In magnetic trilayer systems, spin pumping is generally addressed as a reciprocal mechanism characterized by one unique spin mixing conductance common to both interfaces. However, this assumption is questionable in cases where different types of interfaces are present in the material. Here, we present a general theory for analyzing spin pumping in cases with more than one unique interface. The theory is applied to analyze layer-resolved ferromagnetic resonance experiments on the trilayer system Ni20Fe80/Ru/Fe49Co49V2 where the Ru spacer thickness is varied to tune the indirect exchange coupling. The results show that the spin pumping in trilayer systems with dissimilar magnetic layers is non-reciprocal, with a surprisingly large difference between spin-pumping induced damping of different interfaces. Our findings have importance on dynamics of spintronic devices based on magnetic multilayer materials.
Introduction:Spin transport in thin film heterostructures can generate a rich spectrum of physical effects and its use has great potential for realizing new spintronic functionality and low power operation [1,2]. Spin currents without an accompanying charge current can be generated from ferromagnets with a temperature gradient via the spin Seebeck effect [3] while the spin Hall effect introduces spin currents from Z 2 -topological quantum paramagnets into ferro-/ anti-ferromagnets [4,5]. Such techniques can be used to inject and transport spin currents [6-8], and even realize new phenomena such as formation of Bose-Einstein superfluids from injected spins [9]. Control of spin currents presents a channel to manipulate magnetic materials via spin transfer torque [10,11] without application of an external field.Spin pumping in layered magnetic materials presents an additional way to generate spin currents. Pure spin currents can be generated in metallic ferromagnetic (FM) / non-magnetic (NM) heterostructures via spin pumping [12] where spins excited into precession in a FM generate a spin current in the direction transverse to the static spin direction of the FM, and the spin currents propagate diffusively away from the FM / NM interface and into the NM layer. Propagation of spin currents in the NM can lead to non-local effects such as spin accumulation in the NM [13] and spin-to-charge current conversion via the inverse spin-Hall effect (ISHE) [14]. Another characteristic signature of spin pumping is the increased Gilbert-like damping in the FM layer [15], resulting from the additional loss of angular momentum in the precessing FM system from the spins pumped into the NM [16]. Spin pumping can also act as a non-local perturbation