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 (vg), relaxation time (τ), and decay length (ld) 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.