Direct Visualization of Magnetic Correlations in Frustrated Spinel ZnFe₂O₄

Abstract

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adma.202207152. Magnetic materials with the spinel structure (A 2+ B 3+2 O 4 ) form the core of numerous magnetic devices, and ZnFe 2 O 4 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.

Benchmark Crystal Structure of Defect-Free Spinel ZnFe2O4

“…This large difference makes neutron data better suited for the robust determination of the degree of inversion compared with XRD. To establish the inversion, the occupancies were constrained such that all sites were fully occupied and that the overall composition matched the molar ratio, as determined by previously measured micro-X-ray fluorescence spectroscopy (XRF) (see ref ). When revisiting the XRF data, we found that a small error had led to the previously reported molar ratio of n Fe 2 O 3 / n ZnO = 1.06(2), while the correct ratio is in fact found to be slightly closer to ideal stoichiometry at 1.03(2) corresponding to the formula unit stoichiometry Zn 0.98(1) Fe 2.02(1) O 4 .…”

“…In the present study, we provide benchmark single-crystal ADPs for the archetypical spinel structure of ZnFe 2 O 4 , and we show that our crystals have limited defects (interstitials, inversion). It is exactly the defect-free nature of our samples that make them excellent for studying the frustrated magnetism in the system, since all the magnetic Fe atoms are located on the pyrochlore sublattice, which cannot support the antiferromagnetic order . The diffraction data were measured with high-energy radiation and to high resolution to avoid as many systematic errors as possible.…”

“…Single crystals of ZnFe 2 O 4 were grown using the flux method, with PbO as the flux material. Full details are provided in ref .…”

“…The magnetic behavior of ZnFe 2 O 4 has been widely studied, but the published results have been somewhat contradictory. Early investigations reported a low-temperature antiferromagnetic transition, − which later has been attributed to the presence of structural disorder, with the evidence that pristine ZnFe 2 O 4 is in fact geometrically frustrated with no long-range magnetic order. − However, recent findings suggest that the opposite is true, that magnetic disorder is a result of structural disorder, while pristine samples exhibit long-range antiferromagnetic order at low temperatures, casting further doubt on the intrinsic properties of this system …”

“…The crystal structure allows for extensive chemical substitution, and the structural diversity is further enhanced by the ability of the spinel structure to accommodate point defects, with the antisite defect (“inversion”) between A 2+ and Be 3+ being the most pronounced . Since the magnetic coupling differs between the A and B sites, cation inversion is a key handle to manipulate the magnetic properties. − The spatial arrangement of the A sites mirrors that of carbon atoms in diamond, and the B sites form a pyrochlore sublattice comprising a network of corner-sharing tetrahedra, and thus even defect-free crystals can have magnetic frustration. − …”