Abstract
We report on the first comprehensive measurements of critical superflow velocities in3He-B which allow different mechanisms of vortex formation to be identified. As a function of temperatureT and pressureP, we measure the critical angular velocity Ωc(T, P) at which vortices start to form in slowly accelerating rotation in a cylindrical container filled with3He-B. Owing to the long coherence length ξ(T, P)∼10–100 nm, either trapped remanent vorticity or intrinsic nucleation may dominate vortex formation, depending on the roughness of the container wall and the presence of loaded traps.
NMR measurement with a resolution of one single vortex line allows us to distinguish between different processes: (1) Three extrinsic mechanisms of vortex formation have been observed. One of them is the vortex mill, a continuous periodic source which is activated in a rough-walled container well below the limit for intrinsic nucleation. (2) In a closed smooth-walled container intrinsic nucleation is the only mechanism available, with a critical velocity vc(T, P)=Ωc(T, P), whereR is the radius of the container. We findv c (T, P) to be related to the calculated intrinsic stability limitv ch (T, P) of homogeneous superflow. The existence of this connection in the form of a scaling law implies that nucleation takes place at an instability, rather than by thermal activation or quantum tunneling which become impossible because of an inaccessibly high energy barrier.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Onsager,Nuova Cimento Suppl. 6, 249 (1949).
R. P. Feynman, inProg. in Low Temp. Phys., Vol. 1, C. J. Gorter (ed.), (North-Holland Publ. Co., Amsterdam (1955), p. 17.
R. J. Donnelly,Quantized Vortices in Helium II, Cambridge University Press, Cambridge, UK (1991).
D. R. Tilley and J. Tilley,Superfluidity and Superconductivity, IOP Publishing Ltd, Bristol UK (1990).
W. E. Keller,Helium-3 and Helium-4, Plenum Press, New York (1969).
Earlier measurements on critical velocities in rotating3He-B: P. J. Hakonen,Physica B 178, 83 (1992); J. P. Pekola and J. T. Simola,J. Low Temp. Phys. 58, 555 (1985); P. L. Gammel, T.-L. Ho, and J. D. Reppy,Phys. Rev. Lett. 55, 2708 (1985);ibid. 52, 121 (1984);ibid. 43, 1332 (1979).
The present work is a continuation of the measurements in Refs. 30, 33, and 23.
G. E. Volovik, Modern problems in condensed matter sciences, inHelium Three, W. P. Halperin and L. P. Pitaevskii (eds.), Elsevier, Amsterdam (1990), Vol. 26, p. 27.
G. W. Rayfield and F. Reif,Phys. Rev. 136, A1194 (1964).
D. R. Allen, R. M. Bowley, and P. V. E. McClintock,Phys. Rev. Lett. 36, 1313 (1976); T. Ellis and P. V. E. McClintock,Phil. Trans. Roy. Soc. A 315, 259 (1985).
A. I. Ahonen, J. Kokko, O. V. Lounasmaa, M. A. Paalanen, R. C. Richardson, W. Schoepe, and Y. Takano,Phys. Rev. Lett. 37, 511 (1976).
C. A. M. Casteljins, K. F. Coates, A. M. Guenault, S. G. Mussett, and G. R. Pickett,Phys. Rev. Lett. 56, 69 (1986).
D. D. Awschalom and K. W. Schwarz,Phys. Rev. Lett. 52, 49 (1984).
G. A. Williams,J. Low Temp. Phys. 89, 91 (1992), and references therein.
E. Varoquaux G. G. Ihas, O. Avenel, and R. Aarts,Phys. Rev. Lett. 70, 2114 (1993).
W. I. Glaberson and R. J. Donnelly,Phys. Rev. 141, 208 (1966).
K. W. Schwarz,Phys. Rev. Lett. 64, 1130 (1990).
S. V. Iordanski,Zh. Eksp. Teor. Fiz. 48, 708 (1965) [Sov. Phys. JETP 21, 467 (1965)].
J. S. Langer and M. E. Fisher,Phys. Rev. Lett. 19, 560 (1967); J. S. Langer and J. D. Reppy, inProgress in Low Temperature Physics, C. J. Gorter (ed.). North-Holland, Amsterdam (1970), Vol. 6 p. 1.
P. W. Anderson,Rev. Mod. Phys. 38, 298 (1966).
G. G. Ihas, O. Avenel, R. Aarts, R. Salmelin, and E. Varoquaux,Phys. Rev. Lett. 69, 327 (1992); S. Burkhart, M. Bernard, O. Avenel, and E. Varoquaux,Phys. Rev. Lett. 72, 380 (1994); O. Avenel, G. G. Ihas, and E. Varoquaux,J. Low Temp. Phys. 93, 1031 (1993); E. Varoquaux and O. Avenel,Physica B 197, 306 1994.
A. Amar, Y. Sasaki, R. L. Lozes, J. C. Davis, and R. E. Packard,Phys. Rev. Lett. 68, 2624 (1992); J. C. Davis, J. Steinhauer, K. Schwab, Yu. M. Mukharsky, A. Amar, Y. Sasaki, and R. E. Packard,Phys. Rev. Lett. 69, 323 (1992); R. E. Packard and J. C. Davis,Physica B 197, 315 (1994).
Ü. Parts, V. M. H. Ruutu, J. H. Koivuniemi, Yu. M. Bunkov, V. V. Dmitriev, M. Fogelström, M. Huebner, Y. Kondo, N. B. Kopnin, J. S. Korhonen, M. Krusius, O. V. Lounasmaa, P. I. Soininen, and G. E. Volovik,Europhys. Lett. 31, 449 (1995).
P. W. Anderson and G. Toulouse,Phys. Rev. Lett. 38, 508 (1977).
C. M. Muirhead, W. F. Vinen, and R. J. Donnelly,Phil. Trans. Roy. Soc. A311, 433 (1984).
P. C. Hendry, N. S. Lawson, P. V. E. McClintock, C. D. H. Williams, and R. M. Bowley,Phys. Rev. Lett. 60, 604 (1988), and references therein.
R. M. Bowley,J. Low Temp. Phys. 87, 137 (1992).
J. Steinhauer, K. Schwab, Yu. Mukharsky, J. C. Davis, and R. E. Packard,Phys. Rev. Lett. 74, 5056 (1995).
K. W. Schwarz,Phys. Rev. Lett. 59, 1167 (1987);ibid. Phys. Rev. Lett. 69, 3342 (1992);J. Low Temp. Phys. 93, 1019 (1993);Physica B 197, 324 (1994).
Y. Kondo, J. S. Korhonen, Ü. Parts, M. Krusius, O. V. Lounasmaa, and A. D. Gongadze,Physica B 178, 90 (1992).
Experimental reviews on rotating3He superfluids: P. J. Hakonen, O. V. Lounasmaa, and J. T. Simola,Physica B 160, 1 (1989); M. Krusius,J. Low Temp. Phys. 91, 233 (1993).
Theoretical reviews on vortex structures in3He superfluids: M. M. Salomaa and G. E. Volovik,Rev. Mod. Phys. 59, 533 (1987); G. A. Kharadze, Modern problems in condensed matter sciences, inHelium Three, W. P. Halperin and L. P. Pitaevskii (eds.), North-Holland, Amsterdam (1990), Vol. 26, p. 167; G. E. Volovik,Exotic Properties of Superfluid 3 He, World Scientific Publishing Co., Singapore (1992).
Ü. Parts, J. H. Koivuniemi, M. Krusius, V. M. H. Ruutu, and S. R. Zakazov,Physica B 194–196, 771 (1994).
P. Mathieu, J. C. Marechal, and Y. Simon,Phys. Rev. B 22, 4293 (1980).
V. M. Ruutu, J. J. Ruohio, M. Krusius, B. Plaçais, E. B. Sonin, and Wen Xu, Helsinki Univ. of Techn. Rep. TKK-F-A757 (1996), and to be published.
D. Vollhardt, K. Maki, and N. Schopohl,J. Low. Temp. Phys. 39, 79 (1980); H. Kleinert,J. Low Temp. Phys. 39, 451 (1980).
M. Fogelström, unpublished.
D. S. Greywall,Phys. Rev. B 33, 7520 (1986).
G. E. Volovik,Pis’ma Zh. Eksp. Teor. Fiz. 15, 116 (1972) [JETP Lett. 15, 81 (1972)].
P. I. Soininen and N. B. Kopnin,Phys. Rev. B 49, 12087 (1994).
W. F. Vinen, inProgress in Low Temperature Physics, C. J. Gorter (ed.), North-Holland, Amsterdam (1961), p. 1; andLiquid Helium, Proc. Internat. School of Phys. Enrico Fermi, Course 21, Academic Press, New York (1963), p. 336.
L. D. Landau and E. M. Lifshitz,Fluid Mechanics, 2nd ed. Pergamon Press, Oxford (1987), p. 23.
R. E. Packard and T. M. Sanders, Jr.,Phys. Rev. Lett. 22, 823 (1969);Phys. Rev. A 6, 799 (1972).
H. E. Hall,Adv. Phys. 9, 89 (1960).
M. Krusius, J. S. Korhonen, Y. Kondo, and E. B. Sonin,Phys. Rev. B 47, 15 113 (1993-II);Europhys. Lett. 22, 125 (1993).
Wen Xu, B. Plaçais, V. M. Ruutu, and M. Krusius, inProc. 21 Inter. Conf. Low Temp. Phys., S. Danis, V. Gregor, and K. Zaveta (eds.),Czech. J. Phys. 46 Suppl., Pt, Sl, p. 11 (1996).
M. Krusius, E. V. Thuneberg, and U. Parts,Physica B 197, 376 (1994).
K. W. Schwarz,Phys. Rev. Lett. 47, 251 (1981).
N. B. Kopnin and M. M. Salomaa,Phys. Rev. B 44, 9667 (1991).
N. B. Kopnin and A. V. Lopatin,Phys. Rev. B 51, 15291 (1995).
T. D. C. Bevan, A. J. Manninen, J. B. Cook, A. J. Armstrong, J. R. Hook, and H. E. Hall,Phys. Rev. Lett. 74, 750 (1995);Physica B 210, 251 (1995).
V. M. H. Ruutu, J. H. Koivuniemi, Ü. Parts, A. Hirai, and M. Krusius,Physica B 194–196, 159 (1994).
D. Vollhardt and P. Wölfle,The Superfluid Phases of Helium 3, Taylor & Francis, London (1990).
P. J. Hakonen, M. Krusius, M. M. Salomaa, R. H. Salmelin, J. T. Simola, A. D. Gongadze, G. E. Vachnadze, and G. A. Kharadze,J. Low Temp. Phys. 76, 225 (1989).
J. S. Korhonen, Yu. M. Bunkov, V. V. Dmitriev, Y. Kondo, M. Krusius, Yu. M. Mukharskiy, Ü. Parts, and E. V. Thuneberg,Phys. Rev. B 46, 13983 (1992).
J. S. Korhonen, A. D. Gongadze, Z. Janu, Y. Kondo, M. Krusius, Yu. M. Mukharsky, and E. V. Thuneberg,Phys. Rev. Lett. 65, 1211 (1990).
H. N. Scholz,Ph.D. Thesis, Ohio State University, Columbus, Ohio (1981); R. F. Hoyt, H. N. Scholz, and D. O. Edwards,Physica B 107, 287 (1981).
A. I. Ahonen, M. Krusius, and M. A. Paalanen,J. Low Temp. Phys. 25, 421 (1976).
Yu. M. Bunkov, V. V. Dmitriev, Y. Kondo, J. Korhonen, M. Krusius, Yu. M. Mukharsky, and U. Parts,Physica B 194–196, 761 (1994).
O. Avenel, M. Bernard, S. Burkhart, and E. Varoquaux,Physica B 210, 215 (1995).
E. J. Yarmchuk and R. E. Packard,J. Low Temp. Phys. 46, 479 (1982).
P. C. Hendry, N. S. Lawson, R. A. M. Lee, P. V. E. McClintock, and C. D. H. Williams,Physica B 210, 209 (1995);Nature 368, 315 (1994);J. Low Temp. Phys. 93, 1059 (1993).
It is also possible that, instead of saturating,N r may start to decrease at largeN a . This would be the case if all traps with a low critical velocity are loaded and simultaneously with increasingN a the onset of the periodic process decreases, as shown in Fig. 24.
W. I. Glaberson and R. J. Donnelly,Phys. Rev. 141, 208 (1966).
K. W. Schwarz,Phys. Rev. Lett. 64, 1130 (1990);ibid. Phys. Rev. Lett. 71, 259 (1993).
Y. J. Brown and G. B. Hess,J. Low. Temp. Phys. 49, 267 (1982), and references therein.
G. M. Shifflett and G. B. Hess,J. Low Temp. Phys. 98, 591 (1995).
S. M. Tholen and J. M. Parpia,Phys. Rev. Lett. 68, 2810 (1992); D. Kim, M. Nakagawa, O. Ishikawa, T. Hata, T. Kodama, and H. Kojima,Phys. Rev. Lett. 71, 1581 (1993).
J. S. Korhonen, Y. Kondo, M. Krusius, E. V. Thuneberg, and G. E. Volovik,Phys. Rev. B 47 8868 (1993-II);Phys. Rev. Lett. 68, 3331 (1992).
A. J. Leggett,J. Low Temp. Phys. 87, 571 (1992), and references therein.
P. Schiffer, M. T. O’Keefe, M. D. Hildreth, H. Fukuyama, and D. D. Osheroff,Phys. Rev. Lett. 69, 120 (1992).
P. Schiffer and D. D. Osheroff,Rev. Mod. Phys. 67, 491 (1995); P. Schiffer, D. D. Osheroff, and A. J. Leggett, inProgress in Low Temperature Physics, Vol. 14, W. P. Halperin (ed.) Elsevier Science Publ. Amsterdam (1995), p. 159.
V. M. H. Ruutu, V. B. Eltsov, A. J. Gill, T. W. B. Kibble, M. Krusius, Yu. G. Makhlin, B. Plaçais, G. E. Volovik, and Wen Xu,Nature 382, July 334 (1996).
V. M. Ruutu, J. Kopu, M. Krusius, U. Parts, B. Plaçais, E. V. Thuneberg, and Wen Xu,Helsinki Univ. of Techn. Rep. TKK-F-A758 (1996), and to be published.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ruutu, V.M.H., Parts, Ü., Koivuniemi, J.H. et al. Intrinsic and extrinsic mechanisms of vortex formation in superfluid3He-B. J Low Temp Phys 107, 93–164 (1997). https://doi.org/10.1007/BF02396838
Issue Date:
DOI: https://doi.org/10.1007/BF02396838