  Estimating precise metallicity of M dwarfs is a well-known difficult problem
due to their complex spectra. In this work, we empirically calibrate the
metallicity using wide binaries with a F, G, or K dwarf and a M dwarf
companion. With 1308 FGK+M wide binaries well observed by LAMOST, we calibrated
M dwarf's [Fe/H] by using the Stellar LAbel Machine (SLAM) model, a data-driven
method based on support vector regression (SVR). The [Fe/H] labels of the
training data are from FGK companions in range of [-1,0.5] dex. The Teffs are
selected from Li et al. (2021), spanning [3100,4400] K. The uncertainties in
SLAM estimates of [Fe/H] and Teff are ~0.15 dex and ~40 K, respectively, at
snri > 100, where snri is the signal-to-noise ratio (SNR) at i-band of M dwarf
spectra. We applied the trained SLAM model to determine the [Fe/H] and Teff for
~630,000 M dwarfs with low-resolution spectra in LAMOST DR9. Compared to other
literature also using FGK+M wide binaries for calibration, our [Fe/H] estimates
show no bias but a scatter of ~ 0.14-0.18 dex. However, the [Fe/H] compared to
APOGEE shows a systematic difference of ~ 0.10-0.15 dex with a scatter of ~
0.15-0.20 dex. While the Teff compared to APOGEE has a bias of 3 K with a
scatter of 62 K, it is systematically higher by 180 K compared to other
calibrations based on the bolometric temperature. Finally, we calculated the
zeta index for 1308 M dwarf secondaries and presents a moderate correlation
between zeta and [Fe/H].
