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Extracting Stray Magnetic Fields from Thin Ferromagnetic Layers in Hybrid Superconducting/Ferromagnetic Heterostructures

Authors:
Anderson Paschoa
Anderson Paschoa
Anderson Paschoa
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Jorge L. Gonzalez
Jorge L. Gonzalez
Jorge L. Gonzalez
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V. P. Nascimento at Federal University of Espírito Santo
V. P. Nascimento
E. C. Passamani at Federal University of Espírito Santo
E. C. Passamani
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Abstract and Figures

Hybrid Nb(20)/Cu(5)/Py(2), Nb(20)/Cu(5)/Co(40) and Nb(20)/Cu(dCu_{Cu})/Py(2)/Cu(5)/Co(40) heterostructures (values in nanometers and dCu_{Cu} = 0, 2.5 and 5.0) were fabricated using a confocal DC magnetron sputtering setup. Performing magnetotransport measurements and using the anisotropic Ginzburg–Landau approach, the stray field values in zero-applied field (B0CoB_\mathrm{0Co}, B0PyB_\mathrm{0Py} and B0Py+CoB_\mathrm{0Py+Co}) were estimated as being −9 - 9~mT (+31 + 31~mT) for the hybrid Nb/Cu/Co (Nb/Cu/Py) trilayers and +36 + 36~mT for the hybrid ordinary Nb/Cu(5)/Py/Cu/Co spin-valve heterostructure. The effective fields acting on the superconducting layer in the hybrid non-ordinary Nb/Cu/Py and Nb/Cu/Co spin-valve heterostructures and its dependence with the applied magnetic field were also quantified, showing that the stray fields of thin ferromagnetic layers are the same order of magnetide but with different strengths. For an applied field of 1 T, the spin-valve effect values of − 230 -~230~mK (+ 300 +~300~mK), previously found for the hybrid Nb/Cu/Co (Nb/Cu/Py) trilayers and + 140+~140 mK for the Nb/Cu(5)/Py/Cu/Co heterostructure, had their physical origin better discussed and demonstrated. The 2-nm-thick ferromagnetic Py layer strongly contributes to the effective fields, and the low spin-valve effect of + 140+~140 mK for the ordinary Nb/Cu(5)/Py/Cu/Co spin-valve heterostructure would be a consequence of two contributions of opposite signs governed by the Py and Co layers and also due to the proximity effect contribution.
Diagram showing specific details of the experimental setup used to prepare the samples and also to perform the magnetotransport measurements
Diagram showing specific details of the experimental setup used to prepare the samples and also to perform the magnetotransport measurements
… 
(a) Room temperature Grazing incidence X-ray diffraction patterns and (b) R(T,B=1T)R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{R(T, B = 1 T)}{R_0}$$\end{document} plots (R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} is the value obtained at 10 K) recorded for the Nb/Cu/Co (blue) and Nb/Cu/Py (red): open symbols are due to B‖\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\parallel }$$\end{document}-field, while full symbols correspond to the B⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\perp }$$\end{document}-field configuration. Inset in (b) shows TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{C}$$\end{document} determined at the inflection point of the R(T) curves. (c) and (d) show the dependence of TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{C}$$\end{document} for the (B‖\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\parallel }$$\end{document}) and (B⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\perp }$$\end{document}) for the Nb/Cu/Co (red symbols) and Nb/Cu/Py (blue symbols). Full black lines are fits with linear and quadratic theoretical expressions
(a) Room temperature Grazing incidence X-ray diffraction patterns and (b) R(T,B=1T)R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{R(T, B = 1 T)}{R_0}$$\end{document} plots (R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} is the value obtained at 10 K) recorded for the Nb/Cu/Co (blue) and Nb/Cu/Py (red): open symbols are due to B‖\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\parallel }$$\end{document}-field, while full symbols correspond to the B⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\perp }$$\end{document}-field configuration. Inset in (b) shows TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{C}$$\end{document} determined at the inflection point of the R(T) curves. (c) and (d) show the dependence of TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{C}$$\end{document} for the (B‖\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\parallel }$$\end{document}) and (B⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\perp }$$\end{document}) for the Nb/Cu/Co (red symbols) and Nb/Cu/Py (blue symbols). Full black lines are fits with linear and quadratic theoretical expressions
… 
(a) R(T,B=0T)R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{R(T, B = 0 T)}{R_0}$$\end{document} curves recorded for zero-field case [Cu spacer thickness (dCu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{Cu}$$\end{document}) = 0 (orange); 2.5 (green) and 5.0 nm (black)] and (b) the behavior of TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{C}$$\end{document} of the 20-nm-thick Nb film as a function of dCu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{Cu}$$\end{document} in hybrid Nb/Cu(dCu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{Cu}$$\end{document})/Py/Cu/Co. The full line in (b) is result of a fit with linear function, also shown
(a) R(T,B=0T)R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{R(T, B = 0 T)}{R_0}$$\end{document} curves recorded for zero-field case [Cu spacer thickness (dCu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{Cu}$$\end{document}) = 0 (orange); 2.5 (green) and 5.0 nm (black)] and (b) the behavior of TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\mathrm{C}$$\end{document} of the 20-nm-thick Nb film as a function of dCu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{Cu}$$\end{document} in hybrid Nb/Cu(dCu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{Cu}$$\end{document})/Py/Cu/Co. The full line in (b) is result of a fit with linear function, also shown
… 
M(B) loops recorded for the B⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\perp }$$\end{document}-field configuration at 3 and 10 K for the hybrid Nb/Cu/Co (a) and Nb/Cu/Py (b). Plots of the ΔTC(B)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta T_\mathrm{C}(B)$$\end{document} data using data shown in Fig. 2); data for the hybrid Nb/Cu/Co (c) and Nb/Cu/Py (d) are also shown. The full lines (blue and red) of (c) and (d) are results of linear fits
M(B) loops recorded for the B⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\perp }$$\end{document}-field configuration at 3 and 10 K for the hybrid Nb/Cu/Co (a) and Nb/Cu/Py (b). Plots of the ΔTC(B)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta T_\mathrm{C}(B)$$\end{document} data using data shown in Fig. 2); data for the hybrid Nb/Cu/Co (c) and Nb/Cu/Py (d) are also shown. The full lines (blue and red) of (c) and (d) are results of linear fits
… 
300 K M(B) loop recorded for the hybrid Nb/Cu/Co in the B⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\perp }$$\end{document}-field configuration. The insert shows a zoom in the low field region
+2
300 K M(B) loop recorded for the hybrid Nb/Cu/Co in the B⊥\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{\perp }$$\end{document}-field configuration. The insert shows a zoom in the low field region
… 
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Vol.:(0123456789)
1 3
https://doi.org/10.1007/s10948-021-06052-0
ORIGINAL PAPER
Extracting Stray Magnetic Fields fromThin Ferromagnetic Layers
inHybrid Superconducting/Ferromagnetic Heterostructures
AndersonPaschoa1 · JorgeL.Gonzalez1 · ValbertoP.Nascimento1 · EdsonC.Passamani1
Received: 21 June 2021 / Accepted: 26 September 2021
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
Abstract
Hybrid Nb(20)/Cu(5)/Py(2), Nb(20)/Cu(5)/Co(40) and Nb(20)/Cu(d
Cu
)/Py(2)/Cu(5)/Co(40) heterostructures (values in
nanometers and d
Cu
= 0, 2.5 and 5.0) were fabricated using a confocal DC magnetron sputtering setup. Performing magne-
totransport measurements and using the anisotropic Ginzburg–Landau approach, the stray field values in zero-applied field
(
B0Co
,
B0Py
and
B0Py+Co
) were estimated as being
−9
mT (
+31
mT) for the hybrid Nb/Cu/Co (Nb/Cu/Py) trilayers and
+36
mT
for the hybrid ordinary Nb/Cu(5)/Py/Cu/Co spin-valve heterostructure. The effective fields acting on the superconducting
layer in the hybrid non-ordinary Nb/Cu/Py and Nb/Cu/Co spin-valve heterostructures and its dependence with the applied
magnetic field were also quantified, showing that the stray fields of thin ferromagnetic layers are the same order of magnet-
ide but with different strengths. For an applied field of 1 T, the spin-valve effect values of
mK (
+300
mK), previously
found for the hybrid Nb/Cu/Co (Nb/Cu/Py) trilayers and
+140
mK for the Nb/Cu(5)/Py/Cu/Co heterostructure, had their
physical origin better discussed and demonstrated. The 2-nm-thick ferromagnetic Py layer strongly contributes to the effec-
tive fields, and the low spin-valve effect of
+140
mK for the ordinary Nb/Cu(5)/Py/Cu/Co spin-valve heterostructure would
be a consequence of two contributions of opposite signs governed by the Py and Co layers and also due to the proximity
effect contribution.
Keywords Hybrid systems· Spin-valve effect· Stray field· Magnetic domains· Proximity effects
1 Introduction
Hybrid superconductor/ferromagnet (SC/FM) metamateri-
als are strong candidates for applications in several super-
conducting spintronic and magnonics devices [1–14]. For
instance, in this hybrid SC/FM heterostructures [often
named as spin-valves (SV) devices], the critical temperature
variation (
ΔTC
) is mainly determined by (i) the proximity
effect, which accounts for the penetration of superconduct-
ing correlations inside FM layers with different spin struc-
tures [1, 9] and (ii) the interaction between the potential
vector from the effective stray field of the FM layers and the
SC order parameter (orbital effect) [6, 9, 10]. Therefore, the
role played by these both effects (also the interplay between
them) is still a huge challenge to be elucidated. While the
proximity effect seems to be acceptable in the explanation
of the
ΔTC
effect [1, 9], the part related to stray fields of FM
layers is still an embryo. In this regard, at least, two points
need to be better understood in hybrid SC/FM heterostruc-
tures: (a) the magnitude of the stray field of FM layers that
acts on the SC layer and (b) the influence of the spin configu-
rations of the FM layers and its modification by an applied
magnetic field.
Indeed, the (a) and (b) issues are very important for the
design of heterostructures, wherein superconducting proper-
ties can be controlled by an appropriated choice of the FM
layers. For example, it has recently been demonstrated that
Nb films decorated with cobalt (Co) nanostripes and vice
versa, i.e., Co films decorated with Nb nanostripes, can be
used to manipulate Abrikosov vortices achieving ultrafast
vortex velocities [6]. On the basis of these heterostructures,
some new metamaterials have been proposed for applica-
tions in magnonics [4].
Considering the question of stray fields of FM layers, we
have recently developed a theoretical framework to explain a
significant SV effect measured by our group in non-ordinary
Nb/Co heterostructures [8]. The model has suggested that
* Edson C. Passamani
edson.caetano@ufes.br
1 Departamento de Física, CCE, Universidade Federal
doEspírito Santo, Vitória, ES29075-910, Brazil
/ Published online: 14 October 2021
Journal of Superconductivity and Novel Magnetism (2021) 34:3115–3124
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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