Density of states in the presence of spin-dependent scattering in SF bilayers: a numerical and analytical approach

Tairzhan Karabassov; Valeriia D Pashkovskaia; Nikita A Parkhomenko; Anastasia V Guravova; Elena A Kazakova; Boris G Lvov; Alexander A Golubov; Andrey S Vasenko

doi:10.3762/bjnano.13.117

Density of states in the presence of spin-dependent scattering in SF bilayers: a numerical and analytical approach

Beilstein J Nanotechnol. 2022 Dec 1:13:1418-1431. doi: 10.3762/bjnano.13.117. eCollection 2022.

Authors

Tairzhan Karabassov¹, Valeriia D Pashkovskaia¹, Nikita A Parkhomenko¹, Anastasia V Guravova¹, Elena A Kazakova², Boris G Lvov¹, Alexander A Golubov^{3

4}, Andrey S Vasenko^{1

5}

Affiliations

¹ HSE University, 101000 Moscow, Russia.
² Sechenov First Moscow State Medical University, 119991 Moscow, Russia.
³ Faculty of Science and Technology and MESA Institute for Nanotechnology, University of Twente, 7500 AE Enschede, Netherlands.
⁴ Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia.
⁵ I. E. Tamm Department of Theoretical Physics, P. N. Lebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia.

Abstract

We present a quantitative study of the density of states (DOS) in SF bilayers (where S is a bulk superconductor and F is a ferromagnetic metal) in the diffusive limit. We solve the quasiclassical Usadel equations in the structure considering the presence of magnetic and spin-orbit scattering. For practical reasons, we propose the analytical solution for the density of states in SF bilayers in the case of a thin ferromagnet and low transparency of the SF interface. This solution is confirmed by numerical calculations using a self-consistent two-step iterative method. The behavior of DOS dependencies on magnetic and spin-orbit scattering times is discussed.

Keywords: Josephson junctions; density of states; proximity effect; superconductivity; superconductor/ferromagnet hybrid nanostructures.

Grants and funding

The numerical calculations of the density of states in S/F bilayers (see Figures 2–6) were supported by the Mirror Laboratories Project of HSE University. The analytical calculations of the density of states in S/F bilayers (see Figure 7 and Figure 9) were supported by the RSF project No. 20-42-09033. The calculations of the current-voltage characteristics of the SFIFS Josephson junctions (see Figure 8) were supported by the Foundation for the Advancement of Theoretical Physics and Mathematics "BASIS".