3 He NMR in Aerogel

1. 3He 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. kF~ 1 Å << la, one expects: no effect on Landau parameters restriction of mean free path Phase diagram “similar” 98 % samples average geometric mfp la~ 200 nm structure correlation xa zero field measure supercooled “A-like” ? la~ x0 of the p-wave pairs suppression of Tc “B-like” superfluid P (bar) HISM and IISM models Parameters l, xa ? “confined” Fermi liquid plus: adsorbed disordered 2D solid Our measures: NMR on three samples from N. Mulders

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

4. Magnetisation 17.5 bar low fields, low powers integrated NMR line Tc,b M (a.u.) Tc,a nsolid(P) Msolid(T) + nliquid(P) Mliquid(T) M(P,T) = Cn Msolid(T) = 1 / (T-QW) QW effective ferromagnetic interaction

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

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

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

8. Transport properties without solid 3He spin diffusion Ds measurement (pulsed NMR, 34 mT) A = 2/3 Ds (g Gz)2 0.5 bar, Gz = 0.25 Gauss/cm ln(H/H0)

9. Spin diffusion T-2 from Sauls, Bunkov, Collin, Godfrin, Sharma, accepted in Phys. Rev B 2004 Ds (cm2/s) 0.5 bar 29.5 bar T (mK) l = 130 nm for both fits HISM; consistent with other measures less good at 30 bars… correlations of the aerogel structure ? specific heat Choi, Yawata, Haard, Davis, Gervais, Mulders, Sharma, Sauls, Halperin, PRL 2004 thermal conductivity Fisher, Guénault, Hale, Pickett, JLTP 2001

10. dense solid layer ~Dbsolid Dbsolid ~ 1/T2,solid > Dbliquid inhomogeneous width ~ Dbliquid ~ bLarmor fast exchange: < b > = Mliquidbliquid + Msolidbsolid < Db > = MliquidDbliquid + MsolidDbsolid Mliquid + Msolid Mliquid + Msolid Mliquid + Msolid Mliquid + Msolid Solid-liquid interactionnormal state 12 bar, 37 mT pure 3He Width (mT) similar to Hammel, Richardson, PRL 1984

11. fast exchange: < Db > = MliquidDbliquid + MsolidDbsolid Mliquid + Msolid Mliquid + Msolid Solid-liquid interactionnormal state 17 bar, 37 mT, various amounts of 4He M (a.u.) Width (mT)

12. strongly localised atoms Inh. width fast exchange: < Db > = MliquidDbliquid + MsolidDbsolid Mliquid + Msolid Mliquid + Msolid Solid-liquid interactionnormal state 17 bar Solid Width (mT) Width (mT) 37 mT

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

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

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

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

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

18. Yuriy’s talk Between Tc,b and Tc,a zero field measure supercooled “A-like” ? “B-like” superfluid P (bar) ? “confined” Fermi liquid

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

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

21. xa = 0 nm xa = 40 nm xa = 44 nm Superfluid state Magnetisation 8 % solid 3He 3 21 % solid He 100 % solid 3He 0 % solid 3He 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 Consistent with other measures: same l as for spin diffusion similar to Sprague, Haard, Kycia,Rand, Lee, Hamot, Halperin, PRL 1995, Barker, Lee, Polukhina, Osheroff, Hrubesh, Poco, PRL 2000

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

23. 2 nEdge = WB,aero F(Amn]Edge) + nLarmor 2 nLarmor Superfluid state Frequency shift With 4He 29.5 bar 17.5 bar Dmitriev, Fomin, JLTP 2004 19.5 bar (scaled for the Tc,a’s) WB,Aero2(Hz2) 2 2 WBaD cB consistent with Tc suppression and take F(Amn]Edge) ~ 0.80 (similar to « flared-out »)

24. 2 nEdge = WB,aero F(Amn]Edge) + nLarmor 2 nLarmor Superfluid state Frequency shift With 4He 29.5 bar 17.5 bar same texture for both pressures… < F(Amn) > / F(Amn]Edge) 2 and <n> = WB,aero < F(Amn) > + nLarmor 2 nLarmor

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

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

27. Texture? < F(Amn) > / F(Amn]Edge) ? Superfluid state Lower and lower with the temperature 24.5 bar, 37 mT, pure 3He bLarmor Position (mT)

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

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

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

31. 3He NMR in Aerogel Thanks! Lots of questions…

32. Additional slides

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

34. Satellite peaks 17 bar, 37 mT 29.5 bar, 37 mT Tc,a Tc,a 17 % 17 % M (a.u.) M (a.u.) Tc,b Tc,b 21 % 3He solid left pure 3He no 3He solid 8 % 3He solid left main NMR signal: 17 % reduction! which goes partially or totally to the measured satellite peaks

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

36. 2 nPeak = WB F(Amn) + nLarmor 2 nLarmor Satellite peaks 5.4 bar, 34 mT fit to bulk-B phase, scaled by 0.6 sample E2 sample E4 WB2 (Hz2) F(Amn) ~ 0.6 topological defects ?

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

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