Magnetization isotherms and pore-space geometry

A model of the magnetization response of a ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He mixture in a porous medium is studied as the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is carried through a capillary-condensation hysteresis loop. This response appears as a magnetization hysteresis loop that has important qualitative and quantitative features related to the geometry of the pore space. It is suggested that an experimental exploration of the magnetization isotherm can provide valuable information about pore-space geometry.