  The frontiers of quantum electronics have been linked to the discovery of new
refrigeration methods since the discovery of superconductivity at a temperature
around $4\,$K, enabled by the liquefaction of helium. Since then, the advances
in cryogenics led to discoveries such as the quantum Hall effect and new
technologies like superconducting and semiconductor quantum bits. Presently,
nanoelectronic devices typically reach electron temperatures around $10\,$mK to
$100\,$mK by commercially available dilution refrigerators. However, cooling
electrons via the encompassing lattice vibrations, or phonons, becomes
inefficient at low temperatures. Further progress towards lower temperatures
requires new cooling methods for electrons on the nanoscale, such as direct
cooling with nuclear spins, which themselves can be brought to microkelvin
temperatures by adiabatic demagnetization. Here, we introduce indium as a
nuclear refrigerant for nanoelectronics and demonstrate that solely on-chip
cooling of electrons is possible down to $3.2\pm0.1\,$mK, limited by the heat
leak via the electrical connections of the device.
