Figure 10
Plots of [T c (0) − T c (π/2)]/T cs , where T c (α) is the critical temperature of an S/HM bilayer with an interfacial magnetic misalignment α, and T cs is the critical temperature of a bulk superconductor. Top left: We fixed the halfmetal length to 12 ξ S, and varied the superconductor length and spin-mixing conductance. Above the black region, i.e. for small superconductors or strong spin-mixing, we see both T c (π/2) and T c (0) go to zero. Below the black region, i.e. for large superconductors and weak spin-mixing, both T c (π/2) and T c (0) converge to the same finite value. The black curve delineates a critical region where T c (π/2) drops to zero while T c (0) remains finite, leading to a very large difference. Top right: We fixed the halfmetal length to 12 ξ S and the superconductor length to 1 ξ S, and highlight how T c (0) and T c (π/2) behave. This illustrates why the top-left curve looks like it does. Bottom left: We fixed the superconductor length to 1 ξ S, and varied the halfmetal length and spin-mixing conductance. We also checked lengths L H up to 12 ξ S and find that the halfmetal length is essentially irrelevant for L H > 2 ξ S. Bottom right: We fixed the superconductor length to 1 ξ S and halfmetal length to 12 ξ S, and varied the 2nd order conductance G χ and spin-mixing conductance G φ . We see that the 2nd order terms basically produce a quantitative shift of the transition region towards higher values of G φ , but does not appear to qualitatively change anything.
