Magnetoelastic coupling, phonon and magnons in inverse spinel NiFe₂O₄

The inverse spinel NiFe₂O₄ has attracted enormous interest due to the potential applications in several important fields such as electronic devices and catalysis. NiFe₂O₄ exhibits a cation distribution of (Fe³⁺)_A(Ni²⁺Fe³⁺)_BO₄, with Fe³⁺ occupying the tetrahedral(A) sites forming a diamond lattice, and Ni²⁺ and Fe³⁺ sharing the octahedral(B) sites forming a pyrochlore lattice. Powder neutron diffraction reveals the cubic spinel structure persisting down to 5 K. A collinear ferrimagnetic order with antiparallel moments between A and B sites is found below T_N ≈ 860 K with a magnetoelastic coupling at T_N. Magnetization measurements further reveal NiFe₂O₄ enters a state with the coexistence of a ferrimagnetic order and a spin glass like state below the freezing temperature T_f ≈ 40 K. A few branches of phonons and magnons with a crossing feature are observed via single-crystal inelastic neutron scattering at 100 K (T_f <T<T_N) and 5 K (T< T_f). All these results and magnetic exchange constants will be compared to the well-known magnetite Fe₃O₄ to reveal the distinct spin, lattice and orbital degrees of freedom.