Step 1: Understanding Ellingham diagram.
Ellingham diagram represents the variation of Gibbs free energy change ($\Delta G^\circ$) with temperature for oxide formation reactions.
Step 2: Reason for change in slope.
A sudden change in slope occurs when there is a phase change in either reactant or product, such as melting or boiling, which changes entropy.
Step 3: Analysis of given oxides.
For magnesium oxide formation, magnesium undergoes a phase change at higher temperature, leading to a sudden change in slope in the Ellingham diagram.
Step 4: Conclusion.
Hence, the oxide that shows a sudden change in slope is $\mathrm{MgO$}.