  Context. Several new techniques to determine the metallicity of M dwarfs with
better precision have been developed over the last decades. However, most of
these studies were based on empirical methods. In order to enable detailed
abundance analysis, standard methods established for warmer solar-like stars,
i.e. model-dependent methods using fitting of synthetic spectra, still need to
be used. Aims. In this work we continue the reliability confirmation and
development of metallicity determinations of M dwarfs using high- resolution
infrared spectra. The reliability was confirmed though analysis of M dwarfs in
four binary systems with FGK dwarf companions and by comparison with previous
optical studies of the FGK dwarfs. Methods. The metallicity determination was
based on spectra taken in the J band (1.1-1.4 {\mu}m) with the CRIRES
spectrograph. In this part of the infrared, the density of stellar molecular
lines is limited, reducing the amount of blends with atomic lines enabling an
accurate continuum placement. Lines of several atomic species were used to
determine the stellar metallicity. Results. All binaries show excellent
agreement between the derived metallicity of the M dwarf and its binary
companion. Our results are also in good agreement with values found in the
literature. Furthermore, we propose an alternative way to determine the
effective temperature of M dwarfs of spectral types later than M2 through
synthetic spectral fitting of the FeH lines in our observed spectra.
Conclusions. We have confirmed that a reliable metallicity determination of M
dwarfs can be achieved using high-resolution infrared spectroscopy. We also
note that metallicites obtained with photometric metallicity calibrations
available for M dwarfs only partly agree with the results we obtain from
high-resolution spectroscopy.
