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Understanding spin wave (SW) damping, and how to control it to the point ofbeing able to amplify SW-mediated signals, is one of the key requirements tobring the envisaged magnonic technologies to fruition. Even widely usedmagnetic insulators with low magnetization damping in their bulk, such asyttrium iron garnet, exhibit 100-fold increase in SW damping due to inevitablecontact with metallic layers in magnonic circuits, as observed in very recentexperiments [I. Bertelli et al., Adv. Quantum Technol. 4, 2100094 (2021)]mapping SW damping in spatially-resolved fashion. Here, we provide microscopicand rigorous understanding of wavevector-dependent SW damping using extendedLandau-Lifshitz-Gilbert equation with nonlocal damping tensor, instead ofconventional local scalar Gilbert damping, as derived from Schwinger-Keldyshnonequilibrium quantum field theory. In this picture, the origin of nonlocalmagnetization damping and thereby induced wavevector-dependent SW damping isinteraction of localized magnetic moments of magnetic insulator with conductionelectrons from the examined three different types of metallic overlayers --normal, heavy, and altermagnetic. Due to spin-split energy-momentum dispersionof conduction electrons in the latter two cases, the nonlocal damping isanisotropic in spin and space, and it can be dramatically reduced by changingthe relative orientation of the two layers when compared to the usage of normalmetal overlayer.

Nonlocal damping of spin waves in a magnetic insulator induced by  normal, heavy, or altermagnetic metallic overlayer: a Schwinger-Keldysh field  theory approach