Unveiling the Cosmic Chemistry: Revisiting the Mass-Metallicity Relation with JWST/NIRSpec at 4 < z < 10

We present star formation rates (SFR), the mass-metallicity relation (MZR), and the SFR-dependent MZR across redshifts 4 to 10 using 81 star-forming galaxies observed by the JWST NIRSpec employing both low-resolution PRISM and medium-resolution gratings, including galaxies from the JADES GOODS-N and GOODS-S fields, the JWST-PRIMAL Legacy Survey, and additional galaxies from the literature in Abell 2744, SMACS-0723, RXJ2129, BDF, COSMOS, and MACS1149 fields. These galaxies span a 3 dex stellar mass range of $10^7 < M_{\ast}/M_{\odot} < 10^{10}$, with an average SFR of $7.2 \pm 1.2 M_{\odot} {\rm yr}^{-1}$ and an average metallicity of $12+{\rm log(O/H)} = 7.91 \pm 0.08$. Our findings align with previous observations up to $z=8$ for the MZR and indicate no deviation from local universe FMR up to this redshift. Beyond $z=8$, we observe a significant deviation $\sim 0.27$ dex) in FMR, consistent with recent JWST findings. We also integrate CEERS (135 galaxies) and JADES (47 galaxies) samples with our data to study metallicity evolution with redshift in a combined sample of 263 galaxies, revealing a decreasing metallicity trend with a slope of $0.067 \pm 0.013$, consistent with IllustrisTNG and EAGLE, but contradicts with FIRE simulations. We introduce an empirical mass-metallicity-redshift (MZ-$z$ relation): $12+{\rm log(O/H)}=6.29 + 0.237 \times{\rm log}(M_{\ast}/M_{\odot}) - 0.06 \times (1+z)$, which accurately reproduces the observed trends in metallicity with both redshift and stellar mass. This trend underscores the ``Grand Challenge'' in understanding the factors driving high-redshift galactic metallicity trends, such as inflow, outflow, and AGN/stellar feedback -- and emphasizes the need for further investigations with larger samples and enhanced simulations.