Rotating Superfluid 3 He in Aerogel

1. Rotating Superfluid 3He in Aerogel Takao Mizusaki Department of Physics, Graduate School of Science, Kyoto University Collaborators: Kyoto University, M. Yamashita, A. Matsubara, R. Ishiguro# and Y. Sasaki Osaka City University, O. Ishikawa ISSP, Univ. Tokyo, Y. Kataoka and M. Kubota CNTB-CNRS, Yu. M. Bunkov #ENS-Paris

2. Rotating Superfluid 3He in Aerogel Comparison with other data without rotation The sample is 98 % arogel (Bunkov’s sample) (2) Singular core cortex and the l-texture is strongly pinned in A-like Phase (3) Critical velocity for vortex penetration and persistent current in B-Phase Outline

3. Rotation experiment of 3He superfluid in aerogel: non-uniformities of superfluid in aerogel or amorphous superfluid 1. Extremely hard type II superfluidity B → φ Hc１ → Ωc１〜 Hc２ → Ωc２~ 2. What kind of vortices? 3. Texture in aerogel and its coupling with flow The texture is pinned strongly in A-like phase and weakly in B-phase. 4. Vortex and pinning effect Amorphous superfluidity → flux creep model Purpose P-wave superfluidity in aerogel: Impurity effect of p-wave superfluid in aerogel

4. §1. Phase diagram of superfluid in aerogel (cooling process) Porosity 98 % Pressure = 3.0 MPa, H0 = 22 mT Frequency shift (kHz) MLiquid/Mtotal Two Phases: 1) A-like phase (ESP) 2) B-phase T (mK)

5. Frequency shift (kHz) MLiquid/Mtotal Phase diagram of superfluid in aerogel (warming process) T (mK) B-phase is superheated up to Tcaero

6. T = 0.83 Tc (1.75 mK) W = W (T = Tc) P = 3.4 MPa Frequency shift (kHz) Cooling conditions through Tc CASE 1: 0 rad/s, 2 mK/min. CASE 2: 0 rad/s, 20 mK/min. CASE 3: +0.10 rad/s, 3 mK/min. CASE 4: -0.01 rad/s, 1 mK/min. CASE 5: +6.28 rad/s, 1 mK/min. CASE 6: -6.28 rad/s, 1 mK/min. §2. A-phase under rotation • Results: • No change for cooling conditions • nor with rotation • No signal for spin-wave vortex signal Result for a bulk sample (JLTP 60, 187 (1985) )

7. NMR in A phase under rotation (continuous vortex) ( Without rotation) Spin Wave attached to the soft core vortex Result for a bulk sample (JLTP 60, 187 (1985) )

8. T = 0.83 Tc P = 3.4 MPa Frequency shift (kHz) Change of the A-phase Texture due to Rotation Normalized Peak Height Rotation speed (rad/s) The peak height deceases for any change of rotation speed and direction. 2) The A-phase texture is strongly pinned by aerogel and is deformed elastically by rotation. (Annealing effects) The main peak height decreased and the spectrum becomes slightly broader to higher frequency : ( 0→-6.26 rad/s→0)

9. Summary for A-phase under rotaion • A-phase texture is strongly pinned by aerogel • 2) The texture is slightly and elastically deformed by • rotation • 3) No signal for a soft core vortex even when it is cooled through Tc under 6.28 rad/s • ●Singular core vortex exits since the l-texture is • strongly pinned • or • ● The life time of spin-wave is short in aerogel • and NMR spectrum for spin wave is broadened.

10. The cw-NMR spectrum is broader than that of the flare-out texture in bulk §3. B-phase under rotation B-phase spectrum at rest

11. NMR Spectra in Rotation NMR absorption (arb. unit) Frequency shift (kHz) Frequency shift (kHz) 6.28 and 5.5 rad/s: The spectrum changed in a reverse way. 4 and 3 rad/s: NMR spectrum is almost the same as that taken before rotation. 0 and 1 rad/s: No change 2 and 3 rad/s: The absorption shifted to the higher frequency region. 4-6.28 rad/s: This change stopped. 2 - 0 rad/s: The spectrum shifted again. P = 3.0 MPa, T = 0.59 TC ( in B-like Phase) Acceleration Deceleration

12. B-phase NMR B-phase NMR under flow 2) For large velocity : Relative velocity 1) For small velocity Counter flow peak

13. Counter flow peaks for a bulk sample Note:Flare-put texture for W=0

14. Analysis for counter flow peaks under rotation Frequency shift (kHz) • Counterflow vs. Frequency shift f (r,W): • NMR intensity I( f , W) vs.f (r,W): • (Local Approx.) Intensity of Counterflow Assume that some part is completely pinned and the other part is completely free.

15. cw-NMR absorption by flow Wc : critical velocity for creeping of vortex T = 0.68 Tc WD : critical velocity for n-texture deformation W (rad/s) Note: no deformation until (VN-VS) > VD

16. Superfluid experiment in Al2O3 Detection ofPersistent current (H. Kojima et. al. P.R.L.27, 714 (1971) ) (wn – ws)/2p w/2p (rot/s) Hysteresis curve of (VN-VS) ＝Moment of the relative velocity Hysteresis curve due to vortex pinning T = 0.68 Tc Rotation speed (rad/s)

17. Flow pattern to explain the hysteresis curve for Acceleration deceleration

18. Hysteresis curve for the flow pattern WC = 2.5 rad/s Vortex is pinned until (VN-VS) exceeds the de-pinning critical velocity Vc

19. Moment of Counter flow In bulk liquid, vortices can move freely. Counterflow decreases for W > Wc. In aerogel vortices are strongly pinned large counter flow velocity is needed for vortex creeping.

20. Critical Velocity Critical angular velocity (rad/s) WC vs. reduced temperature Glaberson Donnely Instability d = 10.5 m m d: the average distance between pinning centers Depinning Mechanism

21. Glaberson Donnelly Instability :Self-induced velocity :Counterflow W.I. Glaberson and R.J. Donnelly Phys. Rev. 141, 208 (1966) Pinning is infinitely strong. Critical velocity is determined by the average distance d d = 10.5 mm

22. Critical Velocity for de-pinning Vortex Pinning may occur due to a local inhomogeneities of the condensation energy dD This model has a mild temperature dependence, which should be observable in the experiment.

23. What determines d ? 130 nm 5 nm d = 10.5 mm? Small-angle x-ray scattering (J. V. Porto and J. M. Parpia, P.R.B. 59, 14583 (1999) )

24. A-phase： No vortex signal was observed in aerogel ( this is different from bulk sample) The l-texture is pinned to aerogel Summary for rotation experiment for superfluid 3He in aerogel • B-phase: The n-texture was deformed by flow and • the counter-flow peak appeared. • The hysteresis was appeared when the relative • flow velocity exceeded above Vc. • The critical velocity did not depend on temperature • This was caused by expansion of vortex(G-D instability) from • the pinning center and the creeping of vortex started . • The average distance of the pinning centers was about10 mm

27. Rotating ULT Cryostat and Experimental Set-up Nuclear Stage RRR=500 (not well-annealed) Residual horizontal-field cancellation coil (No magnetic material near the cryostat) ○Sub-mK temperature under 1 rot/sec ○ Excess heat input due to a rotation of 1 rot/sec < 1 nW ○ Continuous run for one month after a demagnetization Rotating Ultra-low Temperature Cryostat built at ISSP.

28. Structure of vortex in bulk liquid−array of vortex Continuous vortex Singular Vortex ~ 10 mm A phase 4 types B phase 3 types ~ 100 nm

29. fL Analysis for counter flow peaks under rotation Derivation of (Vn-Vs) from cw-NMR spectrum ：Dipole frequency in B-phase ：Larmor frequency :Critical velocity for Fredericks Transition , where Frequency shift (kHz)

30. Counterflow Intensity vs. W 1. 0 ~ WD: No change due to insensitivity of nvector for |VN - VS| < VD 2. WD ~ WC: Linear increase due to the solid body rotation of Normal fluid velocity 3. WC < W : Decrease of counterflow from the linear behavior of normal flow, it is due to appearance of superfluid velocity created by vortices. 4. W < WV: The counterflow |VN - VS| increased again even in deceleration and remained at 0 rad/s, which shows the superflow remained at 0 rad/s by pinning of vortices. nV (r): vortex density The curve showed the hysteresis behavior once W exceeds WC. T = 0.59 TC This pinned superflow at 0 rad/s is so stable that the dissipation was not observed within 40 hours.

31. 130 nm 5 nm d = 10.5 mm? Small-angle x-ray scattering (J. V. Porto and J. M. Parpia, P.R.B. 59, 14583 (1999) )