Phonon-Induced Corrections to the Van Vleck Temperature-Independent Susceptibility

The dynamic spin-phonon correction to the Van Vleck temperature-independent susceptibility is computed for Eu³⁺ in a cubic crystalline-field environment. A T⁴ law is predicted for the temperature-dependent part of the correction. A numerical estimate indicates the effect to be very small for orbit-lattice parameters appropriate to a "slow-relaxing" model, but a sizeable correction if parameters appropriate to a "fast-relaxing" model are assumed. It is shown that U⁴⁺(5f²) in a cubic environment where the singlet (Γ₁) lies below the triplet (Γ₅) would be an excellent prospect for observation of this correction, in part because of the larger dynamic crystalline-field coefficients expected in the actinide series.