  We study the magnetic properties of Gadolinium-Yttrium Iron Garnet
($\text{Gd}_{x}\text{Y}_{3-x}\text{Fe}_5\text{0}_{12}$, $x=3,1.8$) ferrite
ceramics. The complex initial permeability is measured in the temperature range
2 K to 295 K at frequency of 1 kHz, and in the frequency range 100 Hz to 200
MHz at temperatures 4 K, 77 K, and 295 K. The magnetic viscosity-induced
imaginary part of the permeability is observed at low frequencies. Measurements
of the magnetization noise are made at 4 K. Using the fluctuation-dissipation
theorem, we find that the observed magnetization fluctuations are consistent
with our measurements of the low-frequency imaginary part of permeability. We
discuss some implications for proposed precision measurements as well as other
possible applications.
