1. 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev Chamrousse, 17-22 December 2004

2. Phase diagram “similar” 98 % samples average geometric mfp l a ~ 200 nm structure correlation  a Our measures: NMR on three samples from N. Mulders k F ~ 1 Å << l a, one expects: no effect on Landau parameters restriction of mean free path “confined” Fermi liquid “B-like” superfluid ? supercooled “A-like” ? plus: adsorbed disordered 2D solid HISM and IISM models Parameters l,  a zero field measure P (bar) l a ~  0 of the p-wave pairs suppression of T c

3. Experimental setup vibrating wire NMR coils magnetic field Stycast cells Ag sinters B // Cell Pt powder Aerogel

4. Magnetisation M(P,T) = C n n solid (P) M solid (T) + n liquid (P) M liquid (T) M solid (T) = 1 / (T-  W ) 17.5 bar low fields, low powers integrated NMR line M (a.u.) T c,a T c,b  W effective ferromagnetic interaction

5. Fermi liquid magnetisation effectively: no change in the Landau parameters Bulk Aerogel T F ** (mK) New measures of T F **: 10 % smaller than in textbooks!

6. Solid contribution M (a.u.)  W (mK) Solid 3 He (in % of liquid at 0 bar) fit from T c,b to the highest temperature densification in the disordered solid ~ 1.5 layers ~ 3 layers from BET surface similar to fluorocarbon, Schuhl, Maegawa, Meisel, Chapellier, Phys. Rev. B 1987

7. Removing the 3 He solid 17.5 bar M (a.u.)  W (mK) adding 4 He removes the localised 3 He atoms: allows to study the confined liquid properties alone

8. Transport properties without solid 3 He spin diffusion D  measurement (pulsed NMR, 34 mT) 0.5 bar, G z = 0.25 Gauss/cm ln(H/H 0 ) A = 2/3 D  (  G z ) 2

9. Spin diffusion l = 130 nm for both fits HISM; consistent with other measures less good at 30 bars… correlations of the aerogel structure ? T (mK) D  (cm 2 /s) 0.5 bar 29.5 bar specific heat Choi, Yawata, Haard, Davis, Gervais, Mulders, Sharma, Sauls, Halperin, PRL 2004 thermal conductivity Fisher, Guénault, Hale, Pickett, JLTP 2001 from Sauls, Bunkov, Collin, Godfrin, Sharma, accepted in Phys. Rev B 2004 T -2

10. Solid-liquid interaction normal state Width (mT) 12 bar, 37 mT pure 3 He inhomogeneous width ~  b liquid dense solid layer ~  b solid fast exchange: = M liquid  b liquid + M solid  b solid = M liquid  b liquid + M solid  b solid M liquid + M solid ~ b Larmor  b solid ~ 1/T 2,solid >  b liquid similar to Hammel, Richardson, PRL 1984

11. Solid-liquid interaction normal state fast exchange: = M liquid  b liquid + M solid  b solid M liquid + M solid Width (mT) 17 bar, 37 mT, various amounts of 4 He M (a.u.)

12. Solid-liquid interaction normal state 17 bar Solid Width (mT) Width (mT) strongly localised atoms Inh. width fast exchange: = M liquid  b liquid + M solid  b solid M liquid + M solid 37 mT

13. Line shapes normal state Width (mT) 12 bar, pure 3 He 17 bar, 4 He 37 mT

14. Line shapes normal state Width (mT) 12 bar, pure 3 He 17 bar, 4 He Absorption (a.u.) 4.1 mK, no 3 He solid: Gaussian 37 mT

15. Line shapes normal state Width (mT) 12 bar, pure 3 He 17 bar, 4 He Absorption (a.u.) 100 mK, 3 He solid: Gaussian 37 mT

16. Line shapes normal state Width (mT) 12 bar, pure 3 He 17 bar, 4 He Absorption (a.u.) 4.1 mK, 3 He solid: Lorentzian! 37 mT

17. Line shapes normal state from Lorentzian to Gaussian line shapes 37 mT Shape factor 12 bar, pure 3 He 17 bar, 4 He Gaussian summ of independent lines Shape factor = Second Moment Full Width Half Height fast exchange… need a fast exchange model for the full line

18. Between T c,b and T c,a “confined” Fermi liquid “B-like” superfluid ? supercooled “A-like” ? zero field measure P (bar) Yuriy’s talk

19. Superfluid state position of the peak shifts: well defined transition (~50  K) Position (mT) 25 bar, 37 mT Pure 3 He T c,a

20. Superfluid state position of the peak shifts: well defined transition (~50  K) A phase like supercooling Position (mT) 25 bar, 37 mT Pure 3 He T c,a first studied by Barker, Lee, Polukhina, Osheroff, Hrubesh, Poco, PRL 2000

21. Superfluid state Consistent with other measures: same l as for spin diffusion  a = 0 nm  a = 40 nm  a = 44 nm 8 % solid 3 He 100 % solid 3 He 0 % solid 3 He Magnetisation similar to Sprague, Haard, Kycia,Rand, Lee, Hamot, Halperin, PRL 1995, Barker, Lee, Polukhina, Osheroff, Hrubesh, Poco, PRL 2000 l = 130 nm P = 17 bar l = 130 nm P = 29.5 bar from Sauls, Bunkov, Collin, Godfrin, Sharma, accepted in Phys. Rev B 2004

22. Superfluid state Frequency shift With 4 He 1.2 mK 1.4 mK 1.5 mK 1.6 mK 1.8 mK b Larmor 17 bar, 37 mT Absorption (a.u.)

23. Superfluid state  B   2 2 BB Frequency shift With 4 He Edge =  B,aero F(A  ] Edge ) + Larmor 2 2 Larmor and take F(A  ] Edge ) ~ 0.80 (similar to « flared-out »)  B,Aero 2 (Hz 2 ) 29.5 bar 17.5 bar 19.5 bar Dmitriev, Fomin, JLTP 2004 (scaled for the T c,a ’s) consistent with T c suppression

24. Superfluid state Frequency shift With 4 He Edge =  B,aero F(A  ] Edge ) + Larmor 2 2 Larmor and 29.5 bar 17.5 bar  =  B,aero + Larmor 2 2 Larmor / F(A  ] Edge ) same texture for both pressures…

25. Superfluid state assumtions: average position computed from fast exchange expression edge shift taken from the interpolation of 17 bar and 29 bar 29.5 bar 17.5 bar / F(A  ] Edge ) 24.5 bar, pure 3 He Frequency shift With 4 He, compared to pure 3 He 4 He again same texture with/without 4 He…

26. Superfluid state But… Position (mT for 37 mT) us: 17 bar E2 E3 E4 Haard et al. 2001 Northwestern: 18 bar B ┴ Cell B // Cell SAME T c,a if the same surface, then …. different textures…. Anisotropy? b Larmor

27. Superfluid state Lower and lower with the temperature 24.5 bar, 37 mT, pure 3 He Position (mT) b Larmor ? / F(A  ] Edge ) Texture?

28. Superfluid state Lower and lower with the temperature 24.5 bar, 37 mT pure 3 He Position (mT) b Larmor linear down linear up constant

29. Superfluid state Lower and lower with the temperature 24.5 bar, 37 mT pure 3 He 17.5 bar, 37 mT with 4 He Absorption (a.u.) redistribution of the spectral weight 3 peaks 3 peaks b Larmor 1.2 mK T/T c,a ~0.6 0.5 mK T/T c,a ~0.25

30. Superfluid state Lower and lower with the temperature 24.5 bar, pure 3 He assumtions: solid still described by Curie-Weiss law fast exchange solid/liquid B phase like superfluid / F(A  ] Edge ) ? sudden reorientation of the texture n ┴ B state? stable texture for B phase in Aerogel n ┴ B, Fomin, to be published

31. 3 He NMR in Aerogel Lots of questions…

32. Additional slides

33. Between T c,b and T c,a Absorption (a.u.) 17.5 bar, no solid, 37 mT, 1.8 mK Absorption (a.u.) 29.5 bar, no solid, 37 mT, 1.8 mK Absorption (a.u.) 29.5 bar, no solid, 37 mT, 2.2 mK

34. Satellite peaks M (a.u.) 17 bar, 37 mT29.5 bar, 37 mT 17 % main NMR signal: 17 % reduction! which goes partially or totally to the measured satellite peaks no 3 He solid 21 % 3 He solid left 8 % 3 He solid left pure 3 He T c,b T c,a

35. Satellite peaks M sat /M n 29.5 bar, 37 mT 8 % 3 He solid left pure 3 He M sat /M n 17.5 bar, 37 mT no 3 He solid left 73 % 3 He solid left similar, BUT different, on two « identical » samples… similar sample studied in Bunkov et al., PRL 2000

36. Satellite peaks  B 2 (Hz 2 ) 5.4 bar, 34 mT sample E2 sample E4 fit to bulk-B phase, scaled by 0.6 F(A  ) ~ 0.6 topological defects ? Peak =  B F(A  ) + Larmor 2 2 Larmor

37. Main NMR line Width (mT) M (a.u.) satellite(s) T c,b ? 8.3 bar, 37 mT

38. Main NMR line 8.3 bar, 37 mT Width (mT) T c,b Absorption (a.u.) 1 mK, 2 mK, scaled to NMR line area what is the state of the fluid/solid system between T c,b and T c,a ?