Interspin interactions in ZnFe₂O₄:  Theoretical analysis of neutron scattering study

We carried out a theoretical analysis of the recent neutron scattering study on ZnFe₂O₄ based on a simple classical Heisenberg spin model to elucidate the magnetic interactions in the system. The central issue is the possible frustration phenomena realized in the corner-shared tetrahedral arrangement of spins with an antiferromagnetic nearest-neighbor interaction. The results are summarized as follows: (i) From the diffuse intensity distributions in (h k 0)- and (h h 1)-zones, it is concluded that, contrary to the anticipation, the nearest-neighbor interaction is ferromagnetic, while the third-neighbor interaction is antiferromagnetic. (ii) From the shift of the peak position of the diffuse maximum as the temperature is varied, it is inferred that the ratio of the first- and the third-neighbor interactions J₃/|J₁| is effectively temperature dependent. The value tends to be diminished at T>50K, which is consistent with the observation of a positive Curie-Weiss temperature deduced from the susceptibility measurement. (iii) From the systematic absence of the diffuse intensity around specific Bragg points, the lowest-energy “mode” of the spin-density fluctuations is characterized to be the “acoustic” mode.