Proton Spin-Lattice Relaxation in(Nd,La)2Mg3(NO3)12·24H2O in High Fields and Low Temperatures

The dependence of the proton relaxation time $T_{1p}$ on field $H$ and temperature $T$ in a crystal of ${\mathrm{}(\mathrm{N}\mathrm{d},\mathrm{L}\mathrm{a})\mathrm{}}_2$ ${\mathrm{Mg}}_3$ ${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{12}$·24${\mathrm{H}}_2$O grown from a solution containing 1% Nd is measured over the ranges $10\leqq H\leqq 50$ kOe and $0.5\leqq T\leqq 3^{\circ }\mathrm{K}$ using a ${\mathrm{He}}^3$ cryostat in a superconducting solenoid. Over these wide ranges the relaxation data for $c\perp \mathbf{H}$ are well fitted by the expression ${T_{1p}}^{-1\mathrm{}}=2.1\mathrm{}\times {10}^{-16\mathrm{}}{H}^3 coth\left(2.7\mathrm{}\frac{\beta H}{2kT}\right) {sech}^2\left(2.7\mathrm{}\frac{\beta H}{2kT}\right)+9.9\mathrm{}\times {10}^{-8\mathrm{}}H coth\left(4.4\mathrm{}\frac{\beta H}{2kT}\right) {sech}^2\left(4.4\mathrm{}\frac{\beta H}{2kT}\right) invsec$ where $\beta =\mathrm{Bohr}\mathrm{magneton}$, $k=\mathrm{Boltzmann}\text{'}\mathrm{s}\mathrm{constant}$, and $H$ is in Oe. The first term is due to ${\mathrm{Nd}}^{3+}$, the second to a small impurity of a non-Kramers ion, possibly ${\mathrm{Fe}}^{2+}$. Both are in agreement with predictions from a shell-of-influence model, including diffusion effects. At 19.5 kOe and 0.5°K, we find $T_{1p}=40\mathrm{}$ h, showing that dynamically induced proton polarization in this crystal can be maintained for very long times. In particular, the data display well the ${\mathrm{sech}}^2$ factor, leading to exponentially increasing proton relaxation times at high fields and low temperatures, $T_{1p}\mathrm{}\left(T\right)\mathrm{}\infty$ $\exp \left(\frac{g\beta H}{\mathrm{kt}}\right)$, due to the depopulation of the upper ${\mathrm{Nd}}^{3+}$ Zeeman level.