Study of upper critical field of superlattices cntaining ferromagnetic layrs

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There are experimental observations which show d_f dependence of the transition temperature T_c for the superconducting and ferromagnetic superlattices, where d_f is the thickness of the ferromagnetic layr. The transition temperature T_c, in general, decreases monotonically and saturetes with increasing d_f for the fixed superconducting layr. Using the microscopic theory developed by de Gennes and extended by Takahashi and Tachiki, we have made numerical calculations for T_c, which explain the experimental observations (Czech.J.Phys : 66 3219, (1997) ).The superconducting superlattices are usually characterized by the BCS interaction V,the density of states N,the diffusion constant D and the exchange potential I.In the real systems, the values of the Debye frequency omega_D are different from each metal. Up to now, there is no theoretical investigation of this effect. We have shown that the magnitude of the attractive interaction is given by the BCS interaction and its range by the Debye frequency (J.Phys.Soc.Jpn : 66 3219, (1997) ).From the fact that the difference of the Debye frequency gives the qualitatively similar effect on T_c and H_<c2> as that of the BCS coupling constant, we have investigated the upper critical field H_<c2> for the superconducting and ferromagnetic superlattices as the functions of N,D and I.For the large potential interaction I,the transition temperature T_c shows nonmonotonic behavior as a functon of d_f. We have shown that this peculiar behavior arises from the appearance of the pi phase of the pair function and calculated spatial variation of the pair function in order to interpret quantitatively the results (Phys.Rev B : (1998) in press).