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Generalized Fulde-Ferrell-Larkin-Ovchinnikov state in heavy-fermion and intermediate-valence systems

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Zeitschrift für Physik B Condensed Matter

Abstract

Anomalous properties of the magnetization, the crystal dilatation, and other physical quantities observed in the mixed state of compounds such as UPd2Al3 and CeRu2 suggest the occurrence of a new state near H c2. In such compounds with large spin susceptibility and high H c2, a new inhomogeneous superconducting state is theoretically predicted to occur in high magnetic fields. In this inhomogeneous state which is shown to be a generalized Fulde-Ferrell-Larkin-Ovchinnikov state, the order parameter is spatially modulated, and planar nodes of the order parameter are periodically aligned perpendicular to the vortices. Various theoretical predictions are compared with experimental results on UPd2Al3 and CeRu2 related to this new superconducting high-field state.

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References

  1. Modler, R., Gloos, K., Geibel, C., Komatsubara, T., Sato, N., Schank, C., Steglich, F.: Int. J. Mod. Phys. B7,42 (1993); Modler, R.: diploma thesis, Darmstadt (1992), unpublished

  2. Gloos, K., Modler, R., Schimanski, H., Bredl, C.D., Geibel, C., Steglich, F., Buzdin, A.I., Sato, N., Komatsubara, T.: Phys. Rev. Lett. 70, 501 (1993)

    Google Scholar 

  3. Fulde, P., Ferrell, R.A.: Phys. Rev. 135, 550 (1964)

    Google Scholar 

  4. Larkin, A.I., Ovchinnikov, Yu. N.: Zh. Eksp. Teor. Fiz. 47,1136 (1964) [Sov. Phys. JETP 20, 762 (1965)]

  5. Campbell, A.M., Evetts J.E.: Adv. Phys. 21, 327 (1972)

    Google Scholar 

  6. Finnemore, D.K., Stromberg, T.F., Swenson, C.A.: Phys. Rev. 149,231 (1966); Weber, H.W., Seidl, E., Laa, C., Schachinger, M., Prohammer, M., Junod, A., Eckert, D.: Phys. Rev. B 44, 7858 (1991)

  7. Tenya, K., Ikeda, M., Tayama, T., Mitamura, H., Amitsuka, H., Sakakibara, T., Maezawa, K., Kimura, N., Settai, R., Onuki, Y.: J. Phys. Soc. Jpn. 64, 1063 (1995)

    Google Scholar 

  8. Huxley, A.D., Paulsen, C., Laborde, O., Tholence, J.L., Sanchez, D., Junod, A., Calemczuk, R.: J. Phys.: Condens. Matter 5, 7709 (1993)

    Google Scholar 

  9. Yagasaki, K., Hedo, M., Nakama, T.: J. Phys. Soc. Jpn. 62,3825 (1993) _

  10. Sugawara, H., Yamazaki, T., Kimura, N., Settai, R., Õnuki, Y.: Physica C 206-207, 196 (1995)

  11. Goshima, H., Suzuki, T., Fujita, T., Hedo, M., Nakama, T., Yagasaki, K.: Physica C 206-207, 193 (1995)

  12. Kadowaki, K., Hirata, K., Takeya, H.: (preprint 1995)

  13. Isino, M., Kobayashi, T., Toyota, N., Fukase, T., Muto, Y.: Phys. Rev. B 38, 4457 (1988)

    Google Scholar 

  14. Uehara, M.: (private communication)

  15. The large susceptibilities of the u-based compounds mag indicate substantial, if not dominating, orbital contributions. The astonishing discrepancy between the Zeeman and condensation energies in the case of UBe13 is related to the highly unusual H c2(T) behavior of this compound [16]

  16. Thomas, F., Wand, B., Luhmann, T., Gegenwart, P., Stewart, G.R., Steglich, F., Brison, J.P., Buzdin, A.I., Glemot, L., Flouquet, J.: J. Low Temp. Phys. (in press)

  17. Geibel, C., Schank, C., Thies, S., Kitazawa, H., Bredl, C.D., Bbhm, C.D., Rau, M., Grauel, A., Caspary, R., Helfrich, R., Ahlheim, U., Weber, G., Steglich, F.: Z. Phys. B 84, (1991)

  18. Steglich, F., Ahlheim, U., Bbhm, C.D., Bredl, C.D., Caspary, R., Geibel, C., Grauel, A., Helfrich, R., Kbhler, R., Lang, M., Mehner, A., Modler, R., Schank, C., Wassilew, C., Weber, G., Assmus, W., Sato, N., Komatsubara, T.: Physica C 185-189, 379 (1991)

  19. gCspin corresponds to - 2.10−3 emu/mole characterizing the "superconducting 5f subsystem": Feyerherm R., Amato, A., Gygax, F.N., Schenk, A., Geibel, C., Steglich, F., Sato, N., Komatsubara, T.: Phys. Rev. Lett. 73, 1849 (1994)

    Google Scholar 

  20. Steglich, F., Modler, R., Gegenwart, P., Deppe, M., Weiden, M., Lang, M., Geibel, C., Luhmann, T., Paulsen, P., Tholence, J.L., Onuki, Y., Tachiki, M., Takahashi, S.: Physica C (in press)

  21. γo = 115 mJ/K2 mol, characterizing the "superconducting 5f subsystem" has been used: Caspary, R., Hellmann, P., Keller, M., Sparn, G., Wassilew, C., Kbhler, R., Weber, G., Geibel, C., Schank, C., Steglich, F., Phillips, N.E.: Phys. Rev. Lett. 71, 2146 (1993)

    Google Scholar 

  22. Orlando, T.P., McNiff, E.J. Jr., Foner, S., Beasley, M.R.: Phys. Rev. B 19, 4545 (1979)

    Google Scholar 

  23. de Visser, A., Menovsky, A.A., Franse, J.J.M.: Physica B 147, 81 (1987)

  24. Yin, G., Maki, K.: Phys. Rev. Lett. 47, 892 (1993)

    Google Scholar 

  25. Koziol, Z.: Ph.D. Thesis, Amsterdam (1994) (unpublished)

  26. Frings, P.H., Franse, J.J.M., de Boer, F.R., Menovsky, A.A.: J. Mag. Mag. Mat. 31-34, 1595 (1983)

    Google Scholar 

  27. van Dijk, N.H., de Visser, A., Franse, J.J.M., Taillefer, L.: J. Low Temp. Phys. 93, 101 (1993)

    Google Scholar 

  28. Rauchschwalbe, U.: Physica B 147, 1 (1987)

  29. Ott, H.R., Rudigier, H., Fisk, Z., Smith, J.L.: Phys. Rev. Lett. 50, 1595 (1983)

    Google Scholar 

  30. Lieke, W., Rauchschwalbe, U., Bredl, C.D., Steglich, F., Aarts, J., de Boer, F.R.: J. Appl. Phys. 63, 2111 (1982)

    Google Scholar 

  31. Geibel, C., Thies, S., Kaczorowski, Grauel, A., Seidel, A., Ahlheim, U., Helfrich, R., Petersen, K., Bredl, C.D., Steglich, F.: Z. Phys. B 83, 305 (1991); x, has been estimated by an extrapolation of the normal-state susceptibility below TN to T ->0

  32. Dalichaouch, Y., de Andrade, M.C., Maple, M.B.: Phys. Rev. B 46, 8671 (1992)

    Google Scholar 

  33. Burkhardt, H., Rainer, D.: Ann. Phys. 3, 181 (1994)

    Google Scholar 

  34. Gruenberg, L.W., Gunther, L.: Phys. Rev. Lett. 16, 996 (1966)

    Google Scholar 

  35. Larkin, A.I., Ovchinnikov Yu.N.: J. Low Temp. Phys. 34, 409 (1979)

    Google Scholar 

  36. Ferrell, R.A.: Phys. Rev. Lett. 3, 262 (1959)

    Google Scholar 

  37. Anderson, P.W.: Phys. Rev. Lett. 3, 325 (1959)

    Google Scholar 

  38. Eilenberger, G.: Z. Phys. 214, 195 (1966)

    Google Scholar 

  39. Note that a differs from αGG in [34] α/αGG = (2ɛ2+γ)−1

  40. Machida, K. and Nakanishi, H.: Phys. Rev. B 30, 122 (1995)

  41. Burkhardt and Rainer [33] have shown in their two-dimensional model the transition from the FFLO state to the uniform superconducting state is of second order. The presence of the vortices suppresses the mixing of the higher harmonics of the order parameter in the GFFLO state. The suppression makes the phase transition from the GFFLO state to the pure vortex state to be of first order

  42. In Figs. 4-7, a = 1, and a = 2, respectively, were chosen in order to enlarge the field range of the GFFLO state

  43. Lühmann, T., Gegenwart, P., Reinders, P.H., Geibel, C., Steglich, F., Paulsen, C., Tholence, J.L.: Physica C 235-240, 95 (1994)

  44. Steglich, F., Geibel, C., Gloos, K., Hellmann, P., Köhler, R., Lang, M., Modler, R., Schank, C.: Physica C 235-240, 95 (1994)

  45. Ishiguro, A., Sawada, A., Kimura, J., Suzuki, M., Sato, N., Komatsubara, T.: J. Phys. Soc. Jpn. 64, 378 (1995)

    Google Scholar 

  46. Vidberg, H.J., Serene, J.W.: J. Low Temp. Phys. 29, 179 (1977)

    Google Scholar 

  47. Modler, R., Lang, M., Geibel, C., Schank, C., Steglich, F.: Physica B199-200, 145 (1994)

  48. Gegenwart, P.: Diploma Thesis, TH Darmstadt (1994) (unpublished)

  49. Modler, R.: Dissertation, TH Darmstadt (1995) (unpublished)

  50. Norman, M.R.: Phys. Rev. Lett. 71, 3391 (1993)

    Google Scholar 

  51. Aoi, K., Dieterich, W., Fulde, P.: Z. Phys. 267, 223 (1974)

    Google Scholar 

  52. Shimahara, H.: Phys. Rev. B 50, 12760 (1995)

    Google Scholar 

  53. Dupuis, N.: Phys. Rev. B 51, 9074 (1995)

    Google Scholar 

  54. Inada, Y., Ishiguro, A., Kimura, J., Sato, N., Sawada, A., Komatsubara, T.: Physica C 206-207, 33 (1995)

  55. Hedo, M., Inada, Y., Ishida, T., Yamamoto, E., Haga, Y., Onuki, Y., Higuchi, M., Hasegawa, A. J. Phys. Soc. Jpn. (submitted for publication)

  56. Sandratskii, L.M., Kübler, J., Zahn, P., Mertig, L: Phys. Rev. B 50, 15834 (1995)

    Google Scholar 

  57. Yanase, A.: J. Phys. F.: Met. Phys. 16, 1501 (1986)

    Google Scholar 

  58. We can show, in the strong paramagnetic limit of a >∞, that the phase transition at H c2 is of first order in the temperature range of 0.1317 < T/T c, < 0.5615. Our calculation shows that in a two-dimensional system the phase transition at H c2 is of second order in the whole temperature range below T c, which is consistent with the result of [33]

  59. Matsuo, S., Shimahara, H., Nagai, K.: J. Phys. Soc. Jpn. 64, 371 (1995)

    Google Scholar 

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Authors and Affiliations

  1. Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980, Japan

    M. Tachiki & S. Takahashi

  2. Institut für Festkörperphysik, Technische Hochschule Darmstadt, Hochschulstrasse 8, D-64289, Darmstadt, Germany

    P. Gegenwart, M. Weiden, M. Lang, C. Geibel, F. Steglich & R. Modler

  3. Forschungszentrum Karlsruhe GmbH, INFP, D-76031, Karlsruhe, Germany

    R. Modler

  4. CRTBT, CNRS, 38042, Grenoble Cedex 9, France

    C. Paulsen

  5. Department of Physics, Osaka University, Toyonaka, Osaka, 560, Japan

    Y. Ōnuki

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  1. M. Tachiki
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  2. S. Takahashi
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  3. P. Gegenwart
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  4. M. Weiden
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  5. M. Lang
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  6. C. Geibel
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  7. F. Steglich
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  8. R. Modler
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  9. C. Paulsen
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  10. Y. Ōnuki
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Dedicated to Professor Peter Fulde on the occassion of his 60th birthday

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Tachiki, M., Takahashi, S., Gegenwart, P. et al. Generalized Fulde-Ferrell-Larkin-Ovchinnikov state in heavy-fermion and intermediate-valence systems. Z. Phys. B 100, 369–380 (1997). https://doi.org/10.1007/s002570050135

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  • DOI: https://doi.org/10.1007/s002570050135

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