Thickness dependence of the triplet spin-valve effect in superconductor–ferromagnet–ferromagnet heterostructures

Background: In nanoscale layered S/F₁/N/F₂/AF heterostructures, the generation of a long-range, odd-in-frequency spin-projection one triplet component of superconductivity, arising at non-collinear alignment of the magnetizations of F₁ and F₂, exhausts the singlet state. This yields the possibility of a global minimum of the superconducting transition temperature T_c, i.e., a superconducting triplet spin-valve effect, around mutually perpendicular alignment.

Results: The superconducting triplet spin valve is realized with S = Nb a singlet superconductor, F₁ = Cu₄₁Ni₅₉ and F₂ = Co ferromagnetic metals, AF = CoO_x an antiferromagnetic oxide, and N = nc-Nb a normal conducting (nc) non-magnetic metal, which serves to decouple F₁ and F₂. The non-collinear alignment of the magnetizations is obtained by applying an external magnetic field parallel to the layers of the heterostructure and exploiting the intrinsic perpendicular easy-axis of the magnetization of the Cu₄₁Ni₅₉ thin film in conjunction with the exchange bias between CoO_x and Co. The magnetic configurations are confirmed by superconducting quantum interference device (SQUID) magnetic moment measurements. The triplet spin-valve effect has been investigated for different layer thicknesses, d_F1, of F₁ and was found to decay with increasing d_F1. The data is described by an empirical model and, moreover, by calculations using the microscopic theory.

Conclusion: The long-range triplet component of superconducting pairing is generated from the singlet component mainly at the N/F₂ interface, where the amplitude of the singlet component is suppressed exponentially with increasing distance d_F1. The decay length of the empirical model is found to be comparable to twice the electron mean free path of F₁ and, thus, to the decay length of the singlet component in F₁. Moreover, the obtained data is in qualitative agreement with the microscopic theory, which, however, predicts a (not investigated) breakdown of the triplet spin-valve effect for d_F1 smaller than 0.3 to 0.4 times the magnetic coherence length, ξ_F1.