Spin-valve effect in S/F/F and F/S/F structures of atomic thickness

We show that the peculiarities of the electron band structure strongly affect the spin-valve effect in heterostructures consisting of a superconductor (S) and two ferromagnetic layers F1 and F2. For the S/F1/F2 systems the energy shift between the electron bands in the S and F2 layers determines wether the critical temperature $T_c$ of the superconductor increases or decreases as a function of the angle $\theta$ between the magnetic moments in the ferromagnets. In the case of half-metallic F2 layer the type of the spin-valve effect becomes dependent on the position of the only occupied spin-band and the minimum of $T_c$ may correspond to the anti-parallel, parallel or non-collinear orientations of magnetic moments. Also, for the first time, we analytically demonstrate the possibility of the triplet spin-valve effect in the F/S/half-metal structures.