Intrinsic Damping Phenomena from Quantum to Classical Magnets:An ab-initio Study of Gilbert Damping in Pt/Co Bilayer

Abstract

A fully quantum mechanical description of the precessional damping of Pt/Co bilayer is presented in the framework of the Keldysh Green function approach using {\it ab initio} electronic structure calculations. In contrast to previous calculations of classical Gilbert damping (${\alpha }_{GD}$), we demonstrate that ${\alpha }_{GD}$ in the quantum case does not diverge in the ballistic regime due to the finite size of the total spin, $S$. In the limit of $S\to \infty$ we show that the formalism recovers the torque correlation expression for ${\alpha }_{GD}$ which we decompose into spin-pumping and spin-orbital torque correlation contributions. The formalism is generalized to take into account a self consistently determined dephasing mechanism which preserves the conservation laws and allows the investigation of the effect of disorder. The dependence of ${\alpha }_{GD}$ on Pt thickness and disorder strength is calculated and the spin diffusion length of Pt and spin mixing conductance of the bilayer are determined and compared with experiments.

arXiv comment8 pages, 5 figures

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• Microscopic Origin of Spin-Orbit Torque in Ferromagnetic Heterostructures: A First Principles Approach
• First-principles quantum transport modeling of spin-transfer and spin-orbit torques in magnetic multilayers
• Magnon decay theory of Gilbert damping in metallic antiferromagnets
• Damping and Anti-Damping Phenomena in Metallic Antiferromagnets: An ab-initio Study
• Charge-Spin Interconversion in Epitaxial Pt Probed by Spin-Orbit Torques in a Magnetic Insulator
• Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences
• Gilbert damping in metallic ferromagnets from Schwinger-Keldysh field theory: Intrinsically nonlocal and nonuniform, and made anisotropic by spin-orbit coupling
• Magnetoelastic and Magnetostrictive Properties of Co${}_2$XAl Heusler Compounds
• Elasto-Dynamical Induced Spin and Charge Pumping in Bulk Heavy Metals