Spin-Lattice Relaxation of Protons in Uranium Hydride

$\beta -\mathrm{U}{\mathrm{H}}_3$ is known to be ferromagnetic below 180 °K. The spin-lattice relaxation time $T_1$ of the protons in the paramagnetic state has been measured in the temperature range 189-700 °K. At low temperatures close to the ferromagnetic transition, there is a steep rise in $T_1$ with temperature. At high temperatures, around 613 °K, there is a local minimum in $T_1$. It is shown that there are three mechanisms contributing to the relaxation rate: (a) time-dependent nuclear dipole-dipole interaction caused by hydrogen diffusion; (b) contact interaction between the conduction electrons and the protons, causing Korringa relaxation; and (c) Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the protons and the localized $f$ electrons via the conduction electrons; the relaxation caused by this interaction was found to fit Fradin's model. Separation of the three contributions from each other is achieved using their different temperature dependence. Measurement of the spin echo $T_2$ yields the value $E_a=19.25\mathrm{}$ kcal/mole for the activation energy of hydrogen diffusion. The Korringa contribution is $\frac{1}{T_{1K}T}=0.135\mathrm{}\pm 0.021$ sec ${}_{}{}^{-1\mathrm{}}{}_{}{}^{}\mathrm{°}\mathrm{K}_{}^{-1\mathrm{}}{}_{}{}^{}$. The paramagnetic part is $\frac{1}{T_{1f}T}=\frac{(101\mathrm{}\pm 3)}{(T-\Theta )}$ ${\sec }^{-1\mathrm{}}$ °${\mathrm{K}}^{-}$. Using Fradin's model we get for the density of states of the $s$-type conduction electrons at the Fermi level, $N\left(E_F\right)=1.65\mathrm{}$ states/eV. The coupling constant for the contact interaction is $\Delta =5.6\mathrm{}\times {10}^{-7\mathrm{}}$ eV. The exchange constant between the localized $5f$ electrons and the $s$-type conduction electrons is $\Gamma =0.18\mathrm{}$ eV. The Knight factor is $\xi =0.12\mathrm{}$. If one assumes a spherical Fermi surface and a free-electron behavior in the RKKY interaction, then the degree of ionicity of the uranium ion is shown to be ${\mathrm{U}}^{+3\mathrm{}}$.