  We demonstrate significant cooling of electrons in a nanostructure below 10
mK by demagnetisation of thin-film copper on a silicon chip. Our approach
overcomes the typical bottleneck of weak electron-phonon scattering by coupling
the electrons directly to a bath of refrigerated nuclei, rather than cooling
via phonons in the host lattice. Consequently, weak electron-phonon scattering
becomes an advantage. It allows the electrons to be cooled for an
experimentally useful period of time to temperatures colder than the dilution
refrigerator platform, the incoming electrical connections, and the host
lattice. There are efforts worldwide to reach sub-millikelvin electron
temperatures in nanostructures to study coherent electronic phenomena and
improve the operation of nanoelectronic devices. On-chip magnetic cooling is a
promising approach to meet this challenge. The method can be used to reach low,
local electron temperatures in other nanostructures, obviating the need to
adapt traditional, large demagnetisation stages. We demonstrate the technique
by applying it to a nanoelectronic primary thermometer that measures its
internal electron temperature. Using an optimised demagnetisation process, we
demonstrate cooling of the on-chip electrons from 9 mK to below 5 mK for over
1000 seconds.
