Spin-filter tunneling and spin hall conductivity in the ferrimagnetic NiFe₂O₄

Spin-filter tunneling and charge-to-spin conversion play an important role in producing spin-polarized currents crucial for spintronics. In this work, based on the density functional theory calculations, we report on a study on the spin-filter tunneling through the NiFe₂O₄ by analyzing the decay rates for different wave vectors from the spin-dependent complex band structure. We show that the spin-filter efficiency reaches 100% with a thick barrier. More intriguingly, depending on the position of Fermi energy, the spin-filter efficiency reveals both positive and negative signs. In addition, we explore the intrinsic spin Hall conductivity in electron doped NiFe₂O₄ and demonstrate a large spin Hall angle of ∼0.12 for certain doping concentration. Those findings add unexplored functionality to the ferrimagnetic spinel NiFe₂O₄ and open avenues for potential applications.