Direct Visualization of Magnetic Correlations in Frustrated Spinel ZnFe₂ O₄

Magnetic materials with the spinel structure (A²⁺ B³⁺ ₂ O₄ ) form the core of numerous magnetic devices, and ZnFe₂ O₄ constitutes a peculiar example where the nature of the magnetism is still unresolved. Susceptibility measurements revealed a cusp around T_c  = 13 K resembling an antiferromagnetic transition, despite the positive Curie-Weiss temperature determined to be Θ_CW  = 102.8(1) K. Bifurcation of field-cooled and zero-field-cooled data below T_c in conjunction with a frequency dependence of the peak position and a non-zero imaginary component below T_c shows it is in fact associated with a spin-glass transition. Highly structured magnetic diffuse neutron scattering from single crystals develops between 50 K and 25 K revealing the presence of magnetic disorder which is correlated in nature. Here, the 3D-mΔPDF method is used to visualize the local magnetic ordering preferences, and ferromagnetic nearest-neighbor and antiferromagnetic third nearest-neighbor correlations are shown to be dominant. Their temperature dependence is extraordinary with some flipping in sign and a strongly varying correlation length. The correlations can be explained by orbital interaction mechanisms for the magnetic pathways and a preferred spin cluster. This study demonstrates the power of the 3D-mΔPDF method in visualizing complex quantum phenomena thereby providing a way to obtain an atomic-scale understanding of magnetic frustration.