  Spin waves in yttrium iron garnet (YIG) nano-structures attract increasing
attention from the perspective of novel magnon-based data processing
applications. For short wavelengths needed in small-scale devices, the group
velocity is directly proportional to the spin-wave exchange stiffness constant
$\lambda_\mathrm{ex}$. Using wave vector resolved Brillouin Light Scattering
(BLS) spectroscopy, we directly measure $\lambda_\mathrm{ex}$ in Ga-substituted
YIG thin films and show that it is about three times larger than for pure YIG.
Consequently, the spin-wave group velocity overcomes the one in pure YIG for
wavenumbers $k > 4$ rad/$\mu$m, and the ratio between the velocities reaches a
constant value of around 3.4 for all $k > 20$ rad/$\mu$m. As revealed by
vibrating-sample magnetometry (VSM) and ferromagnetic resonance (FMR)
spectroscopy, Ga:YIG films with thicknesses down to 59 nm have a low Gilbert
damping ($\alpha < 10^{-3}$), a decreased saturation magnetization $\mu_0
M_\mathrm{S}~\approx~20~$mT and a pronounced out-of-plane uniaxial anisotropy
of about $\mu_0 H_{\textrm{u1}} \approx 95 $ mT which leads to an out-of-plane
easy axis. Thus, Ga:YIG opens access to fast and isotropic spin-wave transport
for all wavelengths in nano-scale systems independently of dipolar effects.
