Unveiling the hidden entropy in ZnFe_2O_4

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The antiferromagnetic (AFM) transition of the normal ZnFe_2O_4 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 delta approximate to 0 or delta = 0. As delta drastically impacts the magnetic properties, it is logical to question how a delta value slightly different from zero can affect the magnetic properties. In this work, (Zn_(1-delta)Fe_delta)[Zn_delta Fe_(2-delta)]O_4 with delta = 0.05 and delta = 0.27 have been investigated with calorimetry at different applied fields. It is shown that a delta 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 delta approximate to 0 instead of ideal delta = 0.
©2022 by the author(s). Licensee MDPI The authors acknowledge ILL and the D1B-CRG (Ministerio de Ciencia, e Innovación, Spain) with proposal numbers CRG-2710, CRG-2797 and 5-31-274 2 for the beam time allocated at both the D1B and D2B instruments. This research has been funded by Spanish Ministries of Science Innovation and Universities and of Economy and Competitiveness by means of the AFORMAR (PID2019-109334RB), RTI2018-095303-B-C51 and RTI2018-095856-B-C21 projects. The support of the grants from the Community of Madrid numbers S2018/NMT-4381-MAT4.0-CM and P2018/NMT-4321 is also recognized.