We report the discovery of weak magnetic fields in three white dwarfs within the local 20pc volume (WD 0816-310, WD 1009-184, and WD 1532+129), and we confirm the magnetic nature of a fourth star (WD 2138-332) in which we had previously detected a field at a 3 sigma level. The spectra of all these white dwarfs are characterised by the presence of metal lines and lack of H and He lines, that is, they belong to the spectral class DZ. The polarisation signal of the Ca II H+K lines of WD 1009-184 is particularly spectacular, with an amplitude of 20% that is due to the presence of a magnetic field with an average line-of-sight component of 40kG. We have thus established that at least 40% of the known DZ white dwarfs with an He-rich atmosphere contained in the 20pc volume have a magnetic field, while further observations are needed to establish whether the remaining DZ white dwarfs in the same volume are magnetic or not. Metal lines in the spectra of DZ white dwarfs are thought to have originated by accretion from rocky debris, and it might be argued that a link exists between metal accretion and higher occurrence of magnetism. However, we are not able to distinguish whether the magnetic field and the presence of a polluted atmosphere have a common origin, or if it is the presence of metal lines that allows us to detect a higher frequency of magnetic fields in cool white dwarfs, which would otherwise have featureless spectra. We argue that the new highly sensitive longitudinal field measurements that we have made in recent years are consistent with the idea that the magnetic field appears more frequently in older than in younger white dwarfs.
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