1. Rotating Superfluid 3 He 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. Outline Rotating Superfluid 3 He in Aerogel (1) 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

3. Purpose P-wave superfluidity in aerogel: Impurity effect of p-wave superfluid in aerogel Rotation experiment of 3 He superfluid in aerogel: non-uniformities of superfluid in aerogel or amorphous superfluid 1. Extremely hard type II superfluidity B→φ H c １ →Ω c １〜 H c ２ → Ω c ２ ~ 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

4. §1. Phase diagram of superfluid in aerogel (cooling process) T (mK) Frequency shift (kHz) M Liquid /M total Pressure = 3.0 MPa, H 0 = 22 mT Two Phases: 1) A-like phase (ESP) 2) B-phase Porosity 98 %

5. Phase diagram of superfluid in aerogel (warming process) T (mK) Frequency shift (kHz) M Liquid /M total  -phase is superheated up to T c aero

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

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

8. Change of the A-phase Texture due to Rotation Rotation speed (rad/s) T = 0.83 Tc P = 3.4 MPa Frequency shift (kHz) Normalized Peak Height The main peak height decreased and the spectrum becomes slightly broader to higher frequency : ( 0→-6.26 rad/s→0) 1)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)

9. Summary for A-phase under rotaion 1)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 T c 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. §3. B-phase under rotation B-phase spectrum at rest The cw-NMR spectrum is broader than that of the flare-out texture in bulk

11. 2 - 0 rad/s: The spectrum shifted again. 2 and 3 rad/s: The absorption shifted to the higher frequency region. 4-6.28 rad/s: This change stopped. P = 3.0 MPa, T = 0.59 T C ( in B-like Phase) 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. Frequency shift (kHz) 0 and 1 rad/s: No change Frequency shift (kHz) NMR absorption (arb. unit) AccelerationDeceleration NMR Spectra in Rotation

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

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

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

15. cw-NMR absorption by flow  (rad/s) T = 0.68 Tc  c : critical velocity for creeping of vortex  D : critical velocity for n-texture deformation Note: no deformation until (V N -V S ) > V D

16. Hysteresis curve of (V N -V S ) Hysteresis curve due to vortex pinning Rotation speed (rad/s) T = 0.68 Tc ＝ Moment of the relative velocity  /2  (rot/s) (  n –  s )/2  Superfluid experiment in Al 2 O 3 Detection of Persistent current (H. Kojima et. al. P.R.L.27, 714 (1971) )

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

18. Hysteresis curve for the flow pattern  C = 2.5 rad/s Vortex is pinned until (V N -V S ) exceeds the de-pinning critical velocity V c

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

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

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

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

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

24. Summary for rotation experiment for superfluid 3 He 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 V c. 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 about 10  m A-phase ： No vortex signal was observed in aerogel ( this is different from bulk sample) The l-texture is pinned to aerogel

27. Rotating Ultra-low Temperature Cryostat built at ISSP. 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 ULT Cryostat and Experimental Set-up

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

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

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

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