Intermediate mixed state of Type-II superconductors

For magnetic fields in the range $(1-D)H_{c1}<H<H_t$, 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. $H_{c1}$ is the lower critical field and $H_t$ is the field at which this linear dependence terminates. For finite D, $H_t<H_{c1}$. 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 $H_{c1}$ when D=0. 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.