Study of π phase for superconducting superlattices with ferromatnetic layers

一些实验观察表明，对于一定厚度的超导层，转变温度T_c(D_F)随铁磁层厚度d_f有一个极小值。这是由于π相的存在，即两个铁磁层之间的对函数的相位差随π的变化而变化。我们指出交换作用的强度是重要的，并计算了临界温度T_c和上临界场H_&lt；c_2&gt；，T_c和H_&lt；c_2&gt；是由序参数的线性顺序决定的。在远离相变温度和上临界场的情况下，序参数的非线性项起着重要作用。我们推导出了超导超晶格的解析表达式。利用得到的项，数值计算了表示磁化强度与温度关系的κ_2参数，并进一步推导出了扩散常数D(Z)随空间变化的超导超晶格的上临界场H&lt；c2&gt；，其中磁场几乎沿层的法线方向施加。将这些结果应用于最近对Nb/NbZr超晶格的观察，指出Nb/NbZr超晶格的本征性质是重要的。

Some experimental observations show that the transition temperature T_c(d_f) has a minimum as a function of the thickness d_f of the ferromagnetic layer for the fixed thickness of the superconducting layer. This is due to the occurence of the π phase, that is, the phase difference of the pair function between the two ferromagnetic layers changes by π. We pointed out that the strength of the exchange interaction is important and calculated the critical temperature T_c and the upper critical field H_<c2>.The above quantities such as T_c and H_<c2> are determined by the linear order of the order parameter. Far from the transition temperature and the upper critical field, the nonlinear term of the order parameter are important. We have derived its analytical expression for the superconducting superlattices. Using the obtained term, we numerically calculated the κ_2 parameter, which expresses the temperature dependence of the magnetization.Further angular dependence of the upper critical field H_<c2> was derived for the superconducting superlattice with spatial variation of the diffucion constant D(z), where the magnetic field is applied nearly along the normal direction of layers. The results are applied to the recent observations for Nb/NbZr superlattice and we point out that the intrinsic properites of Nb/NbZr superlattice are important.