Step 1: State Fajans' Rules for covalent character in ionic compounds.
Covalent character in an ionic bond increases when: (i) the cation is small and highly charged, and (ii) the anion is large and highly charged. The cation polarizes the electron cloud of the anion.
Step 2: Evaluate the polarizing power of cations.
Polarizing power = charge/size. A smaller, more highly charged cation has greater polarizing power. Options to compare: Li+, Na+, Mg2+, Al3+. Among these, Al3+ and Mg2+ have high charge; Mg2+ is relatively small.
Step 3: Evaluate polarizability of anions.
Larger anions with high charge are more polarizable. O2- is small but highly charged; Cl-, Br-, I- are large. However, O2- is highly charged (2-).
Step 4: Apply Fajans' Rules to the given options.
The combination Mg2+ + O2-: Mg2+ is a small, doubly-charged cation with high polarizing power; O2- is a doubly-charged anion. The high charge on both means greater covalent character.
Step 5: Compare with other options.
Combinations with singly-charged ions (Na+, K+ with Cl-) have less polarizing power and lower covalent character. Mg2+/O2- shows maximum covalent character due to high charges on both ions.
Step 6: State the conclusion.
Among the given combinations, Mg2+ and O2- form an ionic compound with maximum covalent character due to the high charge density of Mg2+ and the high polarizability of O2-.
\[ \boxed{Mg^{2+} \text{ and } O^{2-}} \]