Stellar Mass--Gas-phase Metallicity Relation at $0.5\leq z\leq0.7$: A
  Power Law with Increasing Scatter toward the Low-mass Regime
  We present the stellar mass ($M_{*}$)--gas-phase metallicity relation (MZR)
and its scatter at intermediate redshifts ($0.5\leq z\leq0.7$) for 1381 field
galaxies collected from deep spectroscopic surveys. The star formation rate
(SFR) and color at a given $M_{*}$ of this magnitude-limited ($R\lesssim24$ AB)
sample are representative of normal star-forming galaxies. For masses below
$10^9 M_\odot$, our sample of 237 galaxies is $\sim$10 times larger than those
in previous studies beyond the local universe. This huge gain in sample size
enables superior constraints on the MZR and its scatter in the low-mass regime.
We find a power-law MZR at $10^{8} M_\odot < M_{*} < 10^{11} M_\odot$:
${12+log(O/H) = (5.83\pm0.19) + (0.30\pm0.02)log(M_{*}/M_\odot)}$. Our MZR
shows good agreement with others measured at similar redshifts in the
literature in the intermediate and massive regimes, but is shallower than the
extrapolation of the MZRs of others to masses below $10^{9} M_\odot$. The SFR
dependence of the MZR in our sample is weaker than that found for local
galaxies (known as the Fundamental Metallicity Relation). Compared to a variety
of theoretical models, the slope of our MZR for low-mass galaxies agrees well
with predictions incorporating supernova energy-driven winds. Being robust
against currently uncertain metallicity calibrations, the scatter of the MZR
serves as a powerful diagnostic of the stochastic history of gas accretion, gas
recycling, and star formation of low-mass galaxies. Our major result is that
the scatter of our MZR increases as $M_{*}$ decreases. Our result implies that
either the scatter of the baryonic accretion rate or the scatter of the
$M_{*}$--$M_{halo}$ relation increases as $M_{*}$ decreases. Moreover, our
measures of scatter at $z=0.7$ appears consistent with that found for local
galaxies.
