Controlling the electromagnetic proximity effect by tuning the mixing between superconducting and ferromagnetic order

We present low-energy muon-spin rotation measurements on $\mathrm{Cu}/\mathrm{Nb}/{\mathrm{AlO}}_x/\mathrm{Co}$ thin films that probe the newly described electromagnetic (EM) proximity effect. By varying the thickness of the insulating ${\mathrm{AlO}}_x$ layer we control the degree of coupling between the superconductor and ferromagnet and thus the EM proximity effect. For barrier thicknesses up to 4 nm we find both a small contact-dependent reduction in the standard Meissner effect and a larger diamagnetic contribution originating at the $\mathrm{Nb}/{\mathrm{AlO}}_x/\mathrm{Co}$ interface which decays away over a lengthscale far exceeding the superconducting coherence length. This second component we attribute to the EM proximity effect. Our analysis provides compelling experimental evidence for previously neglected electromagnetic effects within proximity coupled systems.

Figure 1

Sample transmission electron microscopy image showing the $\mathrm{Cu}/\mathrm{Nb}/{\mathrm{AlO}}_x\left(2\mathrm{nm}\right)/\mathrm{Co}$ sample. The insulating layers are shown in black and the conducting layers are bright.

Figure 2

A schematic of the different field profiles. $B_{\text{0}}$ is the constant normal state flux density and $B_{\text{NSIF}}$ the superconducting state profile given by Eq. (2). $B_{\text{NSIF}}$ can be decomposed into an EM contribution (shaded region) and a standard Meissner contribution ($B_{\text{NS}}^{*}$) determined from the bilayer response ($B_{\text{NS}}$) by including pair breaking. $A_{\text{EM}}$ and $A_{\text{SF}}$ are the EM and pair-breaking amplitudes, respectively.

Figure 3

Top panel: Muon stopping profiles for several selected implantation energies. The profiles for $E\ge 20$ keV extend into the $Y$ layers. A schematic of the sample structure is shown for reference. Bottom panel: Example results of the LE-$\mu \mathrm{SR}$ measurements for an applied field of around 300 G. The average field values as a function of average depth are plotted as points, above and below $T_{\text{c}}$, for a range of samples of the form $\mathrm{Cu}\left(40\right)/\mathrm{Nb}\left(50\right)/Y$ where $Y=\mathrm{Si}$, Co/Si, ${\mathrm{AlO}}_x\left(2\mathrm{nm}\right)/\mathrm{Co}/\mathrm{Si}$ for the N/S, N/S/F, and N/S/I/F samples, respectively. All normal (superconducting) state data were measured at 10 K (2.5 K) and are plotted in open (closed) symbols. The error bars are 0.1–0.3 G and are thus smaller than the symbol size. The solid lines represent the best-fit imposed field profiles which determine the full spatial dependence.

Figure 4

The extracted proximity amplitudes as a function of $d_{\text{I}}$. The open and closed data points represent the extracted $A_{\text{SF}}$ and $A_{\text{EM}}$ amplitudes, respectively. The horizontal dotted line represents the NS bilayer for which both amplitude contributions are zero. The light shaded region indicates a relatively constant “band” of $A_{\text{EM}}$ amplitudes for $d_{\text{I}}\le 4\mathrm{nm}$.