  The sensitivity of experimental searches for axion dark matter coupled to
photons is typically proportional to the strength of the applied static
magnetic field. We demonstrate how a permeable material can be used to enhance
the magnitude of this static magnetic field, and therefore improve the
sensitivity of such searches in the low frequency lumped-circuit limit. Using
gadolinium iron garnet toroids at temperature 4.2 K results in a factor of 4
enhancement compared to an air-core toroidal design. The enhancement is limited
by magnetic saturation. Correlation of signals from three such toroids allows
efficient rejection of systematics due to electromagnetic interference. The
sensitivity of a centimeter-scale axion dark matter search based on this
approach is on the order of $g_{a\gamma\gamma}\approx10^{-9}$ GeV$^{-1}$ after
8 hours of data collection for axion masses near $10^{-10}$ eV. This approach
may substantially extend the sensitivity reach of large-volume lumped element
axion dark matter searches.
