Giant anisotropic Gilbert damping and spin wave propagations in single-crystal magnetic insulator

Gilbert damping in magnetic systems describes the relaxation of magnetization. This term was phenomenologically introduced into the Landau-Lifschitz-Gilbert (LLG) equation to describe spin dynamics. In most studies, such as magnetic random access memory, spin-wave propagations, and microwave devices, it has been assumed that the Gilbert damping is an isotropic constant. In this study, we uncover a giant anisotropic Gilbert damping parameter of up to 431% in single-crystal thin films of epitaxial [100]-oriented yttrium iron garnet (YIG) using angle-dependent ferromagnetic resonance. In contrast, the Gilbert damping parameter of a [111]-oriented YIG film is almost isotropic. The observed anisotropic damping is shown to have a similar fourfold symmetry with magneto-crystalline anisotropy. The anisotropic spin-wave group velocity (v(g)), relaxation time (tau), and decay length (l(d)) were also experimentally evaluated through spin-wave spectra of [100]-oriented YIG thin film. We developed the LLG equation with the introduction of an anisotropic orbital Gilbert damping term. This anisotropic orbital damping originates from the crystal-field dominated anisotropic spin-orbit coupling and orbital-related magnon-phonon coupling. Our results extend the understanding of the mechanism of anisotropic Gilbert damping in single-crystal magnetic insulators with strong magneto-crystalline anisotropy.