1. Department of Physics, ETH Zürich, Wolfgang-Pauli-Strasse 16, CH-8093 Zürich, Switzerland
2. Los Alamos National Laboratory, IGPP, PO Box 1663, Los Alamos, New Mexico 87545, USA
3. Department of Physics, University of Toronto, 60 St George Street, Toronto, Ontario M5S 1A7, Canada
4. Observatoire de Genève, Université de Genève, 51 Chemin des Maillettes, CH-1290 Sauverny, Switzerland

Correspondence to: Francesco Miniati¹ Correspondence and requests for materials should be addressed to F.M. (Email: fm@phys.ethz.ch).

The origin and growth of magnetic fields in galaxies is still something of an enigma¹. It is generally assumed that seed fields are amplified over time through the dynamo effect^{2, 3, 4, 5}, but there are few constraints on the timescale. It was recently demonstrated that field strengths as traced by rotation measures of distant (and hence ancient) quasars are comparable to those seen today⁶, but it was unclear whether the high fields were in the unusual environments of the quasars themselves or distributed along the lines of sight. Here we report high-resolution spectra that demonstrate that the quasars with strong Mg ii absorption lines are unambiguously associated with larger rotation measures. Because Mg ii absorption occurs in the haloes of normal galaxies^{7, 8, 9, 10, 11} along the sightlines to the quasars, this association requires that organized fields of surprisingly high strengths are associated with normal galaxies when the Universe was only about one-third of its present age.

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