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We present a theory of Landau-Lifshitz-Gilbert damping $\alpha$ for alocalized spin ${\vec S}$ in the junction coupled to the conduction electronsin both leads under an applied volatege $V$. We find the voltage dependence ofthe damping term reflecting the energy dependence of the density of states. Wefind the effect is linear in the voltage and cotrolled by particle-holeasymmetry of the leads.Comment: 6 pages, 3 figure

Voltage dependence of Landau-Lifshitz-Gilbert damping of spin in a current-driven tunnel junction