Helium Crystals
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Background
Helium crystals
Helium is the only substance remaining liquid down to the absolute zero temperature when cooled under its saturated vapor pressure (see the phase diagrams below). Thus, in order to obtain solid helium, elevated pressures have to be applied. The interface between the liquid and solid helium is unique in being the only liquid-solid interface that exists over a wide continuous range of temperatures. Other significant features are the high inherent purity of helium (at low temperatures all impurities are frozen out!) and the fact that at the temperature low enough helium-liquid becomes superfluid which results in fast dynamics of helium crystals. The study on the surface of helium crystals has revealed crucial information on very general properties of all crystal surfaces. At the same time some of their other properties are exceptional and surprising, as is often the case when quantum mechanics plays a major role.
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Crystallization waves
Helium has two stable isotopes, the bosonic 4He and fermionic 3He. The quantitative study of the surface of 4He crystals started in the end of 1970s with conventional optical cryostats where the sample was looked from room temperature through the sets of windows anchored at different temperatures. Direct observations allowed the determination of the crystal orientation, its surface state and the quality of the surface, before performing measurements. Among other findings crystallization waves, the melting-freezing waves on the superfluid-solid interface of 4He were discovered in 1979. These waves propagate because 4He crystals grow and melt very fast at low temperatures. The studies of crystallization waves have therefore yielded precise measurements of the quantities which are difficult to access with usual crystals, namely the surface tension and step energies which control faceting and roughening, that is the appearance and disappearance of facets (smooth atomically flat faces in different crystallographic orientations) on the crystal surface.
Optical studies at ultra low temperatures
3He crystals have been studied optically much less than 4He crystals. The lack of study is, first of all, because of the fact that in 3He the superfluid transition takes place in millikelvin range, at about three orders of magnitude lower temperatures than in 4He. The (new type of) optical cryostats, enabling measurements at submillikelvin temperatures, were only built in the beginning of 1990s. The very first prototype, constructed in the Low Temperature Laboratory (LTL) at the Helsinki University of Technology, used optical fibers to communicate between the room and low temperatures and with that apparatus the free surface of a rotating superfluid 3He was imaged for the first time ever. Later the Interface group of LTL modified that optical setup and carried out high-resolution studies (down to a few nm in best cases) with 4He crystals using a simple two-beam reflection interferometer. In these experiments the sensor of a slow-scan digital camera was installed inside the cryostat and the laser light entered the cryostat through an optical fiber, as before.
Results
3He crystals at ultra-low temperatures
In order to study 3He crystals, we have built a unique low temperature Fabry-Pérot interferometer inside our nuclear demagnetization cryostat. With this interferometer we discovered already in the first set of experiments a multitude of different types of facets nobody had seen before [Phys Rev. Lett. 86, 1042 (2001)]. By using additionally a high-resolution capacitive pressure gauge, we also measured the growth anisotropy of 3He crystals at 0.5 mK. From that data the step free energies of ten different types of facets were extracted and it was found that the step energies vary as the fourth power of the corresponding step height, which refers to the elastic interaction between steps. According to our results, at submillikelvin temperatures the coupling of the liquid-solid interface to the crystal lattice is surprisingly much stronger in 3He than in </sup>4</sup>He, in spite of larger zero-point oscillations in 3He compared with 4He [Phys. Rev. Lett. 88, 045302 (2002)].
Quantum fluctuations of the liquid-solid interface of 3He
Very recently the Interface Group has completed a systematic study on the shape and growth dynamics of the body-centered cubic 3He crystals in the temperature range of 60 ... 120 mK. In 3He this kind of experiments are difficult near 100 mK because there is a large latent heat of crystallization and the thermal conductivity of the normal liquid 3He is very poor which yields slow dynamics as with ordinary crystals. However, we have succeeded in measuring the temperature dependence of the step free energy of the basic (110) facet. In these measurements we applied an original method in which the extremely small (a few Pa) overpressures were extracted from the measured crystal shape, so that no other device, such as a thermometer or a pressure gauge, and no calibrations were needed. Our results are consistent with an extremely weak coupling of the liquid-solid interface to the crystal lattice in 3He at these relatively high temperatures. We have shown, by applying the renormalization group approach developed by Nozières and Gallet, that this uniquely weak coupling is the result of quantum fluctuations which, paradoxically, become suppressed as temperature decreases and thus the interface between two essentially quantum media, superfluid and solid 3He, behaves as a classical surface in the vicinity of the absolute zero temperature [Phys. Rev. Lett. 93, 175301 (2004)]. This surprising result has attracted some general interest as it was referred as one of the research highlights in Nature Materials (Quantum material goes classical, December 2004 issue, p. 839).