Magnetic-coupling-dependent spin-triplet supercurrents in helimagnet/ferromagnet Josephson junctions

The experimental achievements during the past year in demonstrating the existence of long-ranged spin-triplet supercurrents in ferromagnets proximity coupled to singlet superconductors open up the possibility for new interesting physics and applications [for a review, see M. Eschrig, Phys. Today 64(1), 43 (2011]. Our group reported the injection of triplet supercurrents into a magnetically uniform ferromagnet (Co) by sandwiching it between two helimagnet/superconductor (Ho/Nb) bilayers to form a Nb/Ho/Co/Ho/Nb-type Josephson device. In the function of the Ho layer thicknesses, the supercurrent was found to modulate in a complex way that seemed to depend on the magnetic structure of Ho. To understand this unusual behavior, we have theoretically studied the properties of an ideal Josephson device with a helimagnet/ferrromagnet/helimagnet (HM/F/HM) barrier in the clean limit using the Eilenberger equation; we show, in particular, that the maximum triplet supercurrent that can pass across the barrier will depend nonmonotonically on the thicknesses of the HM layers if the HM and F layers are magnetically exchange coupled at their interface.

Figure 1

(a) A superconducting Josephson device with a helimagnet/ferromagnet/helimagnet barrier (S/HM/F/HM/S). The HM layers control the conversion between singlet and triplet Cooper pairing, while the F layer behaves like a spin filter, only allowing triplet Cooper pairs to pass across it. The F and HM layers are magnetically exchange coupled at the F/HM interfaces (b) with an angle of $-\pi ⩽\alpha ⩽\pi$ radians between the F and HM layer moments ($\alpha <0$ in the figure).

Figure 2

The efficiency parameter $B^2$ peaks at particular HM layer thicknesses (a) and the positions and magnitudes of these peaks depend on the magnetic anisotropy angle $\alpha$ between neighboring HM and F layer moments (a,b). In (a) and (b), $q=1$. For optimum HM layer thicknesses, the maximum efficiency parameter $B_{\mathit{max}}^2$ depends sensitively on $q$ and $\alpha$ (c).

Figure 3

Experimental data (bars, adapted from Ref. 19) and calculated and calculated (curves) $I_C{R}_N$ values of a Nb/Ho/Co/Ho/Nb device against the symmetrical thickness of Ho at $4.2$ K. Calculated curves are plotted for $\lambda =3.4$ nm (blue) and $\lambda =6.8$ nm (red), and for a Co thickness of $3.4$ nm (N.B.: the local magnitude of $I_C{R}_N$ only weakly depends on the Co thickness.) For the experimental $I_C{R}_N$ values, the magnetically dead layers present at each Ho surface ($\approx$$1.2$ nm) have been subtracted from the total Ho thickness. Calculated curves are plotted with the following realistic parameter values: $T_C=9.1$ K, $v_s=0.4\times {10}^6$ ms${}^{-1}$, $v_h=v_f^{+}=1.0\times {10}^6$ ms${}^{-1}$, $v_f^{-}=0.75\times {10}^6$ ms${}^{-1}$, ${\ell }_h=4$ nm, ${\ell }_f^{+}=12$ nm, ${\ell }_f^{-}=9$ nm, $I_h=0.25$ eV, and $\alpha =0$.