Meissner effect probing of odd-frequency triplet pairing in superconducting spin valves

Superconducting correlations which are long ranged in magnetic systems have attracted much attention due to their spin-polarization properties and potential use in spintronic devices. Whereas experiments have demonstrated the slow decay of such correlations, it has proven more difficult to obtain a smoking gun signature of their odd-frequency character which is responsible, e.g., for their gapless behavior. Here we demonstrate that the magnetic susceptibility response of a normal metal in contact with a superconducting spin valve provides precisely this signature, namely, in the form of an anomalous positive Meissner effect, which may be tuned back to a conventional negative Meissner response simply by altering the magnetization configuration of the spin valve.

Figure 1

Schematic of the proposed metallic $S/F_1/F_2/N$ junction. The $x$ axis is perpendicular to the interfaces separating the different layers. Two ferromagnetic layers ($F_1$, $F_2$) with thicknesses $d_{F1}$ and $d_{F2}$ are sandwiched between a superconductor ($S$) and normal metal ($N$) with thickness $d_N$. The exchange field in the ferromagnetic layers, ${\vec{h}}_1$ and ${\vec{h}}_2$, may be misaligned as shown in the figure. An external magnetic field ${\vec{H}}_a$ (not shown) is applied in the $z$ direction, resulting in a spatially dependent Meissner supercurrent $\vec{J}\left(x\right)$ flowing in the $y$ direction.

Figure 2

Meissner effect in $S/N$(left panel) and $S/F_1/F_2/N$(middle and right panels) structures as a function of temperature $T$ and magnetic misalignment angle $\theta$. In the $S/N$ structure the singlet superconducting correlations give rise to a conventional Meissner effect ($\chi <0$), while in the $S/F_1/F_2/N$ structure an anomalous Meissner effect ($\chi >0$) appears which may be controlled via the relative magnetization directions in the double $F$ layers.

Figure 3

Meissner effect ($\chi$) in $S/F_1/F_2/N$connections against the noncollinearity angle $\theta$ for various values of $F2$ layer thicknesses: $d_{F2}/{\xi }_S=0.85,1.05,1.35,1.55,1.75,1.95$. The thickness of $F1$ and normal metal layers are fixed at $d_{F1}=0.15{\xi }_S$ and $d_N=2.5{\xi }_S$, respectively. The anomalous Meissner effect ($\chi >0$) also depends on the magnetic layer thicknesses and is strongest where $d_{F2}\gg d_{F1}$, for instance.

Figure 4

Real and imaginary parts of the $y$ component of the decomposed spin Green's function $({\mathbb{T}}_y(\varepsilon ,x))$ versus magnetization misalignment angle $\theta$ at several locations inside the $N$ region of the $S/F_1/F_2/N$configuration considered here. Since energies close to the Fermi level comprise the main contribution to the proximity effect, we have set $\varepsilon$ = 0.1${\Delta }_0$ as a representative choice.