Abstract
Within the Green’s function formalism, the magnetization induced by the inverse proximity effect in bilayers containing a superconductor and a strongly spin-polarized ferromagnetic metal is studied. The Usadel equations written for the dirty superconductor model are solved with boundary conditions suitable for strongly spin-polarized ferromagnetic materials. The cases of near-critical temperatures and a weak proximity effect are considered. The dependences of the induced magnetization on the superconductor thickness, temperature, transparency of the superconductor–ferromagnet interface, and the spin mixing angle are studied. It is shown that the stronger the proximity effect, the weaker the inverse proximity effect.
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REFERENCES
I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and Applications,” Rev. Mod. Phys. 76, No. 2, 323–410 (2004).
M. Eschrig, “Spin-polarized supercurrents for spintronics,” Phys. Today 64, No. 1, 43–49 (2011).
M. Eschrig, “Spin-polarized supercurrents for spintronics: A review of current progress,” Rep. Prog. Phys. 78, No. 10, 104501 (2015).
V. V. Ryazanov, V. A. Oboznov, A. Y. Rusanov, A. V. Veretennikov, A. A. Golubov, and J. Aarts, “Coupling of two superconductors through a ferromagnet: Evidence for a π junction,” Phys. Rev. Lett. 86, No. 11, 2427–2430 (2001).
A. V. Vedyayev, N. V. Ryzhanova, and N. G. Pugach, “Critical current oscillations in S/F heterostructures in the presence of s–d scattering,” J. Magn. Magn. Mater. 305, No. 1, 53–56 (2006).
N. Klenov, V. Kornev, A. Vedyayev, N. Ryzhanova, N. Pugach, and T. Rumyantseva, “Examination of logic operations with silent phase qubit,” J. Phys.: Conf. Ser. 97, 012037 (2008).
N. G. Pugach and A. I. Buzdin, “Magnetic moment manipulation by triplet josephson current,” Appl. Phys. Lett. 101, No. 24, 242602 (2012).
D. M. Heim, N. G. Pugach, M. Y. Kupriyanov, E. Goldobin, D. Koelle, R. Kleiner, N. Ruppelt, M. Weides, and H. Kohlstedt, “The effect of normal and insulating layers on 0- π transitions in josephson junctions with a ferromagnetic barrier,” New J. Phys. 17, No. 11, 113022 (2015).
A. Vedyayev, C. Lacroix, N. Pugach, and N. Ryzhanova, “Spin-valve magnetic sandwich in a josephson junction,” Europhys. Lett. 71, No. 4, 679–685 (2005).
D. M. Heim, N. G. Pugach, M. Y. Kupriyanov, E. Goldobin, and D. Koelle, “Ferromagnetic planar josephson junction with transparent interfaces: A φ junction proposal,” J. Phys.: Condens. Matter 25, No. 21, 215701 (2013).
A. S. Vasenko, F. W. J. Hekking, and F. S. Bergeret, “Andreev current enhancement and subgap conductance of superconducting SFN hybrid structures in the presence of a small spin-splitting magnetic field,” Phys. Rev. B 86, No. 6, 060509 (2012).
R. I. Salikhov, N. N. Garif’yanov, I. A. Garifullin, L. R. Tagirov, K. Westerholt, and H. Zabel, “Spin screening effect in superconductor/ferromagnet thin film heterostructures studied using nuclear magnetic resonance,” Phys. Rev. B 80, No. 21, 214523 (2009).
J. Xia, V. Shelukhin, M. Karpovski, A. Kapitulnik, and A. Palevski, “Inverse proximity effect in superconductor-ferromagnet bilayer structures,” Phys. Rev. Lett. 102, No. 8, 087004 (2009).
F. S. Bergeret, A. F. Volkov, and K. B. Efetov, “Induced ferromagnetism due to superconductivity in superconductor-ferromagnet structures,” Phys. Rev. B 69, No. 17, 174504 (2004).
R. I. Salikhov, I. A. Garifullin, N. N. Garif’yanov, L. R. Tagirov, K. Theis-Broehl, K. Westerholt, and H. Zabel, “Experimental observation of the inverse proximity effect in superconductor/ferromagnet layered structures,” 087003, 1–4 (2008). ArXiv: 0806.4104.
Y. N. Khaydukov, V. L. Aksenov, Y. V. Nikitenko, K. N. Zhernenkov, B. Nagy, A. Teichert, R. Steitz, A. Rühm, and L. Bottyán, “Magnetic proximity effects in V/Fe superconductor/ferromagnet single bilayer revealed by waveguide-enhanced polarized neutron reflectometry,” J. Supercond. Novel Magn. 24, Nos. 1–2, 961–968 (2011).
M. J. Wolf, C. Sürgers, G. Fischer, and D. Beckmann, “Spin-polarized quasiparticle transport in exchange-split superconducting aluminum on europium sulfide,” Phys. Rev. B 90, No. 14, 144509 (2014).
X. Hao, J. S. Moodera, and R. Meservey, “Thin-film superconductor in an exchange field,” Phys. Rev. Lett. 67, 1342–1345 (1991).
S. Kolenda, C. Sürgers, G. Fische, and D. Beckmann, “Thermoelectric effects in superconductor-ferromagnet tunnel junctions on europium sulfide,” Phys. Rev. B 95, No. 22, 224505 (2017).
M. G. Flokstra, N. Satchell, J. Kim, G. Burnell, P. J. Curran, S. J. Bending, J. F. K. Cooper, C. J. Kinane, S. Langridge, A. Isidori, N. Pugach, M. Eschrig, H. Luetkens, A. Suter, T. Prokscha, and S. L. Lee, “Remotely induced magnetism in a normal metal using a superconducting spin-valve,” Nat. Phys. 12, No. 1, 57–61 (2016).
J. Linder, A. Sudbo, T. Yokoyama, R. Grein, M. Eschrig, J. Linder, A. Sudbø, T. Yokoyama, R. Grein, and M. Eschrig, “Signature of Odd-frequency pairing correlations induced by a magnetic interface,” Phys. Rev. B 81, No. 21, 214504 (2010).
O. N. Borisova, V. A. Tumanov, and Yu. N. Proshin, “Controllable josephson 0–π junction based on a four-layer ferromagnetic–superconductor system (FSFS),” Phys. Met. Metallogr. 121, No. 5, 434–438 (2020).
L. S. Uspenskaya, D. S. L’vov, G. A. Penzyakov, and O. V. Skryabina, “Nonreciprocity in yttrium-iron garnet–superconductor structures,” Phys. Met. Metallogr. 121, No. 5, 423–428 (2020).
M. Eschrig, A. Cottet, W. Belzig, and J. Linder, “General boundary conditions for quasiclassical theory of superconductivity in the diffusive limit: application to strongly spin-polarized systems,” New J. Phys. 17, No. 8, 083037 (2015).
J. A. Ouassou, A. Pal, M. Blamire, M. Eschrig, and J. Linder, “Triplet cooper pairs induced in diffusive s‑wave superconductors interfaced with strongly spin-polarized magnetic insulators or half-metallic ferromagnets,” Sci. Rep. 7, No. 1, 1932 (2017).
Mironov S., A. S. Mel’nikov and A. Buzdin, “Electromagnetic proximity effect in planar superconductor-ferromagnet structures,” Appl. Phys. Lett. 113, No. 2, 022601 (2018).
M. Eschrig, “Scattering problem in nonequilibrium quasiclassical theory of metals and superconductors: general boundary conditions and applications,” Phys. Rev. B 80, No. 13, 134511 (2009).
B. P. Vodopyanov and L. R. Tagirov, “Andreev conductance of a ferromagnet-superconductor point contact,” J. Exp. Theor. Phys. Lett. 77, No. 3, 126–131 (2003).
B. P. Vodopyanov and L. R. Tagirov, “Oscillations of superconducting transition temperature in strong ferromagnet-superconductor bilayers,” J. Exp. Theor. Phys. Lett. 78, No. 9, 555–559 (2003).
T. Champel and M. Eschrig, “Effect of an inhomogeneous exchange field on the proximity effect in disordered superconductor-ferromagnet hybrid structures,” Phys. Rev. B 72, No. 5, 054523 (2005).
M. G. Flokstra, T. C. Cunningham, J. Kim, N. Satchell, G. Burnell, P. J. Curran, S. J. Bending, C. J. Kinane, J. F. K. Cooper, S. Langridge, A. Isidori, N. Pugach, M. Eschrig, and S. L. Lee, “Controlled suppression of superconductivity by the generation of polarized cooper pairs in spin-valve structures,” Phys. Rev. B: Condens. Matter Mater. Phys. 91, No. 6, 060501 (2015).
V. O. Yagovtsev and N. G. Pugach, “Magnetization induced in a superconductor due to the effect of proximity with a ferromagnetic dielectric,” Phys. Met. Metallogr. 121, No. 3, 242–247 (2020).
Funding
The calculation in the limit close to Тс was supported by the Ministry of Science and Higher Education of the Russian Federation, Megagrant no. 075-15-2019-1934. The calculation for the case of low transparency of the boundary was supported by the Russian Foundation for Basis Research, project no. 19-02-00316-a. The calculation of the superconducting order parameter was carried out as part of the project “Mirror Laboratories” of the Higher School of Economics and the Bashkir State Pedagogical University, Ufa.
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Translated by E. Chernokozhin
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Yagovtsev, V.O., Pugach, N.G., Ekomasov, E.G. et al. Magnetization in Superconductor–Ferromagnetic Metal Bilayers Induced by the Inverse Proximity Effect. Phys. Metals Metallogr. 122, 847–854 (2021). https://doi.org/10.1134/S0031918X21090143
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DOI: https://doi.org/10.1134/S0031918X21090143