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We report Resonant inelastic x-ray scattering measurements (RIXS) inYbCu$_2$Si$_2$ at the Yb L$_{3}$ edge under high pressure (up to 22 GPa) and atlow temperatures (down to 7 K) with emphasis on the vicinity of the transitionto a magnetic ordered state. We find a continuous valence change towards thetrivalent state with increasing pressure but with a pronounced change of slopeclose to the critical pressure. Even at 22 GPa the Yb$^{+3}$ state is not fullyachieved. The pressure where this feature is observed decreases as thetemperature is reduced to 9 GPa at 7K, a value close to the critical pressure(\itshape{p\normalfont{$_c$}}\normalfont $\approx$ 7.5 GPa) where magneticorder occurs. The decrease in the valence with decreasing temperaturepreviously reported at ambient pressure is confirmed and is found to beenhanced at higher pressures. We also compare the f electron occupancy betweenYbCu$_2$Si$_2$ and its Ce-counterpart, CeCu$_2$Si$_2$.

Valence Instability of YbCu$_2$Si$_2$ through its quantum critical point