Fragile pressure-induced magnetism in FeSe superconductors with a thickness reduction.

The emergence of high transition temperature ($T_c$) superconductivity in bulk FeSe under pressure is associated with the tuning of nematicity and magnetism. However, sorting out the relative contributions from magnetic and nematic fluctuations to the enhancement of $T_c$ remains challenging. Here, we design and conduct a series of high-pressure experiments on FeSe thin flakes. We find that, as the thickness decreases, the nematic phase boundary on temperature-pressure phase diagrams remains robust while the magnetic order is significantly weakened. A local maximum of $T_c$ is observed outside the nematic phase region, not far from the extrapolated nematic endpoint in all samples. However, the maximum $T_c$ value is reduced associated with the weakening of magnetism. No high-$T_c$ phase is observed in the thinnest sample. Our results strongly suggest that nematic fluctuations alone can only have a limited effect while magnetic fluctuations are pivotal on the enhancement of $T_c$ in FeSe.