Abstract
Calculations of critical temperature T c of the phase transition to superconducting state of a superconductor/ ferromagnet/superconductor (SFS) hybrid structure with proximity effect is performed on the base of linearized Usadel equations. It is shown that the proximity effect between S and F metals and the exchange interaction can induce an inhomogeneous superconducting state with longitudinal to layers Δ ∝ exp(ipz) modulation of the superconductivity order parameter, which is characterized by nonzero value of the wave number p, describing the Larkin–Ovchinnikov–Fulde–Ferrell instability. Influence of this instability on transitions between 0- and π-states of the SFS structure is studied. It is shown that the 0–π transition is accompanied by a nonmonotonic dependence of both the critical temperature T c and the effective penetration depth Λ of the magnetic field into the hybrid structure on the characteristic size of the ferromagnetic region.
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References
R. Holm and W. Meissner, Z. Phys. 74, 715 (1932).
L. N. Bulaevskii, V. V. Kuzii, and A. A. Sobyanin, JETP Lett. 25, 290 (1977).
A. I. Buzdin, L. N. Bulaevskii, and S. V. Panyukov, JETP Lett. 35, 178 (1982).
A. I. Buzdin and M. Yu. Kupriyanov, JETP Lett. 53, 321 (1991).
A. I. Buzdin, V. Vuichich, and M. Yu. Kupriyanov, Sov. Phys. JETP 74, 124 (1992).
V. V. Ryazanov, V. A. Oboznov, A. Yu. Rusanov, A. V. Veretennikov, A. A. Golubov, and J. Aarts, Phys. Rev. Lett. 86, 2427 (2001).
T. Kontos, M. Aprili, J. Lesueur, F. Genet, B. Stephanidis, and R. Boursier, Phys. Rev. Lett. 89, 137007 (2002).
J. S. Jiang, D. Davidovic, D. H. Reich, and C. L. Chien, Phys. Rev. Lett. 74, 314 (1995).
I. A. Garifullin, D. A. Tikhonov, N. N. Garif’yanov, L. Lazar, Yu. V. Goryunov, S. Ya. Khlebnikov, L. R. Tagirov, K. Westerholt, and H. Zabel, Phys. Rev. B 66, 020505 (2002).
V. I. Zdravkov, J. Kehrle, G. Obermeier, S. Gsell, M. Schreck, C. Müller, H. A. Krug von Nidda, J. Lindner, J. MoosburgerWill, E. Nold, R. Morari, V. V. Ryazanov, A. S. Sidorenko, S. Horn, R. Tidecks, and L. R. Tagirov, Phys. Rev. B 82, 054517 (2010).
Th. Mühge, N. N. Garif’yanov, Yu. V. Goryunov, G. G. Khaliullin, L. R. Tagirov, K. Westerholt, I. A. Garifullin, and H. Zabel, Phys. Rev. Lett. 77, 1857 (1996).
S. N. Vdovichev, Yu. N. Nozdrin, E. E. Pestov, P. A. Yunin, and A. V. Samokhvalov, JETP Lett. 104, 329 (2016).
M. Weides, M. Kemmler, E. Goldobin, H. Kohlstedt, R. Waser, D. Koelle, and R. Kleiner, Phys. Rev. Lett. 97, 247001 (2006).
S. V. Bakurskiy, N. V. Klenov, I. I. Soloviev, M. Yu. Kupriyanov, and A. A. Golubov, Appl. Phys. Lett. 108, 042602 (2016).
H. Hilgenkamp, J. Mannhart, and B. Mayer, Phys. Rev. B 53, 14586 (1996).
C. Gürlich, S. Scharinger, M. Weides, H. Kohlstedt, R. G. Mints, E. Goldobin, D. Koelle, and R. Kleiner, Phys. Rev. B 81, 094502 (2010).
L. N. Bulaevskii, V. V. Kuzii, and A. A. Sobyanin, Solid State Commun. 25, 1053 (1978).
R. G. Mints, Phys. Rev. B 57, R3221 (1998).
A. Buzdin and A. E. Koshelev, Phys. Rev. B 67, 220504 (2003).
H. Sickinger, A. Lipman, M. Weides, R. G. Mints, H. Kohlstedt, D. Koelle, R. Kleiner, and E. Goldobin, Phys. Rev. Lett. 109, 107002 (2012).
A. K. Feofanov, V. A. Oboznov, V. V. Bol’ginov, J. Lisenfeld, S. Poletto, V. V. Ryazanov, A. N. Rossolenko, M. Khabipov, D. Balashov, A. B. Zorin, P. N. Dmitriev, V. P. Koshelets, and A. V. Ustinov, Nat. Phys. 6, 593 (2010).
A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys. JETP 20, 762 (1964).
P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964).
S. Mironov, A. Mel’nikov, and A. Buzdin, Phys. Rev. Lett. 109, 237002 (2012).
I. V. Bobkova and Yu. S. Barash, JETP Lett. 80, 494 (2004).
S. Mironov and A. Buzdin, Phys. Rev. Lett. 118, 077001 (2017).
T. R. Lemberger, I. Hetel, A. J. Hauser, and F. Y. Yang, J. Appl. Phys. 103, 07C701 (2008).
M. Houzet and J. S. Meyer, Phys. Rev. B 80, 012505 (2009).
M. J. Hinton, S. Steers, B. Peters, F. Y. Yang, and T. R. Lemberger, Phys. Rev. B 94, 014518 (2016).
F. Bergeret, A. F. Volkov, and K. B. Efetov, Phys. Rev. B 64, 134506 (2001).
Y. Asano, A. A. Golubov, Y. V. Fominov, and Y. Tanaka, Phys. Rev. Lett. 107, 087001 (2011).
T. Yokoyama, Y. Tanaka, and N. Nagaosa, Phys. Rev. Lett. 106, 246601 (2011).
N. Pompeo, K. Torokhtii, C. Cirillo, A. V. Samokhvalov, E. A. Ilyina, C. Attanasio, A. I. Buzdin, and E. Silva, Phys. Rev. B 90, 064510 (2014).
A. V. Samokhvalov and A. I. Buzdin, Phys. Rev. B 92, 054511 (2015).
D. Saint-James, G. Sarma, and E. Thomas, Type-II Superconductors (Oxford, Univ. Press, New York, 1969, Mir, Moscow, 1970), rus. p.198.
M. Eschrig, Rep. Prog. Phys. 78, 10450 (2015).
V. P. Mineev and K. V. Samokhin, Introduction to Unconventional Superconductivity (Mosk. Fiz. Tekh. Inst., Moscow, 1998, Gordon and Breach, London, New York, 1999).
L. Usadel, Phys. Rev. Lett. 25, 507 (1970).
A. I. Buzdin, Rev. Mod. Phys. 77, 935 (2005).
F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Rev. Mod. Phys. 77, 1321 (2005).
T. Champel and M. Eschrig, Phys. Rev. B 71, 220506 (2005).
M. Yu. Kupriyanov and V. F. Lukichev, Sov. Phys. JETP 67, 1163 (1988).
Ya. V. Fominov, N. M. Chtchelkatchev, and A. A. Golubov, Phys. Rev. B 66, 014507 (2002).
A. A. Golubov, M. Yu. Kupriyanov, V. F. Lukichev, and A. A. Orlikovskii, Mikroelektronika 12, 355 (1983).
A. I. Buzdin and H. Kachkachi, Phys. Lett. A 225, 341 (1997).
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Original Russian Text © A.V. Samokhvalov, 2017, published in Fizika Tverdogo Tela, 2017, Vol. 59, No. 11, pp. 2123–2129.
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Samokhvalov, A.V. Phase transitions in hybrid SFS structures with thin superconducting layers. Phys. Solid State 59, 2143–2149 (2017). https://doi.org/10.1134/S1063783417110270
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DOI: https://doi.org/10.1134/S1063783417110270