Effects of Crystal Growth/Annealing on Supersolidity of Helium 4

1. Effects of Crystal Growth/Annealing on Supersolidity of Helium 4 Motoshi Kondo Shun-ichi Takada Hitomi Yoshimura Yoshiyuki Shibayama Keiya Shirahama Keio University, Yokohama, Japan Support: Grand-in-Aid for Scientific Research on Priority Area “Physics of Superclean Materials”

2. Outline • Effect of Crystal Growth Velocity • 2. Effect of Crystal Annealing • 3. Discussion: Dislocations? • 4. “Bulk + Porous Media” Preliminary Result

3. Torsional Oscillator and Pressure Cells Thermometers on platform and cell f =1496 Hz

4. Confirmation of the Kim-Chan Experiment M. Kondo et al. cond-mat/0607032, JLTP in press Rim Velocity Velocity-dependent Frequency (period) Shift Dissipation Peak Supersolid Fraction: 1/3 – 1/10 of KC 2.97 MPa

5. Phase Diagram

6. Crystal Growth with Constant Velocity Solidification Start Conjecture End Growth Velocity ~ 10 mm /sec

7. Effect of Growth Velocity

8. Growth-Velocity Dependence of NCRI Velocity-Dependent NCRI Velocity-Independent NCRI

9. Quench Cooling Quench Time(sec )

10. NCRI of Quench-Cooled Samples T = 70 mK Quench Cooled “Quenched” Slowly Grown Slowly Grown “Quenched” sample shows large rs, but not systematic.

11. “Phased Annealing” for Single Samples Quench 0.8K 1K 1.2K 1.4K 1.6K CRI increases by annealing / NCRI decreases

12. NCRI after Annealings at Various Temperatures We repeated the annealing at 0.8, 1.0, ...., 1.6 K. 2.75 MPa Annealing at Higher T: Smaller Supersolid Fraction But could not be eliminated.

13. Effect of Annealing on NCRI and CRI

14. Effect of Annealing on NCRI and CRI Change in CRI NCRI

15. Pressure and NCRI Change in Pressure (65 mK) NCRI

16. Annealing for Many Samples Change in CRI NCRI

17. Growth and Annealing: Result “Fragile”? “Robust” Supersolid Component ~ 0.04%

18. Growth and Annealing: Results • NCRI increases as the growth velocity increases. • VGrowth→0 Limit : Finite NCRI (~0.04 % at 70 mK) • Quenching can further increase NCRI, • but up to ~ 0.25%. • NCRI decreases little by little, • by “phased annealing” above 0.8 K. • 2. ”CRI” increases by annealing above 1 K. • 3. NCRI of 0.04% could not be eliminated: • 1. 1-Day annealing, 20 mK below Tm x 5 times • 2. Annealing without torsional oscillation • →”Robust Supersolid Component” exists • → Consistent with single crystal result (Clark et al.) • “Velocity-Independent NCRI” = “Robust NCRI”

19. Discussion: Increase in CRI Conjecture Annealing

20. Dislocations formed in Crystal Growth Single Crystal Growth by Chochralsky Method Dislocation Density (cm-2) (T. Suzuki, in “Lattice Defects” (in Japanese), edited by H. Suzuki (1978))

21. Crystal Growth with Constant Velocity Solidification Start Conjecture End Growth Velocity ~ 10 mm /sec

22. Growth Velocity and Temperature Gradient

23. Origin of Temperature Gradient Latent Heat Balance of Cooling Power and Latent Heat (F.D.Rosi, RCA Review 19, 349 (1958) (Germanium))

24. Dislocations formed in Crystal Growth F. R. N. Nabarro, Theory of Crystal Dislocations (1967) • Impingement of two lattices • Thermal stresses • Aggregation of vacancies • Segregation of impurities

25. Dislocations formed by Thermal Stresses Solid 4He has very large thermal expansion coefficient. This causes large thermal stress under temperature gradient.

26. Dislocations formed by Thermal Stress Y. Hiki and F. Tsuruoka, Phys. Rev. B 27, 696 (1983) Ultrasound study for hcp 4He grown at constant pressures Sudden temperature change DT ~ 50 mK produces dislocations of 109 cm-2 (diminished ~1 hr)

27. Speculation: Edge/Screw Dislocations Edge Dislocations Screw Dislocations

28. Annealing Effect: Exceptional Behavior Increase in NCRI: Chan et al. Kubota et al. Only once in about 40 annealings Change in Dislocation Connectivity?

29. Helium in Porous Media Helium 4 in Vycor (Adams, Beamish, Brewer, Reppy) “S-S-S Junction” (alias “U-Mass Sandwich”) Vycor chunk Svistunov, Hallock Davis et al.

30. Helium in Nanoporous Gelsil Glass 4He in porous Gelsil (25 A) 4He in Vycor (70 A) (Yamamoto et al. PRL 93, 075302 (2004)) (Shirahama, JLTP 146, 485 (2007) )

31. Torsional Oscillator Bulk helium

32. Ideas • P > 25 bar: • Search for NCRI in bulk solid (0.5 mm thick “disk”) • 2. P > 35 bar: • Search for NCRI of solid in 25 A nanopores • 3. 25 < P < 35 bar: • “Supersolid in contact with • Superfluid Reservoir” • 4. Where is 3He impurity going? • (Kojima, Ceperley, Huse)

33. Preliminary Result 2.99 MPa Solid Tonset liquid Tc Coexistence of bulk supersolid and “nanopore superfluid”

34. Preliminary Result: Dissipation Peak 2.99 MPa Velocity-Dependent Dissipation: “Supersolid” Signal

35. Summary • Effect of Crystal Growth • NCRI is altered by the growth velocity • or temperature gradient in the crystal growth. • “Velocity-Independent NCRI” • 2. Effect of Annealing • NCRI decreases by annealing above 0.8 K. • NCRI of 0.04% could not be eliminated. • →”Robust NCRI” • 3.Supersolid-Superfluid “Double Layer”

36. Frequency and Pressure

37. Control of Crystal Growth Velocity

39. “Slow Cooling” is equivalent to “Annealing” Robust Supersolid Fraction

40. Annealing Effect: Pressure

41. Annealing Effect

42. Annealing Effect

43. Superglass State? Boninsegni, Prokofev & Svistunov, PRL 96, 105301 (2006) ODLRO exists in glassy solids In a glass at low temperatures: C = a T P = b T2 T– linear specific heat has been observed by Lin et al. Note: Mobile Dislocations can also give T2 Term in Pressure (A. Granato, Phys. Rev. 111, 740 (1958))

44. Pressure: T2 term indicates a glassy state? T2 Term: smaller than other data (Grigorev et al., cond-mat/0702133)) decreased after annealing

45. Summary • Attempt of rapid cooling: • produces large supersolid fraction • 2. Substantial annealing effect: • depending on annealing temperature • These results support the Disorder/Defect Scenarios. • 3. “Robust” supersolid fraction (0.1%) • could not be eliminated by annealing • 4. Pressure: small T2 term: decreases by annealing?

46. Effect of Temperature Difference

47. Attempts to Control Crystal Growth Velocity

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