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We studied a novel cooling method, in which $^3$He and $^4$He are mixed atthe $^4$He crystallization pressure at temperatures below $0.5\,\mathrm{mK}$.We describe the experimental setup in detail, and present an analysis of itsperformance under varying isotope contents, temperatures, and operationalmodes. Further, we developed a computational model of the system, which wasrequired to determine the lowest temperatures obtained, since our mechanicaloscillator thermometers already became insensitive at the low end of thetemperature range, extending down to $\left(90\pm20\right)\,\mathrm{\muK\approx}\frac{T_{c}}{\left(29\pm5\right)}$ ($T_{c}$ of pure $^3$He). We didnot observe any indication of superfluidity of the $^3$He component in theisotope mixture. The performance of the setup was limited by the backgroundheat leak of the order of $30\,\mathrm{pW}$ at low melting rates, and by theheat leak caused by the flow of $^4$He in the superleak line at high meltingrates up to $500\,\mathrm{\mu mol/s}$. The optimal mixing rate between $^3$Heand $^4$He, with the heat leak taken into account, was found to be about$100..150\,\mathrm{\mu mol/s}$. We suggest improvements to the experimentaldesign to reduce the ultimate achievable temperature further.

journal of low temperature physics

Performance of adiabatic melting as a method to pursue the lowest  possible temperature in $^3$He and $^3$He-$^4$He mixture at the $^4$He  crystallization pressure