Aims. We aim to investigate how polarimetric observations can improve our understanding of the nature and diversity of M/X-type asteroids.

Methods. Polarimetric observations of the selected M/X-type asteroids were carried out at the Tohoku 0.6-m telescope at Haleakala Observatory, Hawaii (simultaneously in BVR filters), the 2-m telescope of the Bulgarian National Astronomical Observatory in Rozhen (in R filter), and the 2.15-m telescope of the Complejo Astronomico El Leoncito (CASLEO), Argentina (in V filter). We analysed the polarimetric characteristics of M/X-type asteroids along with the available data obtained by other techniques.

Results. New polarimetric observations of 22 M/X-type asteroids combined with published observations provide a data set of 41 asteroids for which the depth of a negative polarisation branch and/or inversion angle were determined. We found that the depth of the negative polarisation branch tends to increase with decreasing steepness of the near-infrared spectra. Asteroids with a deeper negative polarisation branch tend to have a higher radar circular polarisation ratio. We show that, based on the relationship of the depth of the negative polarisation branch and inversion angle, two main sub-types can be distinguished among M-type asteroids. We suggest that these groups may be related to different surface compositions similar to (1) irons and stony-irons and (2) enstatite and iron-rich carbonaceous chondrites.