Herewith, first-principles calculations based on density functional theory are used to describe the ideal magnetization reversal through polarization switching in ${\mathrm{BaCuF}}_{4}$ which, according to our results, could be accomplished close to room temperature. We also show that this ideal coupling is driven by a single soft mode that combines both polarization, and octahedral rotation. The later being directly coupled to the weak ferromagnetism of ${\mathrm{BaCuF}}_{4}$. This, added to its strong Jahn-Teller distortion and its orbital ordering, makes this material a very appealing prototype for crystals in the $AB{X}_{4}$ family for multifunctional applications. The described mechanism behaves ideally as it couples the ferroelectric and the magnetic properties naturally and it has not been reported previously.