论文标题
通过铁磁双层的约瑟夫森连接处的界面磁化，异常的超电流调节
Anomalous supercurrent modulated by interfacial magnetizations in Josephson junctions with ferromagnetic bilayers
论文作者
论文摘要
根据Bogoliubov-De Gennes方程，我们研究了Josephson电流以S/$ f_l $ -f $ -f $ _1 $ - $ f_c $ -f_c $ -f $ -f $ _2 $ - $ f_r $/s交界旋转活性界面。这些接口具有非共线性磁化，并且在$ f_ {l，c，r} $接口处的磁化方位角为$χ_{l，c，r} $。我们证明，如果两个铁磁体都有反平行磁化，那么临界电流会振荡为交换场的函数，而特定$χ_l$或$χ_r$的Ferromagnets的厚度。相比之下，当$ f_c $接口处的磁化范围垂直于$ f_l $和$ f_r $接口时，临界电流就会达到更大的值，并且几乎不受交换场和厚度的影响。有趣的是，如果两个铁磁体都转换为反平行半米，则临界电流将保持恒定值，并且很少随铁磁厚度和方位角角度变化。目前，系统中可能会出现异常的超电流，在这种情况下，即使超导相位差$ ϕ $为零，约瑟夫森电流仍然存在。此超电流满足当前相关关系$ i = i_c \ sin（ϕ+ϕ_0）$，$ i_c $是关键电流，$ ϕ_0 =2χ_c_c-χ_l-χ_r$。我们推断出附加的相位$ ϕ_0 $是从相位叠加产生的，当它们通过每个旋转活性界面时，相位叠加。另外，当两个铁磁体都转化为平行的半米时，$ f_c $接口永远不会为超电流贡献任何阶段，$ ϕ_0 =χ_r-χ_l+π$。在这种情况下，电流关系与S/$ f_l $ -f- $ f_r $/s交界处的关系相似。
Based on the Bogoliubov-de Gennes equations, we investigate the transport of the Josephson current in a S/$f_L$-F$_1$-$f_C$-F$_2$-$f_R$/S junction, where S and F$_{1,2}$ are superconductors and ferromagnets, and $f_{L, C, R}$ are the left, central, and right spin-active interfaces. These interfaces have noncollinear magnetizations, and the azimuthal angles of the magnetizations at the $f_{L, C, R}$ interfaces are $χ_{L, C, R}$. We demonstrate that, if both the ferromagnets have antiparallel magnetizations, the critical current oscillates as a function of the exchange field and the thickness of the ferromagnets for particular $χ_L$ or $χ_R$. By contrast, when the magnetization at the $f_C$ interface is perpendicular to that at the $f_L$ and $f_R$ interfaces, the critical current reaches a larger value and is hardly affected by the exchange field and the thickness. Interestingly, if both the ferromagnets are converted to antiparallel half-metals, the critical current maintains a constant value and rarely changes with the ferromagnetic thicknesses and the azimuthal angles. At this time, an anomalous supercurrent can appear in the system, in which case the Josephson current still exists even if the superconducting phase difference $ϕ$ is zero. This supercurrent satisfies the current-phase relation $I=I_c\sin(ϕ+ϕ_0)$ with $I_c$ being the critical current and $ϕ_0=2χ_C-χ_L-χ_R$. We deduce that the additional phase $ϕ_0$ arises from phase superposition, where the phase is captured by the spin-triplet pairs when they pass through each spin-active interface. In addition, when both the ferromagnets are transformed into parallel half-metals, the $f_C$ interface never contributes any phase to the supercurrent and $ϕ_0=χ_R-χ_L+π$. In such a case, the current-phase relation is similar to that in a S/$f_L$-F-$f_R$/S junction.
