Magnetic Kapitza conductance between liquidHe3in its superfluid phases and magnetic substances

We study theoretically the magnetic Kapitza conductance at the interface between superfluid liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ (in its $A$ and $B$ phases) and paramagnetic substances when the heat transfer across the interface is mostly due to magnetic couplings (either of contact or dipolar type) between the nuclear spins of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and the electronic spins of the paramagnetic substance. We predict that very close to the transition temperature the value of the Kapitza conductance should be higher when ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is in one of its superfluid phases than it would be if ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ could remain in its normal phase at the same temperature; on the other hand at lower temperatures the Kapitza-conductance value drops sharply compared to what it would be in a normal rate at the same temperature.