Reply to "Comment on Yerin et al., Phys. Rev. Lett. 121, 077002 (2018), and Mironov et al., Phys. Rev. Lett. 109, 237002 (2012)" by A. F. Volkov, F. S. Bergeret, and K. B. Efetov

TL;DR

This paper provides a detailed response to a comment on previous work related to superconductivity and ferromagnetism, clarifying the authors' original findings and addressing critiques.

Contribution

The authors offer a comprehensive reply to the comment, defending their theoretical framework and interpretations in the context of superconducting-ferromagnetic systems.

Findings

Clarification of theoretical assumptions

Rebuttal of critique points

Reinforcement of original conclusions

Abstract

Here we reply to the comment by A. F. Volkov, F. S. Bergeret, and K. B. Efetov.

Full text

Reply to “Comment on Yerin et al., Phys. Rev. Lett. 121, 077002 (2018), and Mironov et al., Phys. Rev. Lett. 109, 237002 (2012)” by A. F. Volkov, F. S. Bergeret, and K. B. Efetov [1]

S. V. Mironov

Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia

  

D. Yu. Vodolazov

Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia

  

Y. Yerin

Physics Division, School of Science and Technology, Università di Camerino Via Madonna delle Carceri 9, I-62032 Camerino (MC), Italy

  

A. V. Samokhvalov

Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia

  

A. S. Mel’nikov

Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia

Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, 603950, Nizhny Novgorod, Russia

  

A. Buzdin

University Bordeaux, LOMA UMR-CNRS 5798, F-33405 Talence Cedex, France

Department of Materials Science and Metallurgy, University of Cambridge, CB3 0FS, Cambridge, United Kingdom

Sechenov First Moscow State Medical University, Moscow, 119991, Russia

The first part of the comment Comm concerns the possibility of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state realization in superconductor (S) / ferromagnet (F) bilayer pointed out in the works BVE_PRB ; BVE_PRL by the authors of the comment. In the case of the small thicknesses of S and F layers and effective averaging of magnetism and superconductivity, this possibility seems to be evident for us. In our paper, we do not pretend to introduce this idea, which by the way was mentioned in the works Proshin ; Baladie published before that of the authors of the comment BVE_PRB ; BVE_PRL . Therefore, the first part of the comment Comm seems to be irrelevant to our works Mironov_2012 ; Mironov_2018 .

Further on the authors of the comment refute the criticism of their work BVE_PRB citing from our paper Mironov_2012 the following sentence: “Recently, this observation has been questioned in several theoretical works [3–5] predicting the sign change in the London relation and an unusual paramagnetic response of the hybrid superconductor or ferromagnet (S/F) andsuperconductor or normal metal (S/N) systems”. However, in this sentence there is absolutely no criticism, it is a simple recognition of the previous works and then the comment is also irrelevant to our paper Mironov_2012 .

Finally they cite from our paper Mironov_2018 : “It is exactly this FFLO instability which makes impossible to observe the global paramagnetism predicted in [34-36]. The latter paramagnetic state just does not correspond to the free energy minimum [37]”. They note that in their work BVE_PRB they are dealing with a local change of sign of the coefficient between the current density and vector potential. However, in BVE_PRB on pages 8 and 9 and Figs. 9-11 they provide the total (integrated over the F film thickness) current which changes its sign. From a formal point of view we could, thus, consider the statement of the authors of Comm that they do not calculate the integrated response in BVE_PRB to be a sort of confusion. On the other hand, our citation of the work BVE_PRB also is not completely correct. The important point is that in the above phrase from Mironov_2018 we have mixed up the total current in the F layer (which is induced by the internal magnetic induction in the ferromagnet and has been indeed calculated in BVE_PRB ) with a global response of the S/F system to the external magnetic field. Indeed the calculations of the total current in BVE_PRB were made in a special gauge (vanishing vector-potential at S/F interface). This gauge does not permit to determine the total response, because the presence of the superconductor should modify it. In other words, the full supercurrent induced inside the F film by the internal magnetic induction should be completely compensated by the screening currents inside the S layer. The applied external magnetic field is zero in such problem. As a result, we get the electromagnetic proximity effect predicted in our recent publication Mironov_APL . The result obtained in BVE_PRB relates only to the change of sign of the total current integrated over the ferromagnet and, thus, despite of its importance for further studies does not allow making unambiguous conclusions about the global response of S/F system to the external magnetic field.

In the above citation from our paper Mironov_2018 we are speaking of course about the global response of S/F system to the external magnetic field and, therefore, our citation of the paper BVE_PRB in this context without the additional explanations is misleading.