THE DENSITY OF STATES IN A SUPERCONDUCTING SPIN VALVE WITH FERROMAGNETIC INSULATORS

In the present manuscript we consider a spin valve consisting of one superconducting layer and two ferro magnetic insulators at the edges of the superconductor. The contact is considered in the dirty limit, in which the Greens function of the superconductor obeys the Usadel equation. The Usadel equations are supplemented by ap propriate boundary conditions simulating the effect of proximity of a superconductor with a ferromagnetic insula tor. The system was studied numerically by solving the Usadel equations, coupled with the self-consistency equa tion for the superconducting order parameter. The numerical method is a standard iterative procedure for solving an integro-differential equation. Based on the numerical solution of the Usadel equations, the dependences of the density of electronic states on energy at different angles of disorientation of the magnetization vectors of ferro magnetic insulators and superconductor thicknesses were calculated. Due to the interaction with a ferromagnet, singlet spin correlations are converted into triplet correlations at the boundaries of the superconductor. Their char acteristic feature is the occurrence of a zero bias peak in the density of electronic states on the energy of quasiparticles. As a result of the work, it is shown that this peak actually occurs and its properties are studied in detail. In particular, the change in the position and height of the peak is studied when the angle of disorientation of the magnetization vectors of ferromagnetic layers varies and when the thickness of the superconducting layer changes. The zero bias peak has an effect on the critical temperature of the superconducting junction, suppressing the superconducting gap and, accordingly, increasing the critical temperature. Since its height depends on the mu tual orientation of the magnetization vectors of the ferromagnetic layers, it is shown that by controlling their ori entation it is possible to open and close the passage of a superconducting current through the heterostructure. That is, the spin valve effect has been demonstrated. The results of the numerical calculation are visualized by plotting a three-dimensional graph of the dependence of the density of states on the energy of quasiparticles and the angle of disorientation of the magnetization vectors of ferromagnetic layers. Graphs of the dependence of the density of states at the energy of quasi-particles equal to the Fermi energy on the angle of disorientation of ferromagnetic layers for different thicknesses of the superconducting layer in the heterostructure are also constructed.