  The field of magnonics attracts significant attention due to the possibility
of utilizing information coded into the spin-wave phase or amplitude to perform
computation operations on the nanoscale. Recently, spin waves were investigated
in Yttrium Iron Garnet (YIG) waveguides with widths ranging down to 50 nm and
aspect ratios thickness over width approaching unity. A critical width was
found, below which the exchange interaction suppresses the dipolar pinning
phenomenon and the system becomes unpinned. Here we continue these
investigations and analyse the pinning phenomenon and spin-wave dispersions as
a function of temperature, thickness and material of choice. Higher order
modes, the influence of a finite wavevector along the waveguide and the impact
of the pinning phenomenon on the spin-wave lifetime are discussed as well as
the influence of a trapezoidal cross section and edge roughness of the
waveguides. The presented results are of particular interest for potential
applications in magnonic devices and the incipient field of quantum magnonics
at cryogenic temperatures.
