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  • Title: Wave-Number-Dependent Gilbert Damping in Metallic Ferromagnets.
    Author: Li Y, Bailey WE.
    Journal: Phys Rev Lett; 2016 Mar 18; 116(11):117602. PubMed ID: 27035322.
    Abstract:
    A wave-number-dependent dissipative term to magnetization dynamics, mirroring the conservative term associated with exchange, has been proposed recently for ferromagnetic metals. We present measurements of wave-number-(k-)dependent Gilbert damping in three metallic ferromagnets, NiFe, Co, and CoFeB, using perpendicular spin wave resonance up to 26 GHz. In the thinnest films accessible, where classical eddy-current damping is negligible, size effects of Gilbert damping for the lowest and first excited modes support the existence of a k^{2} term. The new term is clearly separable from interfacial damping typically attributed to spin pumping. Higher-order modes in thicker films do not show evidence of enhanced damping, attributed to a complicating role of conductivity and inhomogeneous broadening. Our extracted magnitude of the k^{2} term, Δα_{kE}^{*}=Δα_{0}^{*}+A_{k}^{*}k^{2}, where A_{k}^{*}=0.08-0.1  nm^{2} in the three materials, is an order of magnitude lower than that identified in prior experiments on patterned elements.
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