"Intermediate Mixed" State of Type-II Superconductors

For magnetic fields in the range $\mathrm{}(1-D)\mathrm{}{H}_{c1\mathrm{}}<H<\mathrm{}{H}_t$, magnetization curves of low-$\kappa$ type-II Pb-In and In-Bi alloys with nonzero demagnetization coefficients $D$ exhibit a linear dependence of the magnetic moment on applied field. $H_{c1\mathrm{}}$ is the lower critical field and $H_t$ is the field at which this linear dependence terminates. For finite $D$, $H_t<H_{c1\mathrm{}}$. This behavior can be explained by a model of alternate regions of superconducting and mixed states. This array may be metastable. The mixed-state regions are all presumed to have the same temperature-dependent fluxoid-lattice spacing characteristic of $H_{c1\mathrm{}}$ when $D=0\mathrm{}$. Thus, as the magnetic field is increased isothermally, the mixed-state regions grow until the whole sample has been converted into the mixed state. This model implies the existence of an attractive interaction between flux lines in low-$\kappa$ materials.