Local-Field Mapping in Mixed-State Superconducting Vanadium by Nuclear Magnetic Resonance

A 10-kG field was applied to polarize the spins; it was then quickly reduced below ${H}_{c2}$, and remained there for about 0.1 sec, during which time a transverse ac probe field of frequency ${\ensuremath{\nu}}_{p}$ was applied. Then the large dc field was reapplied and a rapid-passage resonance signal observed in order to measure the effect of the probe field, the decrease in this subsequent signal reflecting the NMR absorption. Except near ${H}_{c2}$ the probe field only burns a small hole in the nuclear magnetization, and it was also necessary to move the vortex structure about by applying a 100-Hz field of a few gauss during the time that the sample was in the mixed state. Detailed studies are reported for a multiple foil sample of vanadium with main field perpendicular to the surface; aluminum foil was interleaved, and the flux density $B$ was measured using the ${\mathrm{Al}}^{27}$ NMR by exactly the same field-cycling resonance as applied to the vanadium. The magnetization was measured ballistically in the same magnet and field cycle. For flux density around $\frac{1}{2}{H}_{c2}$ the line shape almost uniquely implies a triangular vortex lattice. At high probe power, the effect of the probe field is still confined to the same definite frequency range as at low power, as would be the case for a completely ordered vortex lattice; this implies order over several vortex-lattice spacings. Accurate measurements are presented of the field at a vortex center and at the saddle point halfway between two vortices, and of the average flux density $B$, as a function of $H$, in a fairly clean sample at 1.4\ifmmode^\circ\else\textdegree\fi{}K. These parameters determine an accurate field map. Near ${H}_{c2}$ the field at a vortex center equals $H$, with a deviation of second (or greater) order in $H\ensuremath{-}{H}_{c2}$. The linewidth is greater, for a given magnetization, than would be expected from solutions of the Ginsburg-Landau equations. By extrapolation to zero $B$, it is concluded that the field at the center of a vortex is 1.2\ifmmode\pm\else\textpm\fi{}0.2 times ${\mathrm{H}}_{c1}$. The data are consistent, at low $B$, with a superposition model of independent vortices.