Crossover Induced by Spin-Density-Wave Interference in the Coherence of Singlet Electron Pairs in Cr

To study the interaction of $s$-wave superconductivity with spin-density waves (SDWs), we have measured a series of $\mathrm{Nb}/\mathrm{Cr}/\mathrm{Nb}$ Josephson junctions and determined the coherence length $\xi$ describing the decay of the critical current with Cr thickness, $L$. We observe a crossover in $\xi$ from approximately 14 nm to 4 nm as $L$ increases to 10 nm, which is consistent with a transition from commensurate to incommensurate SDWs expected for this thickness range.

Figure 1

(a) The differential resistance of two different junctions versus bias current at 4.2 K with their corresponding $I\mathrm{\text{−}}V$ curves (inset) superimposed with RSJ fits (●). The $L=19.7\mathrm{nm}$ data are offset from 0 voltage for clarity. (b) Effect of microwaves on the differential resistance of the same junctions in (a) plotted against $V/{\phi }_{0}f$. Inset: asymmetric amplitude in the differential resistance of a junction versus bias current with microwaves applied. (c)–(f) Effect of external magnetic flux on the critical current. Standard Fraunhofer-like functions are superimposed. (g) The average specific resistance of many junctions at 4.2 K versus Cr barrier thickness with a linear least-squares fit.

Figure 2

The decay in the average characteristic voltage of many devices as a function of Cr barrier thickness ($L$) at 4.2 K ($L>8.0\mathrm{nm}$) and extrapolated from higher temperature data ($L<8.0\mathrm{nm}$) as explained in the main text. All $I_c{R}_N$ values fall below the Thouless energy $E_{\mathrm{Th}}$. Curves labeled $a$ and $b$ are described within the main text. Inset: the typical thermal dependence of a junction’s critical current ($I_c$) with a phenomenological fit superimposed, as described in the main text.