© 2016 American Physical Society. The axion is a hypothetical particle considered to be the most economical solution to the strong CP problem. It can also be formulated as a compelling component of dark matter. The haloscope, a leading axion detection scheme, relies on the conversion of galactic halo axions into real photons inside a resonant cavity structure in the presence of a static magnetic field, where the generated photon frequency corresponds to the mass of the axion. For maximum sensitivity it is key that the central frequency of the cavity mode structure coincides with the frequency of the generated photon. As the mass of the axion is unknown, it is necessary to perform searches over a wide range of frequencies. Currently there are substantial regions of the promising preinflationary low-mass axion range without any viable proposals for experimental searches. We show that three-dimensional resonant LC circuits with separated magnetic and electric fields, commonly known as reentrant cavities, can be sensitive dark matter haloscopes in this region, with frequencies inherently lower than those achievable in the equivalent size of empty resonant cavity. We calculate the sensitivity and accessible axion mass range of these experiments, designing geometries to exploit and maximize the separated magnetic and electric coupling of the axion to the cavity mode.