Non-local Gilbert damping and its influence on magnetisation dynamics

Gilbert damping is a key parameter in spintronics, which describes the rate of energy dissipation from the spin system to, e.g., phonons. Here, is typically considered as a scalar parameter in e.g., FMR experiments. However, there is recent experimental evidence that damping ij is a non-local [1], which is also discussed by theory [2-4]. This has consequences to the equation of motion for magnets. In this talk, we give an overview on properties of ij and the impact of it on magnetic observables. 

We calculated non-local damping from a torque-torque correlation model and density functional theory. After, we post-processed the non-local damping within atomistic magnetisation dynamics [5]. 

In our study, we focus first on general characteristics of non-local damping in bcc Fe, fcc Co, fcc Ni. We find quantitative good agreement of the non-local damping between all density functional theory calculations involved as well as literature. 

Next, we focus on bcc Fe1-xCox showing a remarkable ultralow damping at 30% Co concentration, which we could qualitatively verify in our theory compared to experiment [6]. Analysing the non-local damping shows that the on-site damping is much smaller for this compared to other concentration. We perform further a materials mining study to predict even other materials with ultralow damping.

Last, we simulate spin-relaxation and magnons for the above-mentioned systems that include non-local damping. Remarkably, our study predicts longer lifetimes for certain magnon modes compared to a scalar damping case. Results are published in Ref. [7]. Observables of our studies can be linked to experiments, which hopefully motivating measurements of non-local damping in the future.