Results and update from the ABRACADABRA search for sub-$\mu$eV axion dark matter

ABRACADABRA is an experimental concept that searches for axion dark matter (ADM) in the $10^{-14} - 10^{-6}\mathrm{eV}/c^2$ mass range. In ABRACADABRA, ADM couples to the static magnetic field of a toroidal magnet. This coupling induces a small, oscillating magnetic flux in the center of the torus that can be measured by a pickup loop connected to a SQUID current sensor. In this talk we review the ABRACADABRA motivation, concept, and plans. We also present the first results from a one month search for axions with a prototype, ABRACADABRA-10cm. We found no evidence for axion dark matter and present limits in the $3.1\times10^{-10}\,\mathrm{eV} - 8.3\times10^{-9}\,\mathrm{eV}$ mass range. We also present an update from recent running with an upgraded version of ABRACADABRA and our plans towards a cubic meter scale experiment, DMRadio-$1m^3$.