Small Energy Scale for Mixed-Valent Uranium Materials

We investigate a two-channel Anderson impurity model with a ${5f}^1$ magnetic and a ${5f}^2$ quadrupolar ground doublet and a ${5f}^2$ excited triplet. Using the numerical renormalization group method, we find a crossover to a non-Fermi-liquid state below a temperature $T^{*}$ varying as the ${5f}^2$ triplet-doublet splitting to the 7/2 power. To within numerical accuracy, the nonlinear magnetic susceptibility and the ${5f}^1$ contribution to the linear susceptibility are given by universal one-parameter scaling functions. These results may explain ${\mathrm{UBe}}_{13}$ as mixed valent with a small crossover scale $T^{*}$.