近年来，科学家在铁磁约瑟夫森结中观察到了随着铁磁层厚度的改变，约瑟夫森结从0型到π型的转变(电流(I)相位（\phi）关系转变的现象，在超导电子学中有重要的应用价值，因此，铁磁约瑟夫森结中的电流相位关系受到了广泛关注。先前的研究主要集中在铁磁层厚度对电流相位关系的影响，针对铁磁体的磁矩对电流或相位关系的研究相对较少。铁磁层的磁矩指向可能对非磁/铁磁/非磁(NFN)的输运性质造成影响，进而影响到约瑟夫森结的电流相位关系。为了理清其中的缘由，本文将研究不同磁矩指向下的超导/铁磁/超导(SFS)约瑟夫森结的电流相位关系。目前，第一性原理在处理强关联体系，特别是超导体系时，存在明显缺陷。为了研究磁结构对电流相位关系可能造成的影响，我们结合第一性原理和Blonder Tinkham Klapwijk(BTK)方法，提出了研究超导/非磁/非共线铁磁/非磁/超导(SNFNS)约瑟夫森结电流相位关系的方法，并研究了Nb/Ni/Nb约瑟夫森结的电流相位关系。

第一章主要讨论了研究背景，主要从超导与Andreev反射出发，介绍了约瑟夫森效应，以及各种约瑟夫森结的基本性质。最后介绍了铁磁约瑟夫森结的特性，并对本文主要关注的体系以及电流相位关系做出了介绍。

第二章主要介绍了组内发展的铁磁约瑟夫森超流的计算方法。其中的主要思想是：将超导/铁磁/超导(SFS)约瑟夫森结近似拓展成超导/非磁/铁磁/非磁/超导(SNFNS)结。其中超导/非磁(SN)界面的散射矩阵可以利用BTK理论得到，非磁/铁磁/非磁(NFN)结的散射矩阵可以利用第一性原理软件进行研究，两者结合即可以研究整个体系的输运特性。接下来详细介绍了超导/非磁(SN)界面的散射矩阵，以及第一性原理研究NFN结散射矩阵的计算方法。最后详细介绍了SNFNS约瑟夫森结超流相位关系的计算方法。

第三章主要研究了Nb(超导)/Nb(非磁)/Ni(铁磁)/Nb(非磁)/Nb(超导)约瑟夫森结的电流相位关系。从第一性原理出发，利用第二章的研究方法计算了Ni的铁磁层在4-8层厚度的电流相位关系以及4层情况下的不同磁矩方向电流相位关系。研究发现满足短结近似时，铁磁层的磁矩和厚度对电流相位关系的振幅和峰值相位都有影响。这为通过磁场调控磁结构进而调控约瑟夫森结性质提供了可能。

第四章主要阐述了自旋阀型铁磁约瑟夫森结的电流相位关系。这一章主要研究了Nb(超导)/Nb(非磁)/Ni(铁磁层1)/Nb(非磁)/Ni(铁磁层2)/Nb(非磁)/Nb(超导)约瑟夫森结的电流相位关系。中间的Ni(铁磁层1)/Nb(非磁)/Ni(铁磁层2)构成了自旋阀，该自旋阀可以通过调节铁磁层1和铁磁层2的自旋指向进而改变透射率以及其他输运性质。我们从第一性原理出发，计算了不同厚度或磁矩方向不同自旋阀对电流相位关系的影响。发现满足短结近似的非共线体系下，自旋指向的不同以及铁磁层的厚度的改变都会对超流相位关系产生影响。在2层，3层Ni的自旋阀结构下，磁结构的改变对电流的振幅和相位都有明显影响。在4层自旋阀结构下，磁结构的改变对电流的振幅有影响。这也为通过磁矩来调节约瑟夫森结的电流相位关系提供了可能。

最后，在第五章对本文做了总结和展望。

In recent years, scientists have studied the relationship between current (I) and phase(\phi)when going with the change of the thickness of ferromagnetic layer. This transition has important applications in the area of superconducting electronics. For instance the current-phase relationship in the ferromagnetic Josephson junction has received increasing attention. Previous studies have mainly focused on the influence of ferromagnetic layer thickness on the current-phase relationship. On the contrary, just a few studies have focused on the corresponding influence of the magnetic moment. The orientation of the magnetic moment of the ferromagnetic layer may affect the transport properties of the superconducting/normal metal/superconducting (SNS) junction and affect the current-phase relationship of the Josephson junction. To clarify why the orientation of the magnetic moment affects the current-phase relationship, the current phase relationship of the superconducting /ferromagnetic/superconducting (SFS) Josephson junction has been studied in the present paper. At present, the First principle theory has obvious weaknesses when dealing with strongly correlated systems, especially superconductors. For studying the effect of a magnetic structure on the current-phase relationship, an innovative method has here been proposed for the current-phase relationship of a superconducting /non-magnetic /non-collinear ferromagnetic/ non-magnetic/ superconducting (SNFNS) Josephson junction. It combines the First principle theory with the Blonder Tinkham Klapwijk (BTK) method, and will here be used for the study of the current-phase relationship of the Nb/Ni/Nb Josephson junction.

In the first chapter, the background of the study has been presented and discussed. It has mainly introduced the concept of superconductivity, Andreev reflection, Josephson effect, and the basic properties of various Josephson junctions. The properties of the ferromagnetic Josephson junction have also been introduced. In fact, the system and current-phase relationship have been the main concerns in the present paper.

In the second chapter, the calculation method of the ferromagnetic Josephson supercurrent has been introduced, which was developed by our research group. The main idea was to extend the superconducting /ferromagnetic /superconducting (SFS) Josephson junction into a superconducting /non-magnetic /ferromagnetic /non-magnetic /superconducting (SNFNS) junction. The scattering matrix of the superconducting/non-magnetic (SN) interface could be obtained by using the BTK theory. The scattering matrix of the non-magnetic/ ferromagnetic/ non-magnetic (NFN) junction could be calculated by using the First-principle software, and the transport characteristics of the system could be studied by combining the two theoretical methods. Thereafter, the scattering matrix of the superconducting/non-magnetic (SN) interface and the calculation method of the NFN junction scattering matrix were introduced. The calculation method of the supercurrent phase relationship of the SNFNS Josephson junction where finally introduced in detail.

In Chapter 3, the current-phase relationship of the Nb(superconducting) /Nb(non-magnetic) /Ni(ferromagnetic)/Nb(non-magnetic)/ Nb(superconducting) Josephson junction was predominantly studied. By using the First-principle theory, the current-phase relationship between the ferromagnetic layers of Ni, with a thickness of 4-8 layers, has been calculated using the research method introduced in Chapter 2. This was also the situation with the current-phase relationship in different magnetic moment directions of the four layers. It was found that the magnetic moment and thickness of the ferromagnetic layer affected both the amplitude and peak phase of the current-phase relationship when the short junction approximation was satisfied. It was possible to regulate the properties of the Josephson junction by changing the magnetic field of the magnetic structure.

In Chapter 4, the current-phase relationship of the ferromagnetic Josephson junction, with spin valves, was discussed. The current-phase relationship of the Nb(superconducting)/Nb(non-magnetic)/Ni(ferromagnetic1)/Nb(non-magnetic)/Ni (ferromagnetic2)/ Nb(non-magnetic) /Nb(superconducting) Josephson junction was in focus in this chapter. The Ni (ferromagnetic layer 1)/Nb(non-magnetic) /Ni(ferromagnetic layer 2) constituted a spin valve. By adjusting the spin direction of the ferromagnetic layer 1 and ferromagnetic layer 2, the transmission and transport properties could be changed. By using the First principle theory, how the different thicknesses, or magnetic moment directions, affect the phase relation has been calculated. If the non-collinear system satisfied the short junction approximation, different spin directions, or thicknesses, of the ferromagnetic layer affected the current-phase relationship. For the spin-valve structure of a 2-layer and 3-layer Ni, the change in magnetic structure had an obvious influence on the amplitude and phase of the current. For the 4-layer spin valve structure, the change in magnetic structure had an effect on the current amplitude. In the case of a 3-layer Ni, the change in magnetic structure had an obvious influence on the amplitude of the current-phase relationship. It was also possible to adjust the current-phase relationship of the Josephson junction by the magnetic moment.

In Chapter 5, the results from the study have been summarized and prospected.