Extended Data Fig. 1: Long-range supercurrents and spin-valve effect in chiral antiferromagnetic JJs.

a, Normal-state zero-bias resistance R_n (top) and Josephson critical current I_c (bottom) of the Nb/Mn₃Ge/Nb JJs versus the barrier spacing d_s. From R_n(d_s) in a, we extract the resistance-area product r_i of Nb/Mn₃Ge interfaces to be 1.0–1.2 mΩ µm² and the effective resistivity ρ_ch for the Mn₃Ge(40 nm)/Ru(5 nm) track to be 25–27 µΩ cm, employing a standard transmission line (TL) theory³⁴, \(R_n = 2R_i + R_{ch} = \frac{{\rho _{ch}}}{{tw}}\left( {2l_t + d_s} \right)\). Here \(R_i = \frac{{r_i}}{{wl_t}}\) and \(l_t = \sqrt {\frac{{r_i}}{{\frac{{\rho _{ch}}}{t}}}}\) is the charge transfer length (13 nm). t and w is the thickness and width of the Mn₃Ge/Ru track. b, Characteristic voltage V_c = I_cR_n as a function of d_s, from which we determine the decay length \(\xi _{triplet}^{Mn_3Ge}\) of the Josephson supercurrents in the Mn₃Ge barrier to be 157–178 nm using an exponential decay function²⁰, \(exp\left( { - \frac{{\xi _{triplet}^{Mn_3Ge}}}{{d_s}}} \right)\) (black curves). Note that for d_s ≥ \(\xi _{triplet}^{Mn_3Ge}\), the complete supercurrent spin-valve effect appears (see Fig. 2d). All I_c values in a,b are obtained at a fixed temperature T = 2 K. Note that data with circle symbols in a,b are taken from Ref. ²⁰. The error bars in a and b represent the standard deviation.