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The interaction of intense light with matter gives rise to competingnonlinear responses that can dynamically change material properties. Prominentexamples are saturable absorption (SA) and two-photon absorption (TPA), whichdynamically increase and decrease the transmission of a sample depending onpulse intensity, respectively. The availability of intense soft X-ray pulsesfrom free-electron lasers (FEL) has led to observations of SA and TPA inseparate experiments, leaving open questions about the possible interplaybetween and relative strength of the two phenomena. Here, we systematicallystudy both phenomena in one experiment by exposing graphite films to soft X-rayFEL pulses of varying intensity, with the FEL energy tuned to match carbon 1sto $\pi^*$ or 1s to $\sigma^*$ transitions. It is observed for lowerintensities that the nonlinear contribution to the absorption is dominated bySA attributed to ground-state depletion; for larger intensities ($>10^{14}$W/cm$^2$), TPA becomes more dominant. The relative strengths of the twophenomena depend in turn on the specific transition driven by the X-ray pulse.Both observations are consistent with our real-time electronic structurecalculations. Our results reveal the competing contributions of distinctnonlinear material responses to spectroscopic signals measured in the X-rayregime, demonstrating an approach of general utility for interpreting FELspectroscopies.

Saturable absorption of free-electron laser radiation by graphite near the carbon K-edge