Electronic entropy change in Ni-doped FeRh
Graphical abstract
Introduction
The determination of entropy changes in solids at phase transitions of different kinds is of major relevance for understanding fundamental phenomena in materials and a source of information for their design and optimization for applied purposes. Typical examples can be found in the phase transitions of magnetocaloric materials [1], shape memory alloys [2], or piezoelectrics/ferroelectrics [3]. The total entropy change is the result of several contributions coming from the ion lattice, magnetization changes, electrical polarization changes, or conduction electrons. Evaluating the different contributions is necessary to understand the transition processes. Particularly, the entropy associated with the conduction electrons is crucial in the understanding of correlated electron systems [4], including magnetic [5], semiconducting [6], and superconducting [7] materials. In that context, the experimental determination of thermodynamical quantities in low-dimensional systems is a matter of current interest [8].
Here, we investigate the first-order metamagnetic transition in Ni-doped α-FeRh. The transition from a low temperature antiferromagnetic (AF) phase to a high-temperature ferromagnetic (FM) phase [9], [10], [11] shows a large entropy change reaching J kg−1K−1 [12] and a change in lattice parameter [13], [14]. Different works attributed the origin of the transition to processes involving conduction electrons [9], [10], magnetic instability associated with magnon modes [15], or lattice instability [16]. The different entropy contributions to the phase transition were evaluated either theoretically [17] or experimentally using a set of proxy thin film samples (in the terminology used by Cooke et al.) for the different magnetically ordered states [18]. Recent theoretical studies addressed the importance of changes in electronic structure at the phase transition [19], and an additional barrierless martensitic transition was predicted to occur below about 90 K [20].
In this work, we studied the electronic part of that singular phase transition in a Ni-doped FeRh polycrystal using low-temperature heat capacity. In addition, using Seebeck and Hall coefficient measurements, the evolution of the entropy change with applied field was evaluated. The differences between calorimetric and electronic transport approaches are discussed. The Hall coefficient measurements indicate a complex magnetic behavior in the AF phase before the transition and show a small step at around 90 K which could be related to the recently theoretically predicted existence of an additional transition at approximately 90 K. The latter would need further investigation.
Section snippets
Evaluation of the electronic entropy
In the usual experimental approach, heat capacity measurements at low temperatures are performed and interpreted making use of the approximated series expansion , where γ is the electronic specific heat coefficient, are the lattice specific heat coefficients, and is the magnetic contribution to the specific heat. However, in the presence of a phase transition at higher temperatures, typically several samples of different compositions and different magnetic ordering
Experimental results
The experiments were performed on a bulk polycrystalline sample of composition (Fe0.96Ni0.02)Rh1.02 cut in rod shape with rectangular cross section. A thin slice cut off the rod was used for experiments. X-ray diffraction evidenced the well-ordered CsCl-type phase with the presence of the paramagnetic fcc phase. By means of scanning electron microscopy, the amount of the fcc phase was estimated to be approximately 6 vol%. Detailed description of the synthesis procedure can be found elsewhere
Discussion
According to the relation , the effective transported charge needs to be known to extract the entropy information from the Seebeck coefficient. In the case of a single-band material, the extraction of the electronic entropy would be straightforward. In the present case, however, we have the contribution of two carrier types in the FM phase. In the case of multiband conduction, and α are typically regarded as conductivity weighted averages over the contributing bands, different for
Conclusions
The electronic entropy of a Ni-doped FeRh polycrystal was determined using low-temperature measurements with applied magnetic fields. With the analysis of the Seebeck coefficient across the metamagnetic phase transition, we show that the entropy change associated with the conduction electrons is not constant. The applied magnetic field causes the electronic entropy change to increase up to 10% between 0.1 T and 6 T. This result sheds some light on the peculiar transition of FeRh alloys and
Data availability
The raw/processed data required to reproduce these findings cannot be shared at this time because of technical or time limitations.
Conflict of interest
The author declares that they have no conflict of interest.
Acknowledgments
The authors thank Dr. Sebastian Fähler for insightful discussions. TU Darmstadt acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant no. 743116—project Cool Innov).
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