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In the Landauer-Büttiker formulation of transport theory, the conductance is expressed in terms of scattering matrices and the resistivity p can be determined by calculating the resistance R of a variable length L of a disordered system in a scattering region of cross section A as a function of L from AR=pL. An analogous formulation of magnetization relaxation has recently been developed that expresses the Gilbert damping parameter α in terms of derivatives of the scattering matrix with respect to magnetization direction [1]. In substitutional alloys with intrinsic chemical disorder, calculations of the resistivity and Gilbert damping within the framework of first-principles scattering theory resulted in good agreement with experiment without introducing any parameters [2]. In clean metal systems temperature effects in electronic transport are also fundamentally important, where thermal disorder plays a critical role in determining the resistivity and Gilbert damping. The above computational scheme can thus be extended to apply to pure metals by introducing a simple "frozen thermal lattice disorder" scheme where atoms in the scattering region are displaced at random with a Gaussian distribution. Using this method we were able to reproduce qualitatively [3] the conductivity-like and resistivity-like damping behaviour observed at low and high temperatures, respectively, for Fe, Co, and Ni [4]. The obtained good qualitative and reasonable quantitative agreement confirms that our simple method is capable of capturing dominant effect of lattice temperature in magnetization relaxation. By decomposing the microscopic disorder, we demonstrate that resistivity and Gilbert damping depend on the particular details of the disorder. This scheme can be readily applied to complex materials and to the calculation of other temperature dependent properties. [1] A. Brataas, Y. Tserkovnyak, G. E. W. Bauer, Phys. Rev. Lett. 101, 037207 (2008). [2] A. A. Starikov, P. J. Kelly, A. Brataas, Y. Tserkovnyak, and G. E. W. Bauer, Phys. Rev. Lett. 105, 236601 (2010). [3] Y. Liu, A. A. Starikov, Z. Yuan, and P. J. Kelly, Phys. Rev. B 84, 014412 (2011). [4] S. M. Bhagat and P. Lubitz, Phys. Rev. B 10, 179 (1974). |
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