Revealing the Hidden Structural Phases of FeRh

${\it Ab}$ ${\it initio}$ electronic structure calculations reveal that tetragonal distortion has a dramatic effect on the relative stability of the various magnetic structures (C-, A-, G-, A$'$-AFM, and FM) of FeRh giving rise to a wide range of novel stable/metastable structures and magnetic phase transitions between these states. We predict that the ${\it cubic}$ G-AFM structure, which was believed thus far to be the ground state, is metastable and that the ${\it tetragonally}$ expanded G-AFM is the stable structure. The low energy barrier separating these states suggests phase coexistence at room temperature. We propose a novel A$'$-AFM phase to be the ${\it global}$ ground state among all magnetic phases which arises from the strain-induced tuning of the exchange interactions. The results elucidate the underlying mechanism for the recent experimental findings of electric-field control of magnetic phase transition driven via tetragonal strain. The novel magnetic phase transitions open interesting prospects for exploiting strain engineering for the next-generation memory devices.