  Yttrium iron garnet (YIG) is a magnetic insulator with record-low damping,
allowing spin-wave transport over macroscopic distances. Doping YIG with
gallium ions greatly reduces the demagnetizing field and introduces a
perpendicular magnetic anisotropy, which leads to an isotropic spin-wave
dispersion that facilitates spin-wave optics and spin-wave steering. Here, we
characterize the dispersion of a gallium-doped YIG (Ga:YIG) thin film using
electrical spectroscopy. We determine the magnetic anisotropy parameters from
the ferromagnetic resonance frequency and use propagating spin wave
spectroscopy in the Damon-Eshbach configuration to detect the small spin-wave
magnetic fields of this ultrathin weak magnet over a wide range of wavevectors,
enabling the extraction of the exchange constant $\alpha=1.3(2)\times10^{-12}$
J/m. The frequencies of the spin waves shift with increasing drive power, which
eventually leads to the foldover of the spin-wave modes. Our results shed light
on isotropic spin-wave transport in Ga:YIG and highlight the potential of
electrical spectroscopy to map out the dispersion and bistability of
propagating spin waves in magnets with a low saturation magnetization.
