For the ferromagnetic metal/superconductor (FM/S) superlattices, 0 and states with antiferromagnetic ordering of the FM layers magnetizations are predicted. If the S layer thickness d s is less than the threshold value d s , these states have a higher critical temperature T c than the earlier known ferromagnetic states 00 and 0. Therefore, the T c oscillation origin at d s Ͻd s is due to the 0--0 phase transition cascade, whereas at d s Ͼd s it is related to the sequence of transitions 00-0-00. A type of logical device combining the advantages of the superconducting and magnetic recording channels in one sample is offered on the FM/S superlattice base.The competition between superconductivity and ferromagnetism in the ferromagnetic metal/superconductor (FM/S) superlattices leads to the pronounced nonmonotone dependence of the critical temperature T c on the FM layer thickness d f . 1,2 The existing theories of proximity effect for the FM/S superlattices 3-8 relate the T c (d f ) oscillations to the competition between the 0-phase type and the -phase type of superconductivity in the neighboring S layers. But these theories do not take into account the inverse influence of superconductivity on the magnetism of the FM layers and on the mutual orientation of their magnetizations. For similar FI/S structures, where FI stands for a ferromagnetic insulator, one of the authors has shown that a long-range Ruderman-Kittel-Kasuya-Yosida ͑RKKY͒ exchange through the S layers leads to the layered antiferromagnetic superconducting ͑AFS͒ state. 9 In the AFS state the phases of the magnetic order parameter ͑MOP͒ in the neighboring ferromagnetic layers are shifted on . This essentially attenuates the pair-breaking effect of the exchange field I for the S layers and raises T c of the layered system. This mutual accommodation between the superconducting order parameter ͑SOP͒ and the MOP, which reflects the quantum connection between the boundaries and leads to realization of the phase magnetism, should take place in the FM/S superlattices just as it does in the FI/S multilayers. The newest theoretical works investigate part of this problem only for the trilayer structures ͓FM/S/FM ͑Refs. 10 and 11͒ and FI/S/FI ͑Ref. 12͔͒, as well as the cryptoferromagnetic state possibility in the FM/S bilayer. 13 The main physical idea of the paper is as follows. In the AFS state, the pair-breaking effects, induced in the S interlayer by the antiparallel aligned exchange fields of the neighboring FM layers, compensate each other. On the contrary, in the ferromagnetic superconducting ͑FS͒ state with parallel alignment of the FM layer magnetizations, their spin polarizations in the S interlayer enhance each other and can destroy superconductivity. We expect that the FM/S superlattice with the thin S layers will have a higher T c in the AFS state than T c in the FS state. This will take place both in the 0 phase and in the phase superconductivities. The mag-netic coupling between the FM layers falls as the S layer thickness increases, and the mutual o...
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