We aim to characterise the mass-metallicity relation (MZR) and the 3D correlation between the stellar mass, metallicity, and star formation rate (SFR) known as the fundamental metallicity relation (FMR) for galaxies at 5 < z < 7. Using ∼800 [O III ] selected galaxies from deep NIRCam grism surveys, we present our stacked measurements of direct-T _e metallicities, which we used to test recent strong-line metallicity calibrations. Our measured direct-T _e metallicities (0.1–0.2 Z _⊙ for M _★ ≈ 5 × 10 ^7 − 9 M _⊙ , respectively) match recent JWST/NIRSpec-based results. However, there are significant inconsistencies between observations and hydrodynamical simulations. We observe a flatter MZR slope than the SPHINX ²⁰ and FLARES simulations, which cannot be attributed to selection effects. With simple models, we show that the effect of an [O III ] flux-limited sample on the observed shape of the MZR is strongly dependent on the FMR. If the FMR is similar to the one in the local Universe, the intrinsic high-redshift MZR should be even flatter than is observed. In turn, a 3D relation where SFR correlates positively with metallicity at fixed mass would imply an intrinsically steeper MZR. Our measurements indicate that metallicity variations at fixed mass show little dependence on the SFR, suggesting a flat intrinsic MZR. This could indicate that the low-mass galaxies at these redshifts are out of equilibrium and that metal enrichment occurs rapidly in low-mass galaxies. However, being limited by our stacking analysis, we are yet to probe the scatter in the MZR and its dependence on SFR. Large carefully selected samples of galaxies with robust metallicity measurements can put tight constraints on the high-redshift FMR and help us to understand the interplay between gas flows, star formation, and feedback in early galaxies.

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