Phenomenological description of the nonlocal magnetization relaxation in magnonics, spintronics, and domain-wall dynamics
Physical Review B - Condensed Matter and Materials Physics
American Physical Society
A phenomenological equation called the Landau-Lifshitz-Baryakhtar (LLBar) [Zh. Eksp. Teor. Fiz 87, 1501 (1984) [Sov. Phys. JETP 60, 863 (1984)]] equation, which could be viewed as the combination of the Landau-Lifshitz (LL) equation and an extra "exchange-damping" term, was derived by Baryakhtar using Onsager's relations. We interpret the origin of this exchange damping as nonlocal damping by linking it to the spin current pumping. The LLBar equation is investigated numerically and analytically for the spin-wave decay and domain-wall motion. Our results show that the lifetime and propagation length of short-wavelength magnons in the presence of nonlocal damping could be much smaller than those given by the LL equation. Furthermore, we find that both the domain-wall mobility and the Walker breakdown field are strongly influenced by the nonlocal damping.
We acknowledge the financial support from EPSRC's DTC Grant No. EP/G03690X/1. W.W. thanks the China Scholarship Council for financial assistance. The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 247556 (NoWaPhen) and from the European Union's Horizon 2020 research and innovation program under Marie Skłodowska-Curie Grant Agreement No. 644348 (MagIC).
This is the final version of the article. Available from the American Physical Society via the DOI in this record.
Vol. 92, article 054430