  Self-action nonlinearity is a key aspect -- either as a foundational element
or a detrimental factor -- of several optical spectroscopies and photonic
devices. Supercontinuum generation, wavelength converters and chirped pulse
amplification are just a few examples. The recent advent of Free Electron
Lasers (FEL) fostered building on nonlinearity to propose new concepts and
extend optical wavelengths paradigms for extreme ultraviolet (EUV) and X-ray
regimes. No evidence for intrapulse dynamics, however, has been reported at
such short wavelengths, where the light-matter interactions are ruled by the
sharp absorption edges of core-electrons. Here, we provide experimental
evidence for self-phase modulation of femtosecond FEL pulses, which we exploit
for fine self-driven spectral tunability by interaction with sub-micrometric
foils of selected monoatomic materials. Moving the pulse wavelength across the
absorption edge, the spectral profile changes from a non-linear spectral
blue-shift to a red-shifted broadening. These findings are rationalized
accounting for ultrafast ionization and delayed thermal response of highly
excited electrons above and below threshold, respectively.
