The geometry of various few-layered systems. Bilayer F/S (a), two trilayers (b) and (c), tetralayer (d), and pentalayer (e) are shown. Vertical arrows show the directions (in-line) of the magnetizations that play the role of the magnetic order parameter. Here , and thicknesses of outer F layers and S layers are equal to and , where and are thicknesses of inner F and S layers, respectively.
The phase diagrams of the F/S nanostructures for the following values of parameters: , , , , and . In the figure is the reduced temperature, and is the reduced F layer thickness. The phase diagram of the F/S bilayer with one possible state (00) (a); the phase diagram of the F/S/F trilayer for the FM (00) and configurations (b); the phase diagram of the S/F/S trilayer with competition between 0 phase and phase of superconductivity (c); the phase diagram of the F/S superlattice where the thicknesses of all F layers equal , and the thicknesses of all S layers equal (d).
The phase diagrams of the tetralayer for the same set of parameters as in Fig. 2. The curves for the outer layer are denoted using letters with a prime. The letters without a prime indicate the curves for the inner S layer. All denotations of curves correspond to those introduced in Eqs. (20) and (21). In the panels (a) and (b) the arrows show the difference between the states which are discussed in the paper. The phase diagram for the FM configuration of the magnetizations of both F layers (a); the phase diagram for the AFM configuration (b); the combined phase diagram of the tetralayer (c); the generalized phase diagram of the tetralayer (d). Vertical arrows show the direction of the magnetization in the corresponding ferromagnetic layer. The letters S and N stand for the superconducting and normal states of the superconducting layers, respectively.
The phase diagrams of the pentalayer with the same parameters as in Figs. 2 and 3. All denotations of curves and states correspond to those introduced in the last part of Sec. II. The phase diagram for the FM configuration of the magnetizations of all F layers (a); the phase diagram for the AFM configuration (b); the phase diagram for the FMAFM configuration (c); the generalized phase diagram of the pentalayer (the designations follow those used in Fig. 3d) (d).
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