Absence of a structural transition up to 40 GPa in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">MgB</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and the relevance of magnesium nonstoichiometry

We report measurements on ${\mathrm{MgB}}_{2}$ up to $\ensuremath{\sim}40 \mathrm{GPa}.$ Increasing pressure yields a monotonous decrease of the lattice parameters and of the $c/a$ ratio, but no structural transition down to parameters smaller than those of ${\mathrm{AlB}}_{2}.$ The transition superconducting temperature also decreases with temperature in a sample-dependent way. The results are explained by an increase of the filling of the two-dimensional ${p}_{\mathrm{xy}}$ bands with pressure, the Mg stoichiometry determining the starting position of the Fermi level. Our measurements indicate that these hole bands are the relevant ones for superconductivity.