Paramagnetic Resonance and Spin-Lattice Relaxation for Ytterbium in Yttrium Ethyl Sulfate; Large Anisotropies and Evidence for Electric Dipole Transitions

Abstract

Paramagnetic resonance is detected for ${}_{}{}^{172}{}_{}{}^{}\mathrm{Yb}_{}^{3+}{}_{}{}^{}$ ions diluted in crystals of Y${\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_3$ · 9${\mathrm{H}}_2$O at temperatures $1.2\leqq T\leqq 4.2$ °K, and $\nu =23\mathrm{}$ GHz, for $0\leqq \theta \leqq 70°$, where $\theta$ is the angle between the crystal $c$ axis and $\overrightarrow{\mathrm{H}}$. We find $g_{\parallel }=3.328\mathrm{}\pm 0.005$; $g_{\perp }$ is not directly measured, but estimated to be $g_{\perp }\approx 0.01$ from the resonance intensity at $\theta =0\mathrm{}°$. An observed angular variation of ${10}^2$ in linewidth can be explained by a $c$-axis wander throughout the crystal, of order ${\left(\delta \theta \right)}_{\mathrm{rms}}\approx 0.05°$. A striking angular variation in line intensity, of the form $\frac{\left({tan}^2\theta \right)}{cos\theta }$ over five orders of magnitude, is used to deduce that the observed line is an electric dipole transition rather than the usual magnetic dipole transition, observed only at $\theta =0\mathrm{}°$. This is further confirmed by placement of the crystal in the cavity in regions of maximum electric or magnetic field. The electric dipole transition comes about by the combined action of the Zeeman perturbation and admixtures of even-parity states into the odd-parity $4f^{13}$ configuration by odd terms in the $C_{3h}$ crystal field. The direct spin-lattice relaxation rate is measured by a microwave pulse-recovery method and found to be $T_{1d}^{-1\mathrm{}}=134T{tan}^2\theta$ ${\sec }^{-1\mathrm{}}$ ($T$ in °K) at constant frequency $\nu =23.11\mathrm{}$ GHz, which corresponds to $T_{1d}^{-1\mathrm{}}=2.4\mathrm{}\times {10}^{-17\mathrm{}}{H}^5{cos}^3\theta {sin}^2\theta coth\left(\frac{h\nu }{2kT}\right)$ ${\sec }^{-1\mathrm{}}$ ($H$ in oersteds), the theoretically expected form. At large angles the data indicate a phonon bottle-neck. It was found that the EPR signal could be reduced by optical pumping in the $1- \mathrm{to} 3-\mu$ region. An optical pulse-recovery method was used to measure the Raman spin-lattice relaxation rate, $T_{1R}^{-1\mathrm{}}=0.0135\mathrm{}{T}^9$ ${\sec }^{-1\mathrm{}}$. These data are of central importance in the analysis of nuclear spin refrigerators utilizing this unusually anisotropic crystal.