Superconducting Spin Valves Based on a Single Spiral Magnetic Layer

Abstract

A detailed investigation of a superconducting spin-triplet valve is presented. This spin valve consists of a superconducting film covering a metal with an intrinsic spiral magnetic order, which could result from competing isotropic exchanges or, if the crystal lattice breaks central symmetry, from asymmetric Dzyaloshinskii-Moriya exchange. Depending on the anisotropy, such a metal may change its magnetization either from a spiral to uniform order, as seen in $\mathrm{Ho}$ and $\mathrm{Er}$, or in the direction of the spiral itself, as in crystals of the B20-type structure [such as $\mathrm{Mn}\mathrm{Si}$, ($\mathrm{Fe}$,$\mathrm{Co}$)$\mathrm{Si}$, $\mathrm{Fe}\mathrm{Ge}$, etc.]. The nonuniform magnetic order controls the appearance of long-range triplet superconducting correlations at strong exchange fields, affecting the detailed character of the proximity effect. We show that the magnetic control of the spin-valve behavior can also be obtained from moderately low exchange fields (typically associated to negligible long-range triplet correlations), thanks to an orientation-dependent averaging mechanism of the magnetic inhomogeneity on the scale of the Cooper pairs. Our numerical calculations reveal that the spin-valve effect is in fact magnified at moderately low exchange fields, when the exchange splitting in the spiral magnet is comparable to the superconducting gap, and the spiral period is less than or equal to the superconducting coherence length in the magnet multiplied by $2\ensuremath{\pi}$.