Prediction of the hardest BiFeO 3 from first-principles calculations.

BiFeO 3 is the only material with ferroelectric Curie temperature and Néel temperature higher than room temperature, making it one of the most well-studied multiferroic materials. Based on an ab initio evolutionary algorithm, we predicted a new cubic C-type antiferromagnetic structure ( Fd 3̄ m -BiFeO 3 ) at ambient pressure. It was found that Fd 3̄ m -BiFeO 3 is the hardest BiFeO 3 (Vickers hardness ∼ 9.12 GPa), about 78% harder than R 3 c -BiFeO 3 (the well-known multiferroic material), which contributes to extending the life of BiFeO 3 devices. In addition, Fd 3̄ m -BiFeO 3 has the largest shear modulus (83.74 GPa) and the largest Young's modulus (214.72 GPa). Besides, we found an interesting phenomenon that among the common multiferroic materials (BiFeO 3 , BaTiO 3 , PbTiO 3 , SrRuO 3 , KNbO 3 , and BiMnO 3 ), Pnma -BiMnO 3 has the largest bulk modulus, and its bulk modulus is about 15% larger than that of Fd 3̄ m -BiFeO 3 . However, its Vickers hardness (4.47 GPa) is much smaller than that of Fd 3̄ m -BiFeO 3 . This is because the Vickers hardness is proportional to the shear modulus and the shear modulus of Fd 3̄ m -BiFeO 3 is larger than that of Pnma -BiMnO 3 . This work provides a deeper and more comprehensive understanding of BiFeO 3 .