EVN observations of 6.7 GHz methanol maser polarization in massive star-forming regions IV. Magnetic field strength limits and structure for 7 additional sources

MHD simulations show that the magnetic field can drive molecular outflows during the formation of massive protostars. The best probe to observationally measure both the morphology and the strength of this magnetic field at scales of 10-100 au is maser polarization. We measure the direction of magnetic fields at mas resolution around a sample of massive star-forming regions to determine whether there is a relation between the orientation of the magnetic field and of the outflows. In addition, by estimating the magnetic field strength via the Zeeman splitting measurements, the role of magnetic field in the dynamics of the massive star-forming region is investigated. We selected a flux-limited sample of 31 massive star-forming regions to perform a statistical analysis of the magnetic field properties with respect to the molecular outflows characteristics. We report the linearly and circularly polarized emission of 6.7 GHz CH3OH masers towards seven massive star-forming regions of the total sample with the EVN. The sources are: G23.44-0.18, G25.83-0.18, G25.71-0.04, G28.31-0.39, G28.83-0.25, G29.96-0.02, and G43.80-0.13. We identified a total of 219 CH3OH maser features, 47 and 2 of which showed linearly and circularly polarized emission, respectively. We measured well-ordered linear polarization vectors around all the massive YSOs and Zeeman splitting towards G25.71-0.04 and G28.83-0.25. Thanks to recent theoretical results, we were able to provide lower limits to the magnetic field strength from our Zeeman splitting measurements. We further confirm (based on ~80% of the total flux-limited sample) that the magnetic field on scales of 10-100 au is preferentially oriented along the outflow axes. The estimated magnetic field strength of |B_{||}|>61 mG and >21 mG towards G25.71-0.04 and G28.83-0.2, respectively, indicates that it dominates the dynamics of the gas in both regions.