Influence of nonlocal damping on magnon properties of ferromagnets

We study the influence of nonlocal damping on the magnon properties of Fe, Co, Ni, and ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}$ ($x=30%,50%$) alloys. The Gilbert damping parameter is typically considered as a local scalar both in experiment and in theoretical modeling. However, recent works have revealed that Gilbert damping is a nonlocal quantity that allows for energy dissipation between atomic sites. With the Gilbert damping parameters calculated from a state-of-the-art real-space electronic structure method, magnon lifetimes are evaluated from spin dynamics and linear response, where a good agreement is found between these two methods. It is found that nonlocal damping affects the magnon lifetimes in different ways depending on the system. Specifically, we find that in Fe, Co, and Ni, the nonlocal damping decreases the magnon lifetimes, while in ${\mathrm{Fe}}_{70}{\mathrm{Co}}_{30}$ and ${\mathrm{Fe}}_{50}{\mathrm{Co}}_{50}$ an opposite, nonlocal damping effect is observed, and our data show that it is much stronger in the former.