Our newest micro-Kelvin refrigerator became operational in 1998. It provides a platform for ultralow temperature experiments below 100 micro-Kelvin in high magnetic fields up to 7 T. In 1999, the nuclei of a single crystal rhodium sample were cooled in this apparatus to the record breaking temperature of 100 pico-Kelvin.

To Cool or to Refrigerate

We use the term refrigeration in the meaning that the device or method is used to lower the temperature of some external component, whether it be the sample under investigation or an additional refrigeration stage. Cooling, in turn, is to be understood as a process taking place in the system to be studied, thus reducing the temperature of the sample itself.

Dilution Refrigeration

At a given temperature, the entropy of a He-3 atom in the pure phase is lower than it is in the dilute phase mixed with He-4. Thus, if we move He-3 atoms adiabatically from the He-3 rich phase to the dilute phase, we produce cooling of the helium liquid. At low temperatures, massive heat exchangers are needed to make a thermal contact to the helium liquid in order to use this process for refrigeration. Milli-Kelvin temperatures are routinely achieved and maintained by the modern dilution machines. Our unit can keep the constant base temperature of about 2.5 mK without an external load.

Nuclear Demagnetization

At a given temperature, the entropy of a paramagnetic spin system is lower the higher the magnetic field is. Nuclear spins remain paramagnetic down to very low temperatures and are usable for adiabatic demagnetization cooling to achieve temperatures below the limitations of the dilution refrigerators. The entropy of the spin system must be removed at the lowest possible temperature at the highest possible magnetic field. Once the magnetic field is lowered, the thermally isolated spin system will cool down. Depending on the choice of the nuclear coolant, this method may be used for refrigeration down to a few tens of micro-Kelvins. The lower limit is set by the weakening of the energy transfer between the nuclear spins and the electron system or the lattice. Our 100 mole copper nuclear stage with a 9 T superconducting magnet can maintain the temperature around 0.1 mK for a period of a few weeks to make experiments at those temperatures or to refrigerate yet another cooling stage.

Double Stage Nuclear Cooling

We have used cascade adiabatic nuclear demagnetization to produce the record low temperatures of the nuclear spin systems down to the limit, where spontaneous magnetic ordering takes place thus preventing further paramagnetic cooling. This occurs at the nano- or pico-Kelvin range depending on the choice of the second stage nuclear coolant. In these experiments, it is the magnetic ordering of the nuclear spin system, which is the issue of interest, and the subject material itself favorably provides the means to achieve the temperatures low enough for such studies. There are still many unsolved problems in the quantum magnetism, for which nuclear spins provide the cleanest and most tractable model systems.

Cooling Helium Mixtures by Adiabatic Melting

Dilution cooling can be used to reduce the temperature of helium mixtures, if the separation and mixing of the isotopes can be controlled at the temperatures of interest. At the milli-Kelvin range and below this can be devised by the solidification of He-4 by applied pressure, whereby the He-3 component is expelled from the formed crystal. Then, the separated He-3, the entropy reservoir of the system, can be refrigerated by a nuclear demagnetization stage to the desired starting temperature. By controlling the pressure of the experimental cell, we can again melt the He-4 crystal, let the isotopes mix, and produce the dilution cooling. Since the entropy of He-3 drops very rapidly below its superfluid transition temperature, the cooling factor increases very steeply as the starting condition is reduced below that point. By this method we hope to reach the superfluid state of the dilute He-3 yet undiscovered.