Spontaneous spin momentum locking and anomalous Hall effect in BiFeO3

The studies for the discovery of new nontrivial degrees of freedom of Bloch electrons are at the forefront of condensed matter physics. The focus remains on the spin-orbit coupling (SOC)-induced pseudospin valley state and its interplay with time inversion asymmetry. Here we propose a distinct magnetic order-protected, momentum-dependent spin-splitting valley (SSV) state in polar bulk BiFeO3. The octahedral distortion-induced spatial asymmetry of the superexchange interaction path breaks spin degeneracy and antiferromagnetic time -reversal symmetry. The SSV polarization is caused by crystal symmetry-related intrinsic SOC and leads to nonzero anomalous Hall conductivity (AHC) and magneto-optical effects. The anomalous Hall conductivity and magneto-optical effects are expected to be most prominent if magnetic and electric dipoles are orthogonal. Due to the ferroelectric nature of BiFeO3, such unconventional magneto-optical effect and AHC in fully compensated magnetic order offers straightforward tunability under an electric field.