We have measured the response of a torsional oscillator containing
polycrystalline hcp solid $^{4}$He to applied steady rotation in an attempt to
verify the observations of several other groups that were initially interpreted
as evidence for macroscopic quantum effects. The geometry of the cell was that
of a simple annulus, with a fill line of relatively narrow diameter in the
centre of the torsion rod. Varying the angular velocity of rotation up to
2\,rad\,s$^{-1}$ showed that there were no step-like features in the resonant
frequency or dissipation of the oscillator and no history dependence, even
though we achieved the sensitivity required to detect the various effects seen
in earlier experiments on other rotating cryostats. All small changes during
rotation were consistent with those occurring with an empty cell. We thus
observed no effects on the samples of solid $^4$He attributable to steady
rotation.Comment: 8 pages, 3 figures, accepted in J. Low Temp. Phy

Fear, M. J.

Golov, A. I.

Mäkinen, J. T.

Walmsley, P. M.

Zmeev, D. E.

Journal of Low Temperature Physics

English

arXiv

We have measured the response of a torsional oscillator containing polycrystalline hcp solid He to applied steady rotation in an attempt to verify the observations of several other groups that were initially interpreted as evidence for macroscopic quantum effects. The geometry of the cell was that of a simple annulus, with a fill line of relatively narrow diameter in the centre of the torsion rod. Varying the angular velocity of rotation up to 2 rad s showed that there were no step-like features in the resonant frequency or dissipation of the oscillator and no history dependence, even though we achieved the sensitivity required to detect the various effects seen in earlier experiments on other rotating cryostats. All small changes during rotation were consistent with those occurring with an empty cell. We thus observed no effects on the samples of solid He attributable to steady rotation.Peer reviewe

Mäkinen, Jere

Aaltodoc

No Effect of Steady Rotation on Solid 4He in a Torsional Oscillator

Aaltodoc Publication Archive

We have measured the response of a torsional oscillator containing polycrystalline hcp solid 4He to applied steady rotation in an attempt to verify the observations of several other groups that were initially interpreted as evidence for macroscopic quantum effects. The geometry of the cell was that of a simple annulus, with a fill line of relatively narrow diameter in the centre of the torsion rod. Varying the angular velocity of rotation up to 2 rad/s showed that there were no step-like features in the resonant frequency or dissipation of the oscillator and no history dependence even though we achieved the sensitivity required to detect the various effects seen in earlier experiments on other rotating cryostats. All small changes during rotation were consistent with those occurring with an empty cell. We thus observed no effects on the samples of solid 4He attributable to steady rotation

Fear, Matthew

Walmsley, Paul

Zmeev, Dmitriy

Makinen, J. T.

Golov, Andrei

The University of Manchester - Institutional Repository

Noname manuscript No.(will be inserted by the editor)No effect of steady rotation on solid 4He in atorsional oscillatorM.J. Feara · P.M.Walmsleya ·D.E. Zmeeva,b · J. T.Mäkinena,c ·A. I.GolovaReceived: date / Accepted: dateAbstract We have measured the response of a torsional oscillator containingpolycrystalline hcp solid 4He to applied steady rotation in an attempt to ver-ify the observations of several other groups that were initially interpreted asevidence for macroscopic quantum effects. The geometry of the cell was thatof a simple annulus, with a fill line of relatively narrow diameter in the centreof the torsion rod. Varying the angular velocity of rotation up to 2 rad s−1showed that there were no step-like features in the resonant frequency or dis-sipation of the oscillator and no history dependence even though we achievedthe sensitivity required to detect the various effects seen in earlier experimentson other rotating cryostats. All small changes during rotation were consistentwith those occurring with an empty cell. We thus observed no effects on thesamples of solid 4He attributable to steady rotation.Keywords solid helium · torsional oscillator · rotating cryostat1 IntroductionSome of the most striking properties of superfluids, such as persistent currentsand quantized vortices which are due to macroscopic quantum coherence, be-come manifest during rotation. The responses of many different torsional oscil-lator (TO) experiments (undergoing AC rotation) containing solid 4He at tem-peratures below 200 mK were thought to indicate the presence of supersolidityalthough it is now widely accepted that this behaviour can be explained by thetemperature-dependent shear modulus of solid 4He (see reviews in Refs. 1–3).a:School of Physics and Astronomy, The University of Manchester, Oxford Road, M13 9PL,UK.b: Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK.c: Low Temperature Laboratory, Department of Applied Physics, Aalto University, FI-00076AALTO, Finland2 M. J. Feara et al.The observation of further anomalous changes due to applied steady (DC)rotation in the resonant frequency and dissipation of torsional oscillators con-taining solid 4He at low temperatures was also interpreted as evidence for theexistence of superflow and perhaps quantized vortices within the solid sam-ples [4–9]. It was thought that superimposing DC rotation onto the oscillatorymotion of a TO would allow effects due to macroscopic phase coherence (suchas some form of supersolidity) to be distinguished from classical elastic effects.The experiments utilizing DC rotation were carried out by several differentresearch groups using two different rotating cryostats. The ISSP group [4, 5]who used one of their own rotating cryostats and the KAIST [6–8] and Keio[9] groups both independently collaborated with the RIKEN group to usethe RIKEN instrument. The initial interpretations of these experiments wereall based on macroscopic quantum effects, such as some form of quantizedvorticity or analogues of the de Haas-van Alphen or Shubniko-de Haas effects.However, there are notable differences between the experiments which suggeststhat these observations may be due to coupling between the solid samples inthe TOs and cryostat-dependent effects such as rotational noise and vibrationlevels. Rotating dilution refrigerators, due to their complex structure, can havemechanical resonances in either the drivetrain or supporting framework thatare excited at particular values of angular velocity. The mechanical propertiesof solid helium mean that is very sensitive to external perturbations (suchas very low levels of vibration) [10, 11]. The ISSP group observed that thedissipation of their TO increased as the angular velocity, Ω, was increasedwith no corresponding change in frequency but they also point out that theirTO was not functioning reliably above 1.256 rad s−1. On the other hand, themost prominent features of experiments on the RIKEN cryostat are periodicstep-like changes in the TO resonant frequency and dissipation upon sweepingthe rotation velocity and also hysteresis when cycling the rotation velocity atdifferent temperatures.Given that these observations are still unexplained, we have used a rigid TOof relatively simple construction mounted on a recently built rotating dilutionrefrigerator to see if any of these phenomena could be reproduced in anotherlaboratory. The performance of the cryostat was investigated in detail [12] justbefore the commencement of this experiment. We found that the rotation issmooth to around 1 part in 103 and that the amplitude of vibration at theexperimental stage below the mixing chamber is ' 2 nm at the maximumangular velocity of 2.5 rad s−1 making this an ideal platform to use in a newsearch for any effect of rotation on solid 4He. We note that there is very littlepublished information on the detailed performance characteristics of the otherrotating cryostats used for earlier TO studies of solid 4He which limits ourability to make a thorough comparison of the relevant merits of the differentinstruments and whether they have specific features that could lead to anypeculiar behavior of a TO containing solid 4He.No effect of steady rotation on solid 4He in a torsional oscillator 32 Experimental setupThe cell consisted of a BeCu compound TO, a schematic of which is shownin Figure 1. The torsion head was a simple annular geometry with thick endcaps soldered in position in order to maintain the overall rigidity of the wholecell. The annulus was 14.1 mm in height, with an inner radius of 7.0 mm anda radial gap of 0.3 mm. Helium was supplied to the annulus via a 0.4 mmdiameter hole, centered in the 1.9 mm diameter torsion rod. The fill line wassplit inside the torsion head, connecting the annulus to the pressurized linevia two paths on opposite sides of the annulus. The motion of the oscillatorwas driven and detected capacitively using two electrodes that were positionedagainst a flat surface on the large isolator mass. We utilized the resonant modewhere the torsion head and the large isolator mass oscillate in antiphase. Thishad a resonant frequency of f0 ' 880 Hz and a Q value of ' 5 × 105 at lowtemperatures. The drive amplitude was selected such that the rim velocity ofthe annulus did not exceed 10µm s−1. The moment of inertia of the largermass was approximately 60 times larger than that of the torsion head. Whenthe TO was mounted on the rotating cryostat, the coaxial alignment betweenthe TO and cryostat rotation axis was better than 0.1 mm . The cell wasfilled with commercial grade 4He, with a nominal natural 3He impurity of' 3 × 10−7. Starting from a temperature of 3 K, two samples were preparedusing the blocked capillary method at initial pressures of 78 and 80 bar. Theinferred final pressure for these samples was approximately 47 bar [13].Solid heliumElectrode faceTorsion rod:Height - 9.6 mmInner radius - 0.2 mmOuter radius - 0.95 mmAnnulus:Height - 14.1 mmInner radius - 6.7 mmOuter radius - 7.0 mmFig. 1 (color online) Schematic of BeCu torsional oscillator used in this work. The darkershading indicates the regions occupied by solid 4He. The cell was attached to the mixingchamber of a rotating dilution refrigerator [12].3 Measurements at Ω = 0The temperature dependence of the resonant frequency and the inverse qual-ity factor for both the empty TO and when a sample of polycrystalline hcp4 M. J. Feara et al.∆fmax∆fmaxFig. 2 (color online) Temperature dependence of the TO resonant frequency (top) andinverse quality factor (bottom). In both plots, open symbols show measurements for theempty cell and closed symbols are for measurements with a polycrystalline sample of solid4He. The frequency shift is shown with respect to the low temperature value. The insets showthe corresponding shifts due to solid helium after the empty cell data has been subtracted.phase solid 4He was present are shown in Figure 2. In the case of the resonantfrequency, the reduction in frequency due to the mass-loading of the solid sam-ple, fm = 3.25 Hz has been subtracted from the empty cell data. The mainobservation is that in the presence of solid helium, the frequency increasesand the dissipation peaks at around 70 mK, which is qualitatively similar towhat was observed in many earlier TO experiments. However, the maximumnormalized frequency shift, ∆fmax/fm ' 9× 10−5, which occurs at the lowesttemperatures, is very small when compared to many other TO experiments.There are several different mechanisms through which the low temperaturestiffening of solid helium can produce changes in the frequency and dissipationNo effect of steady rotation on solid 4He in a torsional oscillator 5of TOs [14–16]. One important effect for the TO used in this work is thecontribution of the helium in the torsion rod to the effective torsion constant.Beamish et al. [14] showed that this effect will increase the frequency by anamount,∆frodf0=12µHeµBeCu1( rori )4 − 1, (1)where ro and ri are the outer and inner radii of the torsion rod and µHe/µBeCu '2.8 × 10−4 is the ratio of the shear moduli of solid helium relative to BeCu.For our TO, the upper limit for of this effect is ∆frod/fm ∼ 7.4× 10−5 whichis approximately 80% of the maximum frequency shift that we observe. It thusseems likely that most of the effect we observe is due to this mechanism andthat any supersolid fraction must therefore have an upper limit of ' 1×10−5.This is consistent with recent experiments [17] on bulk solid helium, that usedTOs with a very similar geometry to ours but with a separate fill capillaryand solid torsion rod, and found an upper limit for a supersolid fraction of4× 10−6.4 Measurements during rotationThe main purpose of this experiment was to see if there was any effect ofDC rotation on solid helium, which may indicate some form of macroscopicquantum coherence. Typical measurements of the frequency and inverse Qas a function of Ω are shown in Figure 3. Although we tried several differ-ent measurement procedures, the data shown in Fig. 3 were obtained by ini-tially starting steady rotation at Ω = 2 rad s−1 at 500 mK before cooling to avariable lower temperature (the examples shown in the figure are for 28 and110 mK) and then conducting a slow linear spin-down and subsequent spin-up(with |Ω̇| ' 3.4×10−4 rad s−2). This was done to check earlier observations ofhysteresis and staircase-like behavior [6, 7] when using this protocol. Coolingthrough a phase transition into a superfluid state while continuously rotatingshould give the vortex state with the lowest free-energy but starting rota-tion while already in the superfluid state would create the vortex structureswith the lowest critical velocity. In this experiment, there was no dependenceon whether the sample was cooled while continuously rotating compared tostarting rotation after cooling to a low temperature. Neither the frequency ordissipation showed any change compared to the stationary values for rotationwith Ω < 1.3 rad s−1 at any temperature. The frequency was slightly lowerand the dissipation larger at large values of Ω but there was no sign of anyperiodic staircase-like structure. There was also never any hysteresis observedwhen comparing spin-up to spin-down. The small shifts that we did observeat high Ω cannot be related to any Ω-dependent property of solid 4He as verysimilar shifts are also observed when the cell is empty. It seems most likely thatthese empty cell changes are due to some form of coupling between rotationof the cryostat and the TO, perhaps due to the increased rotational noise andvibration levels at high Ω.6 M. J. Feara et al.Fig. 3 (color online) Angular velocity dependence of the shifts in resonant frequency (top)and inverse Q (bottom) relative to the stationary (Ω = 0) values for two different tempera-tures. The solid and dashed curves are for spin-down and spin-up respectively. We obtainedcomparable results for both of the solid 4He samples that were investigated. The solid sym-bols show the corresponding shifts for the empty TO at constant values of Ω after averagingthe resonant frequency and dissipation over 10 minutes. For clarity, the 110 mK data hasbeen shifted upwards by 0.15 mHz in the top panel and 2 × 10−7 in the bottom panel.We have thus not been able to reproduce any of the features observed inother TO experiments conducted on rotating cryostats. The low temperatureshifts in resonant frequency and dissipation that we have found (with Ω = 0)are around two orders of magnitude smaller than those observed in the earlierexperiments, where it seems that the various elastic effects were dominant.Even with the small shifts we have observed, our TO would have still beensensitive to the effects of DC rotation that have been reported. For example,one observation was that rotation linearly suppressed the low temperatureNo effect of steady rotation on solid 4He in a torsional oscillator 7frequency shift [6, 7] such that ∆fmax(Ω) = (1−AΩ)∆fmax(0) where A '0.08 s. However, our measurements for Ω ≤ 1.3 rad s−1 suggests that A <0.02 s. In contrast to our work, the previous observation [7] of hysteresis aftera rotation sweep was unlikely to be an empty cell effect. Instead, the hystereticbehaviour may have been related to the relaxation of internal stress that builtup in the solid 4He sample perhaps related to cryostat-specific effects such asnoise on the angular velocity and coupling between mechanical resonances andthe TO.5 SummaryWe have used a torsional oscillator that was designed to minimize the influenceof the temperature-dependent elastic effects known to exist in solid helium.Very small changes in resonant frequency and dissipation that we did observeat low temperatures can be largely attributed to the stiffening of the solid in-side the torsion rod. By mounting the oscillator on a rotating cryostat capableof smooth rotation with low vibration levels, we found that solid helium doesnot respond to DC rotation up to Ω = 2 rad s−1 contrary to the observationsof other groups. The sensitivity of our measurements exceeded that necessaryfor the observation of the effects reported previously. We have thus found noevidence of any quantum phenomena related to macroscopic phase coherencein solid 4He.Acknowledgements We thank P. Richardson, S. Gillott and M. Sellers for their technicalsupport and acknowledge the assistance of Louis Lu during the early stages of this project.This work was funded by the UK Engineering and Physical Sciences Research Council(EPSRC) grant numbers EP/L001446/1 and EP/I003738/1.References1. M. H. W. Chan, R. B. Hallock and L. Reatto, J. Low Temp. Phys. 172, 317, (2013).2. J. Beamish, J. Low Temp. Phys. 168, 194 (2012).3. S. Balibar, A. D. Fefferman, A. Haziot and X. Rojas, J. Low Temp. Phys. 168, 221(2012).4. P. Gumann, N. Shimizu, A. Penzev, Y. Yasuta and M. Kubota, J. Phys. Conf. Ser. 150,032026 (2009).5. M. Yagi, A. Kitamura, N. Shimizu, Y. Yasuta and M. Kubota J. Low. Temp. Phys. 162,492, (2011).6. H. Choi, D. Takahashi, K. Kono and E. Kim, Science, 330, 1512, (2010).7. H. Choi, D. Takahashi , E. Kim and K. Kono, Phys. Rev. Lett. 108, 105302 (2012).8. W. Choi, D. Takahashi, D. Y. Kim, H. Choi, K. Kono and E. Kim, Phys. Rev. B 86,174505 (2012).9. D. Takahashi, T. Tsuiki, K. Kono and K. Shirahama, Poster presentation at QFS2012,Lancaster, UK (2012); T. Tsuiki, D. Takahashi, S. Murakawa, K. Kono and K. Shira-hama, Poster presentations at QFS2013, Matsue, Japan (2013) and LT27, Buenos Aires,Argentina (2014).10. X. Rojas, A. Haziot, V. Bapst, S. Balibar and H. J. Maris, Phys. Rev. Lett. 105, 145302(2010).8 M. J. Feara et al.11. A. Haziot, A. D. Fefferman, F. Souris, J. R. Beamish, H. J. Maris and S. Balibar, Phys.Rev. B 88, 014106 (2013).12. M. J. Fear et al., Rev. Sci. Inst. 84, 103905 (2013).13. A. Driessen, E. van de Poll, Phys. Rev. B 33 5, 3269, (1986).14. J. R. Beamish, A. D. Fefferman, A. Haziot, X. Rojas and S. Balibar, Phys. Rev. B 85,180501(R) (2012).15. H. J. Maris, Phys. Rev. B 86, 020502(R) (2012).16. J. D. Reppy, X. Mi, A. Justin, E. J. Mueller, J. Low Temp. Phys. 168, 175 (2012).17. D. Y. Kim and M. H. W. Chan, Phys. Rev. B 90, 064503 (2014).

No effect of steady rotation on solid 4He in a torsional oscillator

We have measured the response of a torsional oscillator containing polycrystalline hcp solid 4He to applied steady rotation in an attempt to verify the observations of several other groups that were initially interpreted as evidence for macroscopic quantum effects. The geometry of the cell was that of a simple annulus, with a fill line of relatively narrow diameter in the centre of the torsion rod. Varying the angular velocity of rotation up to 2 rad s-1 showed that there were no step-like features in the resonant frequency or dissipation of the oscillator and no history dependence, even though we achieved the sensitivity required to detect the various effects seen in earlier experiments on other rotating cryostats. All small changes during rotation were consistent with those occurring with an empty cell. We thus observed no effects on the samples of solid 4He attributable to steady rotation

Makinen, J.T.

Golov, A.

Lancaster E-Prints

M. J. Fear

P. M. Walmsley

D. E. Zmeev

J. T. Mäkinen

A. I. Golov

Crossref

No Effect of Steady Rotation on Solid $$^4$$ 4 He in a Torsional Oscillator

https://pure.manchester.ac.uk/ws/files/27697711/POST-PEER-REVIEW-NON-PUBLISHERS.PDF

No Effect of Steady Rotation on Solid $^4$He in a Torsional Oscillator

No Effect of Steady Rotation on Solid $^4$ He in a Torsional Oscillator

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The University of Manchester - Institutional Repository

No Effect of Steady Rotation on Solid 4^44He in a Torsional Oscillator

Abstract

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Aaltodoc Publication Archive

The University of Manchester - Institutional Repository

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The University of Manchester - Institutional Repository

No Effect of Steady Rotation on Solid $^4$ He in a Torsional Oscillator