrm{mT}$, a value which is comparable to the weak dipolar fields at the RE lattice positions. Thus, unlike the molecular magnets, decoherence effects are strongly suppressed, and it may be possible to measure directly the level repulsions at avoided level crossings.

Figure 1

Variation of the low-lying energy states with magnetic field. (a) Levels calculated for ${\mathrm{Ho}}^{3+}$ ion $(J=8)$ with crystal field splitting. (b) Close-up view of the ground-state doublet, which strongly couples to the $I=7∕2$ Ho nucleus, resulting in 16 electro-nuclear states (from Ref. 9).

Figure 2

(a) Time decay of the sample magnetization (normalized to 1 at $t=0$) at $12\mathrm{K}$ and $40\mathrm{K}$ for $\mathrm{Li}{\mathrm{Y}}_{0.998}{\mathrm{Ho}}_{0.002}{\mathrm{F}}_4$ taken at a frequency of $13.30\mathrm{MHz}$. Solid lines are the long-time exponential fits to the data, from which we extract $1∕T_1$. (b) Plot of the recovery of the longitudinal magnetization versus the square root of time at the same two temperatures. Solid lines are guides to the eye.

Figure 3

(a) Temperature variation of the ${}^{19}\mathrm{F}$ spin-lattice relaxation rate at three frequencies. (b) Data in (a), normalized to a maximum value of 1, as a function of $t=T∕T_0$, where $T_0$ is the temperature at which the peak occurs in part (a). The solid line is a fit to Eq. (4) with $\alpha =3.0$.

Figure 4

(a) Variation of the $1∕T_1$ of ${}^{19}\mathrm{F}$ in $\mathrm{Li}{\mathrm{Y}}_{0.998}{\mathrm{Ho}}_{0.002}{\mathrm{F}}_4$ with the applied magnetic field at low field values. The solid curve is a fit of the background relaxation according to $0.96∕H^{0.8}\left({\mathrm{msec}}^{-1}\right)$. The inset shows the peak magnetic field value plotted vs the index $n$ of the level crossing. (b) Plot of the relaxation rate with the background term subtracted vs the component of the applied field in the direction of the anisotropy axis $z$. The solid curve is a fit to the data according to the inelastic contribution as discussed in the text.

Figure 5

Temperature dependence of the ${}^{19}\mathrm{F}$ relaxation rate at a field value corresponding to the energy level crossing at $n=5$, and to a value away from the peak between $n=5$ and $n=6$. The solid curves correspond to a fit of the data according to Eq. (6) (see text).