For explaining about the quantized Barkhausen jump that is observed in iron nanowires system, we introduced the two type spin Josephson junction models. One type of these system are composed of the sandwich structure by FM (ferromagnet)/AM (anti ferromagnet)/FM junction, and its dual junction is consists of the sandwich structure by AF/FM/AF junction. In order to apply to spintronics technology these spin junction models, we constructed a dual control theory by pseudo-spin quantum Hall effect. 3) in the sandwich structure of the FM (ferromagnet)/ AM (antiferromagnet)/FM junction that operates using single domain wall tunneling. As another type of these models which is a dual models of FM/AF/FM junction, we have devised model of antiferromagnetic spin Josephson junction device in the sandwich structure of the AM/FM/AM junction that operates using single magnetic moment tunneling. Figure 1(a) shows the schematic of FM/AF/FM junction.In the FM/AF/FM junction of Fig. 1(a), Antiferromagnetic material (spin-dielectric material) barrier that sandwiched between the ferromagnetic material is functions as a spin capacitor. In Fig. 1(b), shows the conceptual diagram of a spin capacitor. 4,5) In Fig. 1(b), up spin state "¼" can be considered as negative spin charge "ÀQ 0 s " in Fig. 1(c). Similarly, in Fig. 1(b) down spin state "←" can be considered as positive spin charge "þQ 0 s " in Fig. 1(c). Here +S, ¹S are total amount of positive and negative spin-charge (spin magnetic moment) in the spin electrode respectively. In Figs. 2(a)2(d) below shows stepwise tunneling process of single domain wall. In Fig. 2(a), the single domain wall not occur in the electrode. In the negative spin electrode of Fig. 2(b), if the single domain wall is generate by quantum fluctuations, case of the antiferromagnetic layer which is close to this, magnetic reversal occurs, single ferromagnetic magnetic moment are occurs. In Fig. 2(c), the single ferromagnetic magnetic moment transitions to one unit to the positive electrode side. In Fig. 2(c), the single domain wall reaches the positive electrode side, tunneling is completed.As a model for such ferromagnetic spin Josephson systems, first, we consider Hamiltonian of the Heisenberg XXZ spin models 4) as follows:The first term is the Zeeman energy due to the z-component of external magnetic field H z ðjÞ, where ® 0 B is Bohr magneton in E-H corresponding, the second first term describe the Ising spin energy, and the third term describe the XY spin energy. We can rewrite the Hamiltonian from an analogy of Josephson junctions 4,5) as follows: