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Re-t2g-splitting-driven semiconductor gaps in ferrimagnetic double perovskite Ca2MReO6 (M=Cr,Fe) from first principles

Motivated by the observation of nonmetallic nature in double perovskite Ca2CrReO6 and Ca2FeReO6 with high magnetic Curie temperatures of 360 and 522 K, we systematically investigate the structural, electronic, and magnetic properties of Ca2MReO6 (M=Cr,Fe) using the full-potential linear augmented plane wave (FP-LAPW) method within the density functional theory. Our full optimization confirms the stable ground-state structure with $P2_1/n$ symmetry. The modified Becke-Johnson (mBJ) exchange potential is used for investigating electronic structures. Our mBJ calculation shows that they are both ferrimagnetic semiconductors with semiconductor gaps of 0.38 eV and 0.05 eV, respectively, in contrast with wrong metallic phases from the generalized gradient approximation (GGA). The origin of semiconductor gap is due to the further distortion of ReO$_6$ octahedra caused by John-Teller effect, which drives the three partially-occupied Re $t_{2g}$ bands split into two fully-filled bands and one empty band in the minority-spin channel. With the spin-orbit coupling (SOC) taken into account, the Ca2MReO6 (M=Cr,Fe) shows high magneto-crystalline anisotropy (MCA) with the magnetic easy axis along pseudocubic [010] direction, and the total magnetic moments increase by 0.209$μ_B$ and 0.258$μ_B$ per formula unit, respectively, due to the strong SOC effect on Re ion. Although reducing to 0.31 and 0.03 eV, the semiconductor gaps remain open in spite of the SOC broadening of the Re $t_{2g}$-related bands. Therefore, our DFT investigation with mBJ has established the correct ferrimagnetic semiconductor ground state for the double perovskites Ca2MReO6 (M=Cr,Fe). This mechanism, different from that in double perovskite Sr2CrOsO6, can help understand physical properties of other similar compounds.