Dipole energy dissipation and nuclear spin diffusion in mixed-state superconducting vanadium

The decay of nuclear spin-spin energy has been studied in the mixed state of vanadium and anomalously rapid relaxation rates are found as compared to the rates for spin-lattice relaxation of Zeeman energy. The experiment was performed by adiabatically demagnetizing the spins in the rotating frame at a field larger than $H_{c2\mathrm{}}$ and then cycling the field to bring the sample into the mixed state for a variable time. The residual dipolar energy is detected, once the field is raised, by adiabatically remagnetizing the sample on resonance. I show that the relaxation observed, after the vortices are pinned, is due to a cross relaxation of a spin energy associated with the magnetic field gradients in the mixed state and the dipolar energy which is in semiequilibrium with the quadrupole energy. This process is mediated by a current of magnetization, proportional to the diffusion coefficient $D$, which is driven by the field gradients and uses dipolar energy as a heat sink. Using a field distribution in the mixed state calculated by Marcus, I find $D=2.8\mathrm{}\pm 0.9\times {10}^{-12\mathrm{}}$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ from the measurements of the relaxation rate of dipolar energy and of the quadrupole system heat capacity. This measurement of $D$ is the first for a metal or for nuclei with $I>\mathrm{}\frac{1}{2}$ and is twice the value predicted by the moment-moment calculation of Redfield and Yu. In the presence of large field gradients, dynamic quenching of the diffusion coefficient is observed.