Applications of the scattering theory of magnetization damping

Magnetization (or Gilbert) damping results from a combination of spin-orbit coupling and disorder. I review a scattering theoretical formulation of magnetization damping [1] implemented without parameters in density functional theory with a very efficient basis of tight-binding muffin tin orbitals [2]. By being able to handle scattering regions containing in excess of 10,000 atoms, the influence of various types of disorder can be studied, including temperature-induced lattice and spin disorder [3]. I discuss applications to the important itinerant ferromagnets Fe, Co and Ni [4,5] as well as to the binary substitutional ferromagnetic alloys Fe$_x$Ni$_{1-x}$, Fe$_x$Co$_{1-x}$, and Co$_x$Ni$_{1-x}$ [2,5] where the prediction of a very low damping in the Fe$_x$Co$_{1-x}$ system was recently confirmed by experiment [6]. Studies of damping in structurally [7] and magnetically [8] inhomogeneous systems of great current interest lead to a number of new insights and predictions. \newline \newline [1] A. Brataas, Y. Tserkovnyak, and G. E.W. Bauer, PRL\textbf{101}, 037207 (2008); PRB\textbf{84}, 054416 (2011).\newline [2] A.A. Starikov, P.J. Kelly, A. Brataas, Y.Tserkovnyak, and G. E.W. Bauer, PRL\textbf{105}, 236601 (2010).\newline [3] Y. Liu, Z. Yuan, R.J.H. Wesselink, A.A. Starikov, M. van Schilfgaarde and P.J. Kelly, PRB\textbf{91}, 220405 (2015).\newline [4] Y. Liu, A.A. Starikov, Z. Yuan and P.J. Kelly, PRB\textbf{84}, 014412 (2011).\newline [5] H. Ebert, S. Mankovsky, D. Koedderitzsch and P.J. Kelly, PRL\textbf{107}, 066603 (2011).\newline [6] M.A.W. Schoen, D. Thonig, M.L. Schneider, T.J. Silva, H.T. Nembach, O. Eriksson, O. Karis, and J.M. Shaw, Nat. Phys. (2016).\newline [7] Y. Liu, Z. Yuan, R.J.H. Wesselink, A.A. Starikov, and P.J. Kelly, PRL\textbf{113}, 207202 (2014).\newline [8] Z. Yuan, K.M.D. Hals, Y. Liu, A.A. Starikov, A. Brataas and P.J. Kelly, PRL\textbf{113}, 266603 (2014).