letters to nature .............................................................. pffiffiffiffiffiffiffiffi high-Q oscillator shown in Fig. 1 is given by 2p I=G, where I is the Probable observation of a moment of inertia of the torsion bob, which contains helium, and G is the torsional spring constant of the Be-Cu torsion rod. A small hole supersolid helium phase drilled through the centre of the torsion rod allows the introduction of helium into the torsion bob. The oscillator is driven and main- E. Kim & M. H. W. Chan tained at resonance by a pair of electrodes. The onset of superfluidity in the helium inside the torsion bob decreases I, and hence decreases Department of Physics, The Pennsylvania State University, University Park, the resonant period. Bishop et al.8 made measurements of solid Pennsylvania 16802, USA helium from 25 to 48 bar, and concluded that if there is a supersolid ............................................................................................................................................................................. state, then either the supersolid fraction (the fraction of 4He atoms When liquid 4He is cooled below 2.176 K, it undergoes a phase participating in superflow) is less than 5 £ 1026 or the critical transition-Bose­Einstein condensation-and becomes a super- velocity is less than 5 mm s21. (The critical velocity is the maximum fluid with zero viscosity1. Once in such a state, it can flow without velocity of superflow without any detectable dissipation.) dissipation even through pores of atomic dimensions. Although In contrast to the results of Bishop et al.8, our torsional oscillator it is intuitive to associate superflow only with the liquid phase2, it measurements on solid helium grown inside a porous Vycor glass has been proposed theoretically3­5 that superflow can also occur disk show a decrease in the resonant period, characteristic of entry in the solid phase of 4He. Owing to quantum mechanical into a supersolid state. The continuous pore space, constituting fluctuations, delocalized vacancies and defects are expected to 30% of the total volume in Vycor, appears under the transmission be present in crystalline solid 4He, even in the limit of zero electron microscope as a network of randomly and multiply inter- temperature. These zero-point vacancies can in principle allow connected cylindrical channels of about 7 nm diameter and 30 nm the appearance of superfluidity in the solid3,4. However, in spite of length9. There have been a number of experiments10­15, including a many attempts6, such a `supersolid' phase has yet to be observed torsional oscillator measurement by Brewer and collaborators10,11, in bulk solid 4He. Here we report torsional oscillator measure- studying the solidification of 4He inside Vycor glass. 4He remains ments on solid helium confined in a porous medium, a configura- liquid down to temperature T ¼ 0 K, unless a substantial pressure is tion that is likely to be more heavily populated with vacancies applied to the sample. Below 1.3 K, this freezing pressure is than bulk helium. We find an abrupt drop in the rotational essentially constant at 25 bar. Inside Vycor glass, however, a pressure inertia5 of the confined solid below a certain critical temperature. close to 40 bar is required for solidification10­15. At low temperature The most likely interpretation of the inertia drop is entry into the in the presence of 4He vapour, an amorphous surface film is supersolid phase. If confirmed, our results show that all three adsorbed on the walls of the pores by the van der Waals potential. states of matter-gas7, liquid1 and solid-can undergo Bose­ Because of lattice mismatch, this surface film is not favourable for Einstein condensation. the nucleation and continued growth of solid as the pressure is The most direct experiment searching for the supersolid phase in increased and brought towards the bulk freezing pressure. This bulk solid 4He (performed by Bishop, Paalanen and Reppy8) also means that freezing is initiated from the liquid in the centre of the used the torsional oscillator technique. The resonant period of the pore by homogeneous nucleation of crystallites of radius limited by the pore size. The overpressure required to seed a crystallite of Figure 1 Torsional oscillator used in this experiment. The design of the oscillator follows those used by Reppy and collaborators18. The Vycor glass disk has a diameter of 15 mm Figure 2 Resonant period as function of temperature of solid 4He in Vycor glass. The and a thickness of 4 mm. The cylindrical drive and detection electrodes are aligned resonant period for different oscillation amplitudes-and hence different velocities of the off-centre from, and are capacitively coupled to, the central electrode attached to the rim of the Vycor disk, v rim-is shown. A drop in the period (DP), signifying the transition torsion bob. The signal from the detection electrode (proportional to the amplitude) is sent into the supersolid phase, is seen below 175 mK. Although the magnitude of DP depends to the lock-in amplifier through a current preamplifier. The lock-in provides a driving strongly on the rim velocity, no such dependence of the period is seen above the transition voltage, which controls the amplitude of oscillation, to complete the phase-locked loop temperature. For comparison, the empty (without helium) cell period, and the period of an and keep the oscillator in resonance. The mechanical Q of the oscillator is 106 at low atomically thin liquid film adsorbed on the walls of the internal pore space of Vycor, are temperature, allowing the determination of the resonant period to a precision of 0.2 ns. also shown. The film measurement, showing a superfluid transition at 250 mK, is carried The resonant period is 967,640 ns when the Vycor disk is empty, and is 971,900 ns near out with the same torsion cell. For easy comparison, 4,260 ns is added to the empty cell 0.2 K when pressurized with solid 4He at 62 bar. Measurements were also made with a data and 3,290 ns to the film data. The ordinate shows P 2 P*, the difference of the dummy torsional cell with the Vycor glass disk replaced by a solid brass disk. actual period P and P* ¼ 971,000 ns. NATURE | VOL 427 | 15 JANUARY 2004 | www.nature.com/nature 225 © 2004 Nature Publishing Group letters to nature radius r in this geometric model of freezing is predicted to be velocity is smaller than the critical velocity. The temperature proportional to the interfacial tension between the liquid and solid dependence of DP shown in Fig. 2 is probably a reflection of the phases and inversely proportional to r. The large (15 bar) over- velocity profile of the Vycor disk modulated by the temperature- pressure observed for solidification of 4He in Vycor reflects its small dependent critical velocity of the supersolid. Although we do not pore diameter10­15. Solid 4He grown inside Vycor with a tortuous know the exact functional form, the critical velocity is zero at the porous structure and small characteristic pore diameter is likely to transition temperature (175 mK), increases with decreasing tem- be heavily populated with vacancies. perature, and saturates near 300 mm s21 in the low-temperature The solid sample is grown and its density kept constant via the (30 mK) limit. As a comparison, we also show in Fig. 2 the super- standard blocked capillary method10­15. We found that by cooling fluid response of an atomically thin liquid film adsorbed in Vycor (from 3 K) a liquid sample of 75 bar in the torsion cell, the resultant with zero-temperature DP of the same order as that of the solid pressure of the solid sample below 1 K is typically 62 ^ 2 bar. The sample. The measurements were carried out with the same torsional pressure is determined by an in situ strain gauge attached directly on cell. In addition to the different temperature dependence, DP of the the outside of the torsion cell. We have intentionally chosen this film as shown in Fig. 3 is independent of the rim velocity. This is not high pressure so that we can be sure that our helium sample in Vycor surprising, as the critical velocity of an atomically thin liquid 4He glass is deep in the solid phase. Figure 2 shows the resonant period of film adsorbed in Vycor exceeds 200 mm s21 (ref. 16), which is a our Vycor disk torsional oscillator as a function of temperature. As factor of 700 higher than the maximum rim velocity of 300 mm s21 the mechanical Q of the oscillator is 106, and the resonant period is used in this experiment. of the order of 1 ms, the equilibration time for a new resonant Superfluid helium adsorbed inside an oscillating porous disk period reading due to any change in the experimental condition- must execute a tortuous path of potential flow defined by pore for example, a change in temperature-is expected and observed to structure17. As a result, a fraction, x, of the superfluid moment of be of the order of 1,000 s or 15 min. inertia, IS, remains effectively locked to the porous disk and the Below 80 mK, however, the equilibration time of the resonant observed period drop is proportional to the unlocked portion, period depends on whether the measurement is taken during (1 2 x)IS. If we make the assumption that the x factor of supersolid warming or cooling of the torsional cell. In a warming scan, the in Vycor is zero, then the DP0 of 22 ns shown in Fig. 3 is a direct equilibration time is the same as that at higher temperatures; but in measure of the zero-temperature and low-velocity supersolid a cooling scan, this time lengthens noticeably with decreasing temperature and exceeds 60 min below 40 mK. Our period data are obtained during warming scans after waiting for complete equilibration at the lowest temperature. The resonant period was measured with different amplitudes of oscillations. The amplitude, proportional to the linear velocity of the rim of the Vycor disk, can be calculated from the a.c. voltage induced on the detection electrode. The resonant period above 0.2 K does not depend on the rim velocity, and for temperatures above 0.5 K it is similar to that found by Brewer and collaborators10,11. These authors did not extend their measurement below 0.5 K. The central result of our experiment is the additional drop in the period (DP) that begins at 175 mK. This drop is consistent with the confined solid entering the supersolid phase. DP is strongly attenuated with increasing ampli- tude of oscillation (that is, higher rim velocity of the Vycor). Figure 3 shows DP in the low-temperature limit as a function of the rim velocity. The transition temperature at 175 mK, however, does not appear to depend on the rim velocity. For a disk oscillating at a fixed angular velocity, the local linear velocity ranges from zero up to a maximum rim velocity. Supersolid decoupling occurs for solid embedded in the region where the local Figure 4 Resonant periods as a function of temperature for a variety of solid helium samples. The period scale shown corresponds to that for solid 4He. As in Fig. 2, the ordinate shows P 2 P*, the difference of the actual period P and P* ¼ 971,000 ns. The period data for other samples are shifted for clarity and easy comparisons. All measurements were made with the rim velocity of the Vycor disk near 30 mm s21. The plots show that the period drop effect is not related to the stiffening of bulk solid helium in the torsion rod. The effect is not seen in pure 3He, and is not seen in solid mixtures with 3He concentration exceeding 0.1%. The resonant periods in these samples are independent of the rim velocity of the Vycor disk. A period drop is found for mixtures with 10, 30 and 100 p.p.m. of 3He. As in pure 4He, the size of the drop in these samples with Figure 3 DP at the low temperature limit, DP0, as a function of rim velocity of the Vycor low 3He concentrations is rim-velocity dependent. The dotted lines extrapolated smoothly disk. DP0 values are deduced by subtracting the measured periods at 30 mK from the from high temperature are the expected background period in the absence of period (shifted) empty cell period, as shown in Fig. 2. Whereas DP0 of the liquid film is drops. The vertical arrows mark the transition temperatures of these samples. The 3He independent of rim velocity, it is strongly attenuated with higher rim velocity in solid 4He. concentrations listed are the average concentration of the solid inside the Vycor and in the This plot shows that the critical velocity of supersolid at 30 mK is of the order of capillary leading to the cell. The actual 3He concentration inside the Vycor, particularly for 300 mm s21. It also shows that DP0 extrapolates to 22 ns in the limit of low rim velocity. low-concentration samples, could be quite different from the listed values. 226 NATURE | VOL 427 | 15 JANUARY 2004 | www.nature.com/nature © 2004 Nature Publishing Group letters to nature moment of inertia. The resonant period increases by 4,260 ns when populated with vacancies and defects. It seems that these vacancies the porous Vycor glass disk in the torsion bob is filled with solid 4He may be responsible for enhancing Bose­Einstein condensation of at 62 bar, therefore the supersolid fraction-the fraction of 4He the confined solid 4He into the supersolid phase. A atoms that participate in superflow-is 5 parts in 103. On the other hand, if we assume that the x factor of supersolid is 0.8, the same as Received 23 September; accepted 14 November 2003; doi:10.1038/nature02220. that of superfluid in Vycor18, then the supersolid fraction is 25 parts 1. Kapitza, P. Viscosity of liquid helium below the l-point. Nature 141, 74 (1938). in 103. If we assume that the 4He atoms in the supersolid fraction are 2. Penrose, O. & Onsager, L. Bose-Einstein condensation and liquid helium. Phys. Rev. 104, 576­584 (1956). uniformly distributed in the pore space and if we neglect interaction 3. Andreev, A. F. & Lifshitz, I. M. Quantum theory of defects in crystals. Sov. Phys. JETP 29, 1107­1113 between these atoms, then we can use the ideal Bose gas theory to (1969). calculate the Bose­Einstein condensation temperature19. The cal- 4. Chester, G. V. Speculations on Bose-Einstein condensation and quantum crystals. Phys. Rev. A 2, 256­258 (1970). culated transition temperatures are 120 mK and 350 mK, respect- 5. Leggett, A. J. Can a solid be "superfluid"? Phys. Rev. Lett. 25, 1543­1546 (1970). ively, for supersolid fractions of 5 and 25 parts in 103, bracketing the 6. Meisel, M. W. Supersolid 4He-An overview of past searches and future possibilities. Physica B 178, observed transition temperature of 175 mK. 121­128 (1992). In order to rule out non-supersolid mechanisms for the observed 7. Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of Bose-Einstein condensation in a dilute atomic vapour. Science 269, 198­201 (1995). effect, we did a number of control experiments. We made measure- 8. Bishop, D. J., Paalanen, M. A. & Reppy, J. D. Search for superfluidity in hcp 4He. Phys. Rev. B 24, ments with the same torsional cell with pure solid 3He and with 2844­2845 (1981). solid 4He diluted with 10, 30, 100, 1,000 and 10,000 p.p.m. of 3He, 9. Levitz, P., Ehret, G., Sinha, S. K. & Drake, J. M. Porous Vycor glass-the micro structure as probed by all pressurized with the same procedures as that for pure 4He, and electron-microscopy, direct energy-transfer, small-angle scattering, and molecular adsorption. J. Chem. Phys. 95, 6151­6161 (1991). resulting in a final pressure between 60 and 65 bar. The results of 10. Brewer, D. F., Cao, L., Girit, C. & Reppy, J. D. 4He transition in a restrictedgeometry below and above these measurements are shown in Fig. 4. The observed DP seen in the bulk solidification pressure. Physica B 107, 583­584 (1981). pure 4He is not seen for solid 3He, and is also not seen for solid 11. Cao,L.,Brewer,D.F.,Girit,C.,Smith,E.N.&Reppy,J.D.Flowandtorsionaloscillatormeasurements on liquid helium in restricted geometries under pressure. Phys. Rev. B 33, 106­117 (1986). mixtures with 3He concentrations exceeding 0.1%. The fact that the 12. Beamish,J.R.,Hikata,A.,Tell,L.&Elbaum,C.Solidificationandsuperfluidityof4HeinporousVycor effect is not present in 3He, a Fermi system, is reassuring. It is also glass. Phys. Rev. Lett. 50, 425­428 (1983). reasonable that the addition of enough 3He atoms is effective in 13. Molz, E. B. & Beamish, J. R. Freezing and melting of helium in different porous media. J. Low-Temp. quenching the supersolid phase. The behaviour found in samples Phys. 101, 1055­1077 (1995). 14. Adams, E. D., Uhlig, K., Tang, Y. H. & Haas, G. E. Solidification and superfluidity of 4He in confined with even lower 3He concentrations is very intriguing. Besides geometries. Phys. Rev. Lett. 52, 2249­2252 (1984). reducing the magnitude of DP, the introduction of the minute 15. Bittner, D. N. & Adams, E. D. Solidification of helium in confined geometries. J. Low-Temp. Phys. 97, amount of 3He also broadens the transition and increases the 519­535 (1994). transition temperature. 16. Chan, M. H. W., Yanof, A. W. & Reppy, J. D. Superfluidity of thin 4He films. Phys. Rev. Lett. 32, 1347­1350 (1974). Figure 4 also shows measurements made with a dummy torsional 17. Mehl, J. B. & Zimmermann, W. Jr Flow of superfluid helium in a porous medium. Phys. Rev. 167, oscillator consisting of a torsion rod that is identical to the normal 214­229 (1968). torsional cell but with a torsion bob containing a solid brass disk 18. Berthold, J. E., Bishop, D. J. & Reppy, J. D. Superfluid transition of 4He films adsorbed on porous Vycor glass. Phys. Rev. Lett. 39, 348­352 (1977). rather than a Vycor glass disk. During measurements, the hole in the 19. Huang, K. Statistical Mechanics 2nd edn, 293 (Wiley & Son, New York, 1967). torsion rod is pressurized with solid 4He (using the exact same 20. Palaanen, M. A., Bishop, D. J. & Dail, H. W. Dislocation motion in hcp 4He. Phys. Rev. Lett. 46, procedure as that for the Vycor torsional cell) to a final pressure of 664­667 (1981). 62 bar. The resonant period is temperature independent, showing 21. Csa´thy, G. A. & Chan, M. H. W. Effect of 3He on submonolayer superfluidity. Phys. Rev. Lett. 87, 045301 (2001). no decrease at low temperature, similar to that of the empty cell. This means the effect that we have seen with pure solid 4He and with Acknowledgements We acknowledge discussions with J. Banavar, J. Beamish, V. Crespi, 4He diluted with small 3He impurities occurs inside the torsion cell, J. Goodkind, J. Jain, A. Leggett and J. Reppy. This work was supported by the Condensed Matter and is not related to changes occurring in the bulk solid helium Physics Program of the National Science Foundation. inside the torsion rod. Owing to the freezing of dislocations, solid Competing interests statement The authors declare that they have no competing financial helium inside the torsion rod stiffens at low temperature. This interests. stiffening can contribute to the torsional spring constant of the torsion rod20 and lower the resonant period. We have, however, Correspondence and requests for materials should be addressed to M.H.W.C. taken the precaution of using an especially thick (2.2 mm diameter) (chan@phys.psu.edu). torsion rod, so that this effect can be ignored. This assumption is confirmed by our measurements with the dummy cell. It could be argued that solidification inside the Vycor glass is never complete, and that there is a persistent thin liquid film even at .............................................................. 62 bar, 20 bar above the reported solidification pressure. But there are observations that are not consistent with this picture. The Partial order in the non-Fermi-liquid temperature dependence of the supersolid is distinctly different from that of a liquid film, and the critical velocity observed for the phase of MnSi solid is at least 700 times smaller than that in a film16. Figure 4 shows that the introduction of 0.1% of 3He into solid 4He completely C. Pfleiderer1, D. Reznik3,4, L. Pintschovius3, H. v. Lo¨hneysen1,3, eliminates the observed drop in the period. This is in strong contrast M. Garst2 & A. Rosch2 to the findings in liquid films. The addition of 3He into a liquid 4He 1 film smoothly decreases the superfluid transition temperature, and Physikalisches Institut, 2Institut fu¨r Theorie der Kondensierten Materie, a very high concentration of 3He is needed to completely quench the Universita¨t Karlsruhe, D-76128 Karlsruhe, Germany 3Forschungszentrum Karlsruhe, Institut fu¨r Festko¨rperphysik, D-76021 Karlsruhe, transition21. The transition temperature of a pure 4He film at Germany 150 mK was found to decrease to below 20 mK only when the 4Laboratoire Le´on Brillouin, CEA Saclay, F-91191 Gif-sur-Yvette Cedex, France amount of 3He exceeds 20% of all the 4He in the adsorbed film, ............................................................................................................................................................................. including that in the amorphous solid layer21. Only a few metallic phases have been identified in pure crystal- In conclusion, the most reasonable interpretation of the observed line materials. These include normal, ferromagnetic and anti- period drop is that it is a signature of transition into the supersolid ferromagnetic metals, systems with spin and charge density wave state. The microscopic origin of this effect is not understood. We order, and superconductors. Fermi-liquid theory provides a basis have noted that the solid 4He grown in the Vycor pores is heavily for the description of all of these phases. It has been suggested NATURE | VOL 427 | 15 JANUARY 2004 | www.nature.com/nature 227 © 2004 Nature Publishing Group