  According to our current understanding, a subclass of the upper main sequence
chemically peculiar stars, called mercury-manganese (HgMn), is non-magnetic.
Nevertheless, chemical inhomogeneities were recently discovered on their
surfaces. At the same time, no global magnetic fields stronger than 1-100 G are
detected by modern studies. The goals of our study are to search for magnetic
field in the HgMn binary system 66 Eri and to investigate chemical spots on the
stellar surfaces of both components. Our analysis is based on high quality
spectropolarimetric time-series observations obtained during 10 consecutive
nights with the HARPSpol instrument at the ESO 3.6-m telescope. To increase the
sensitivity of the magnetic field search we employed a least-squares
deconvolution (LSD). We used spectral disentangling to measure radial
velocities and study line profile variability. Chemical spot geometry was
reconstructed using multi-line Doppler imaging. We report a non-detection of
magnetic field in 66 Eri, with error bars 10-24 G for the longitudinal field.
Circular polarization profiles also do not indicate any signatures of complex
surface magnetic fields. For a simple dipolar field configuration we estimated
an upper limit of the polar field strength to be 60-70 G. For the HgMn
component we found variability in spectral lines of Ti, Ba, Y, and Sr with the
rotational period equal to the orbital one. The surface maps of these elements
reconstructed with the Doppler imaging technique, show relative underabundance
on the hemisphere facing the secondary component. The contrast of chemical
inhomogeneities ranges from 0.4 for Ti to 0.8 for Ba.
