Equilibrium properties of the fluxoid lattice in single-crystal niobium. I. Magnetization measurements

The field derivative of the superconducting magnetization ($\frac{\mathrm{dM}}{d{H}_a}$) of a single-crystal niobium sphere was measured with the applied magnetic field parallel to the three high-symmetry crystal axes. A field-sweep technique was used to make direct, continuous measurements of $\frac{\mathrm{dM}}{d{H}_a}$, and the data were numerically integrated to obtain the magnetization $M$. Excellent magnetic reversibility indicates the attainment of equilibrium conditions. The Meissner state, the intermediate mixed state, the mixed state, and the normal state show up as distinct field regions of the $\frac{\mathrm{dM}}{d{H}_a}$ vs $H_a$ plots separated by discontinuities in $\frac{\mathrm{dM}}{d{H}_a}$. The results are compared with microscopic theory and with related experimental studies of niobium. The magnetization measurements are compared directly with small-angle neutron-diffraction measurements of the fluxoid lattice in the same sample reported in the following paper.