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Magnetic fields are ubiquitous in the Universe. Recently, cosmologicalsimulations of galaxies have successfully begun to incorporate magnetic fieldsand their evolution in galaxies and their haloes. However, so far they havemostly focused on Milky Way-like galaxies. Here we analyse a sample of highresolution cosmological zoom simulations of disc galaxies in haloes with mass$M_\mathrm{200c}$ from $10^{10}\,\mathrm{M}_\odot$ to$10^{13}\,\mathrm{M}_\odot$, simulated with the Auriga galaxy formation model.We show that with sufficient numerical resolution the magnetic fieldamplification and saturation is converged. The magnetic field strength reachesequipartition with turbulent energy density for galaxies in haloes with$M_\mathrm{200c}\gtrsim 10^{11.5}\,\mathrm{M_\odot}$. For galaxies in lessmassive haloes, the magnetic field strength saturates at a fraction ofequipartition that decreases with decreasing halo mass. For our lowest masshaloes, the magnetic field saturates significantly below $10\%$ ofequipartition. We quantify the resolution we need to obtain converged magneticfield strengths and discuss our resolution requirements also in the context ofthe IllustrisTNG cosmological box simulations. We show that, at $z=0$,rotation-dominated galaxies in our sample exhibit for the most part an orderedlarge scale magnetic field, with fewer field reversals in more massivegalaxies. Finally, we compare the magnetic fields in our cosmological galaxiesat $z=0$ with simulations of isolated galaxies in a collapsing halo setup. Ourresults pave the way for detailed studies of cosmic rays and other physicalprocesses in similar cosmological galaxy simulations that crucially depend onthe strength and structure of magnetic fields.

Magnetic field amplification in cosmological zoom simulations from dwarf galaxies to galaxy groups