Unveiling the Hidden Entropy in ZnFe2O4

Abstract

The antiferromagnetic (AFM) transition of the normal ZnFe2O4 has been intensively investigated with results showing a lack of long-range order, spin frustrations, and a “hidden” entropy in the calorimetric properties for inversion degrees δ ≈ 0 or δ = 0. As δ drastically impacts the magnetic properties, it is logical to question how a δ value slightly different from zero can affect the magnetic properties. In this work, (Zn1-δFeδ)[ZnδFe2-δ]O4with δ = 0.05 and δ = 0.27 have been investigated with calorimetry at different applied fields. It is shown that a δ value as small as 0.05 may affect 40% of the unit cells, which become locally ferrimagnetic (FiM) and coexists with AFM and spin disordered regions. The spin disorder disappears under an applied field of 1 T. Mossbauer spectroscopy confirms the presence of a volume fraction with a low hyperfine field that can be ascribed to these spin disordered regions. The volume fractions of the three magnetic phases estimated from entropy and hyperfine measurements are roughly coincident and correspond to approximately 1/3 for each of them. The “hidden” entropy is the zero point entropy different from 0. Consequently, the so-called “hidden” entropy can be ascribed to the frustrations of the spins at the interphase between the AFM-FiM phases due to having δ ≈ 0 instead of ideal δ = 0.

Ferrimagnetic Clusters as the Origin of Anomalous Curie–Weiss Behavior in ZnFe2O4 Antiferromagnetic Susceptibility

“…As the measuring temperature is well below the Curie point of the ferrimagnetic A-B coupling, i.e., 700 K, the magnetic moment of the clusters can be considered to be constant. When a single Fe atom has jumped from B to A sites in a unit cell, the local δ is increased in an amount of 1/8 [9], and the ferrimagnetic volume of each of these cells is of the order of the unit cell volume, i.e., 6.0 × 10 −28 m 3 . Therefore, if we consider that there is only one jump per unit cell, the fraction these cells that have undergone an elementary inversion is 40% for a macroscopic inversion value δ = 0.05.…”

“…The normal (Zn) A (Fe 2 ) B O 4 is antiferromagnetic but the exchange of few Zn-Fe cations between A and B sites gives place to (Zn 1−δ Fe δ ) A [Zn δ Fe 2−δ ] B O 4 . Recent evidence of coexisting ferrimagnetic clusters inside of an antiferromagnetic matrix [8][9][10] suggests the use of this material as a model to correlate the increase of Zn-Fe exchange with an anomalous increasing positive Curie-Weiss temperature despite the antiferromagnetic character of the sample.…”

“…Among the anomalous characteristics of the antiferromagnetic Zn ferrite, the apparent contradiction between the positive Curie-Weiss temperature, determined experimentally from the measurements of the magnetic susceptibility, and the antiferromagnetic behavior [15][16][17] character of both B-B and A-B exchange interactions [9] has been outlined. Different causes have been proposed in an attempt to explain this contradiction [18].…”

“…Recent calorimetric and Mossbauer results showed that a very small fraction of Fe atoms occupying tetrahedral A sites can profoundly modify the antiferromagnetic behavior [9]. Specifically, the Mossbauer spectra obtained from samples with a low degree of inversion (δ = 0.05) point to the coexistence of three magnetic structures that can be roughly assigned as: (a) the antiferromagnetic matrix (AFM) with a Neel temperature of the order of 10 K, (b) ferrimagnetic clusters (FM) defined around a tetrahedral or A site occupied by Fe ions, which have a Curie temperature of about 700 K [19], and (c) a spin frustrated or spin disordered (SD) region occupying the boundary between the FM and AFM clusters.…”