Magnetic impurities in a superconductor: Effect of domain walls and interference

Abstract

We consider the effect of magnetic impurities, modeled by classical spins, in a conventional superconductor. We study their effect on the quasiparticles, specifically on the spin density and local density of states (LDOS). As previously emphasized, the impurities induce multiple scatterings of the quasiparticle wave functions leading to complex interference phenomena. Also, the impurities induce quantum phase transitions in the many-body system. Previous authors studied the effect of either a small number of impurities (from one to three) or a finite concentration of impurities, typically in a disordered distribution. In this work we assume a regular set of spins distributed inside the superconductor in such a way that the spins are oriented, forming different types of domain walls, assumed stable. This situation may be particularly interesting in the context of spin transfer due to polarized currents traversing the material.

Supercurrent-induced domain wall motion

“…Magnetism and superconductivity typically compete and, therefore, most heterostructures considered tend to separate the ferromagnetic and superconducting regions (often separated by an insulator to prevent proximity effects). The presence of randomly located magnetic impurities in a conventional superconductor destroys the superconducting order for small impurity concentrations 18 but we have shown 19,20 that, if the magnetic moments are correlated, superconductivity is much more robust and prevails for much higher concentrations. Therefore, if the magnetic moments are somewhat diluted we expect that superconducting order should remain.…”

“…We see in the superconducting case that, as J increases, the magnetization increases, but at some points it changes discontinuously between various plateaus. These discontinuities are due to quantum phase transitions in the system 16,17 . In the case of one impurity and for small J the average magnetization vanishes.…”

“…Their solution provide the wave functions in the usual way (see for instance 17 ). The BdG equations are solved self-consistently to find the profile of the gap function inside the superconductor, ∆ n .…”

“…The BdG equations are solved self-consistently to find the profile of the gap function inside the superconductor, ∆ n . The domain wall shape is calculated self-consistently in mean-field 17 ensuring that the energy is minimized and a vanishingly small equilibrium torque. The procedure leads to a domain wall where the magnetization direction interpolates between the z-direction on the left hand side and the −z direction in the right hand side, according to the orientations of the exchange fields in the two ferromagnets.…”

“…We have been interested in the possible interplay between magnetic moments and superconductors 15,16 , specifically the possibility of ordered magnetic moments in the superconductor or in its vicinity 17 . Magnetism and superconductivity typically compete and, therefore, most heterostructures considered tend to separate the ferromagnetic and superconducting regions (often separated by an insulator to prevent proximity effects).…”