Nonlinear Susceptibility: A Direct Test of the Quadrupolar Kondo Effect in UBe13

We present the nonlinear susceptibility as a direct test of the quadrupolar Kondo scenario for heavy fermion behavior and apply it to the case of cubic crystal-field symmetry. Within a single-ion model we compute the nonlinear susceptibility resulting from low-lying ${\Gamma }_3 \left(5\mathrm{}{f}^2\right)$ and Kramers ($5f^3$) doublets. We find that nonlinear susceptibility measurements on single-crystal U${\mathrm{Be}}_{13}$ are inconsistent with a quadrupolar ($5f^2$) ground state of the uranium ion; the experimental data indicate that the low-lying magnetic excitations of U${\mathrm{Be}}_{13}$ are predominately dipolar in character.