Cooling of³He-⁴He dilute solution down to 97 μK. Thermal boundary resistance between dilute solution and metal powder

We have cooled a³He-⁴He dilute solution down to 97 μK, which is the lowest temperature ever been achieved in a dilute mixture. However, there is no sign of the superfluid transition of³He quasiparticles in the solution. In the sub-millikelvin region, we have measured the thermal boundary resistance between the solutions and sintered metal powder as a function of temperature T. We find that the thermal boundary resistence is proportional to T^-2 below 1 mK and that the resistance shows a strong dependence on magnetic fields below 0.1 T. These results suggest that the magnetic coupling is dominant in this temperature region. We have also estimated the heat leak into the dilute solution. It is found that the heat leak is proportional to the power of one third of inverse time, and the main source of the heat leak is ascribed to the viscous movement of³He quasiparticles.