A method with which to calculate the Gilbert damping parameter from a real-space electronic structure method is reported here. The anisotropy of the Gilbert damping with respect to the magnetic moment direction and local chemical environment is calculated for bulk and surfaces of ${\mathrm{Fe}}_{50}{\mathrm{Co}}_{50}$ alloys from first-principles electronic structure in a real-space formulation. The size of the damping anisotropy for ${\mathrm{Fe}}_{50}{\mathrm{Co}}_{50}$ alloys is demonstrated to be significant. Depending on details of the simulations, it reaches a maximum-minimum damping ratio as high as 200%. Several microscopic origins of the strongly enhanced Gilbert damping anisotropy have been examined, where in particular interface/surface effects stand out, as do local distortions of the crystal structure. Although theory does not reproduce the experimentally reported high ratio of 400% [Phys. Rev. Lett. 122, 117203 (2019)], it nevertheless identifies microscopic mechanisms that can lead to huge damping anisotropies.

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• Electronic structure
• First-principles calculations
• Magnetization dynamics
• Methods in magnetism
• Spin dynamics
• Spintronics