@Landau–Lifshitz or Gilbert damping_That is the question.pdfVIP

JOURNAL OF APPLIED PHYSICS 105, 07D315 2009 Landau–Lifshitz or Gilbert damping? That is the question W. M. Saslowa Department of Physics, Texas AM University, College Station, Texas 77843-4242, USA Presented 14 November 2008; received 16 September 2008; accepted 4 January 2009; published online 15 April 2009 In their seminal 1935 paper on magnetics, Landau and Lifshitz LL proposed a form for magnetization damping. In 1955 Gilbert proposed another form, introducing a dimensionless parameter . We derive LL damping using the theory of irreversible thermodynamics, summarize an unbiased Langevin theory of fluctuations that yields LL damping, and argue that inhomogeneous broadening might explain the nonresonance data that led Gilbert to formulate his theory. LL versus Gilbert damping takes on special relevance in the context of bulk spin transfer torque and bulk spin pumping, where the form of damping affects the values of the “adiabatic” and “nonadiabatic” terms. We argue that the adiabatic and nonadiabatic terms are dissipative and reactive, respectively. © 2009 American Institute of Physics. DOI: 10.1063/1.3077204 I. INTRODUCTION dynamics. A recent work on damping in nonuniform ferro- 1 magnetic insulators, including a magnetism-directed intro- Landau and Lifshitz’s seminal 1935 paper on magnetics duction to irreversible thermodynamics, finds that nonunifor- proposes, for the dynamics of the magnetization M of a uni-