No Effect of Steady Rotation on Solid \(^4\) He in a Torsional Oscillator

J Low Temp Phys (2016) 183:106–112 DOI 10.1007/s10909-015-1376-9 No Effect of Steady Rotation on Solid 4 He in a Torsional Oscillator M. J. Fear1 · P. M. Walmsley1 · D. E. Zmeev1,2 · J. T. Mäkinen1,3 · A. I. Golov1 Received: 7 July 2015 / Accepted: 14 November 2015 / Published online: 9 December 2015 © The Author(s) 2015. This article is published with open access at Springerlink.com Abstract 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. Keywords Solid helium · Torsional oscillator · Rotating cryostat 1 Introduction Some of the most striking properties of superfluids, such as persistent currents and quantized vortices which are due to macroscopic quantum coherence, become manifest during rotation. The responses of many different torsional oscillator (TO) experiments B P. M. Walmsley 1 School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK 2 Department of Physics, Lancaster University, Lancaster LA1 4YB, UK 3 Low Temperature Laboratory, Department of Applied Physics, Aalto University, 00076 Aalto, Finland 123 J Low Temp Phys (2016) 183:106–112 107 (undergoing AC rotation) containing solid 4 He at temperatures below 200 mK were thought to indicate the presence of supersolidity although it is now widely accepted that this behaviour can be explained by the temperature-dependent shear modulus of solid 4 He (see reviews in Refs. [1–3]). The observation of further anomalous changes due to applied steady (DC) rotation in the resonant frequency and dissipation of torsional oscillators containing solid 4 He at low temperatures was also interpreted as evidence for the existence of superflow and perhaps quantized vortices within the solid samples [4–11]. It was thought that superimposing DC rotation onto the oscillatory motion of a TO would allow effects due to macroscopic phase coherence (such as some form of supersolidity) to be distinguished from classical elastic effects. The experiments utilizing DC rotation were carried out by several different research 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 [9–11] groups both independently collaborated with the RIKEN group to use the RIKEN instrument. The initial interpretations of these experiments were all based on macroscopic quantum effects, such as some form of quantized vorticity or analogues of the de Haas–van Alphen or Shubniko–de Haas effects. However, there are notable differences between the experiments which suggest that these observations may be due to coupling between the solid samples in the TOs and cryostat-dependent effects such as rotational noise and vibration levels. Rotating dilution refrigerators, due to their complex structure, can have mechanical resonances in either the drivetrain or supporting framework, which are excited at particular values of angular velocity. The mechanical properties of solid helium mean that it is very sensitive to external perturbations (such as very low levels of vibration) [12,13]. The ISSP group observed that the dissipation of their TO increased as the angular velocity, Ω, was increased with no corresponding change in frequency but they also point out that their TO was not functioning reliably above 1.256 rad s−1 . On the other hand, the most prominent features of experiments on the RIKEN cryostat are periodic step-like changes in the TO resonant frequency and dissipation upon sweeping the rotation velocity and also hysteresis when cycling the rotation velocity at different temperatures. Given that these observations are still unexplained, we have used a rigid TO of relatively simple construction mounted on a recently built rotating dilution refrigerator to see if any of these phenomena could be reproduced in another laboratory. The performance of the cryostat was investigated in detail [14] just before the commencement of this experiment. We found that the rotation is smooth to around 1 part in 103 and that the amplitude of vibration at the experimental stage below the mixing chamber is 2 nm at the maximum angular velocity of 2.5 rad s−1 making this an ideal platform to use in a new search for any effect of rotation on solid 4 He. We note that there is very little published information on the detailed performance characteristics of the other rotating cryostats used for earlier TO studies of solid 4 He which limits our ability to make a thorough comparison of the relevant merits of the different instruments and whether they have specific features that could lead to any peculiar behaviour of a TO containing solid 4 He. 123 108 Fig. 1 Schematic of BeCu torsional oscillator used in this work. The darker shading indicates the regions occupied by solid 4 He. The cell was attached to the mixing chamber of a rotating dilution refrigerator [14] (Color figure online) J Low Temp Phys (2016) 183:106–112 Ω 2 Experimental Setup The cell consisted of a BeCu compound TO, a schematic of which is shown in Fig. 1. The torsion head was a simple annular geometry with thick end caps soldered in position in order to maintain the overall rigidity of the whole cell. The annulus was 14.1 mm in height, with an inner radius of 6.7 mm and a radial gap of 0.3 mm. Helium was supplied to the annulus via a 0.4 mm diameter hole centred in the 1.9 mm diameter torsion rod. The fill line was split inside the torsion head, connecting the annulus to the pressurized line via two paths on opposite sides of the annulus. The motion of the oscillator was driven and detected capacitively using two electrodes that were positioned against a flat surface on the large isolator mass. We utilized the resonant mode where the torsion head and the large isolator mass oscillate in antiphase. This had a resonant frequency of f 0  880 Hz and a Q value of 5 × 105 at low temperatures. The drive amplitude was selected such that the rim velocity of the annulus did not exceed 10 µm s−1 . The moment of inertia of the larger mass was approximately 60 times larger than that of the torsion head. When the TO was mounted on the rotati (...truncated)