Structure and Magnetic Properties of Bulk Synthesized Mn2−xFexP1−ySiy Compounds from Magnetization, 57Fe Mössbauer Spectroscopy, and Electronic Structure Calculations

The series of Mn2−xFexP1−ySiy types of compounds form one of the most promising families of magnetocaloric materials in term of performances and availability of the elemental components. Potential for large scale application needs to optimize the synthesis process, and an easy and rather fast process here described is based on the use of two main type of precursors, providing the Fe-P and Mn-Si proportions. The series of Mn2−xFexP1−ySiy compounds were synthesized and carefully investigated for their crystal structure versus temperature and compared interestingly with earlier results. A strong magnetoelastic effect accompanying the 1st order magnetic transition—as well as the parent phosphide–arsenides—was related to the relative stability of both the Fe magnetic polarization and the Fe–Fe exchange couplings. In order to better understand this effect, we propose a local distortion index of the non-metal tetrahedron hosting Fe atoms. Besides, from Mn-rich (Si-rich) to Fe-rich (P-rich) compositions, it is shown that the magnetocaloric phenomenon can be established on demand below and above room temperature. Excellent performance compounds were realized in terms of magnetic entropy ∆Sm and adiabatic temperature ∆Tad variations. Since from literature it was seen that the magnetic performances are very sensitive to the synthesis process, correspondingly here a new effective process is proposed. Mössbauer spectroscopy analysis was performed on Mn-rich, equi-atomic Mn-Fe, and Fe-rich compounds, allowing determination of the distribution of hyperfine fields setting on Fe in the tetrahedral and pyramidal sites, respectively. Electronic structure calculations confirmed the scheme of metal and non-metal preferential ordering, respectively. Moreover, the local magnetic moments were derived, in fair agreement with both the experimental magnetization and the Fe contributions, as determined by Mössbauer spectroscopy.


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A local structure distortion index which can affect the tetrahedral site in which the sensitive Fe-metal (weak-ferro versus strong-ferro character), possibly linking the magnetic correlations with magnetoelastic couplings; -Optimized route to process intermetallic materials, comprising amounts of phosphorous, easily and safely, to deliver bulk samples with high magnetocaloric performances; -Better understanding the magnetic properties from correlated Mössbauer spectroscopy and electronic structure calculations.
For that, apart from the equi-atomic MnFeP 0.5 Si 0.5 , we have focused both on Fe-poor and Fe-rich compounds, with some variation on the P versus content, since the ratios Mn/Fe and P/Si are effective for drastically monitoring the Curie temperature via exchange couplings, steric effects, etc.

Materials and Methods: On Synthesis Routes
The used method to synthesize the ternary phosphides and arsenides was the conventional route of solid-state reaction, where the powder of the considered elements are intimately mixed then placed in an evacuated silica ampoule and annealed at optimized temperatures of reaction that are usually higher than 1100 • C [4,6,7,24]. However, although this technique was successfully employed in the past, its utilization in certain cases is delicate, particularly because of the high vapor pressure of phosphorus at low temperatures, as well as the transformation of its red to white allotropic form occurring close to 450 • C [24,33]. On the other hand, it is worthy to recall that the efforts to perfectly substitute and combine silicon to the TT'X series were made unsuccessful using solid-state reaction routes, even after several months of high temperature treatments [6]. Effectively, at temperature high enough to expect the compounds to homogenize by annealing treatments, traces of binary or ternary based silicide impurities remained visible, since the formation enthalpy of Si-octahedral coordinated T-element appears more favorable than that of the tetrahedral site of the here considered hexagonal (and isotype) TT'X compounds [1]. In order to overpass the associated difficulty with the phosphorus vapor pressure, a group of Amsterdam University has successfully proceeded to low temperature solid-state synthesis by mechanical alloying using the ball milling (BM) method [25][26][27]. Next, the BM method has allowed realization of the low temperature substitution of arsenic by silicon (and Ge) to synthesize the isotype Mn 2−x Fe x P 1−y Si(Ge) y compounds [25,26,29]. It was confirmed that almost pure ternary compounds can be achieved only if Si occupies at maximum the 2c site, with P being restricted to the 1b site [12,30,34]. However, the BM procedure is not an effective route to prepare economically large amounts of MC materials. Additionally, production of extra fine particles before the annealing For all compounds discussed here, XRD patterns were recorded using a reflexion diffractometer Siemens d5000R (Siemens, Berlin and Munich, Germany) and a transmission diffractometer. The reflexion diffractometer (R) working at λ K (Co) = 1.791 Å is equipped with a backscattering graphite (0002) monochromator and the transmission diffractometer (T) working at λ K (Cu) = 1.5412 Å is equipped with a Ge (111) backscattering monochromator. Typical diffraction patterns of MnFeP 0.50 Si 0.50 (a) and Mn 0.6 Fe 1.4 P 0.6 Si 0.4 (b) are shown Figure 1.
From a profile refinement method, the metal atom positions and co-ordinations were found to be in good agreement with literature [25][26][27][28][29][30]. The structure parameters of both samples are reported Table 1. Appendix A: Figure A1 shows the structure and Table A1 set inter-atomic distance examples.
If the compounds appear to be almost pure and well crystallized, the X-ray diffraction technique does not allow refining with either the metal or the non-metal atom distribution or disorder between their respective two possible crystal sites, 3f and 3g on one side and 1b and 2c on the other side. In Table 1 the relative occupancies are attributed according to the experimental rules reported in [1,13], Crystals 2019, 9, 37 5 of 27 being in agreement with the more recent literature. However, few metal and non-metal disorders can be expected, as was mentioned in [28,29,31,34,36]. Crystals 2019, 9, 37 5 of 28 If the compounds appear to be almost pure and well crystallized, the X-ray diffraction technique does not allow refining with either the metal or the non-metal atom distribution or disorder between their respective two possible crystal sites, 3f and 3g on one side and 1b and 2c on the other side. In Table 1 the relative occupancies are attributed according to the experimental rules reported in [1,13], being in agreement with the more recent literature. However, few metal and non-metal disorders can be expected, as was mentioned in [28,29,31,34,36].   For these compounds, as for the other ones synthesized by induction melting using Fe-P and Mn-Si precursors, a few percent's impurities-if present (e.g., Mn 2 Fe 3 Si 3 or MnFe 2 Si type)-were identified using parallel JCPDS files (Joint Committee on Powder Diffraction Standards), thermomagnetic analysis (Curie temperature), and as SEM ZEISS-Ultra (Carl Zeiss, Oberkochen, Germany) + type JEOL JSM-840A (JEOL, Ltd. Akishima, Japan) equipped with Oxford EDX microanalysis (Oxford Instruments plc, Abingdon, UK) The cell parameters at room temperature and the purity level of the phases are shown in Table 2. To investigate the structures behavior versus temperature, a X'PERT PRO MPD PANalytical (PW-3710) θ-2θ diffractometer was used at λ K (Cu) = 1,5412 Å with a backscattering graphite (0002) monochromator (Malvern, Almelo, The Netherlands).
Two Anton Paar systems have enabled us to control the temperature of the samples within ±0.5 K. This ancillary equipment, filled with 5N purity Ar gas, are a TTK for temperatures ranging from 90 to 300 K and an HTK for temperatures ranging from 300 to above 500 K. Figure 2 presents a succession of XRD patterns recorded as a function of temperature for MnFeP 0.5 Si 0.5 . The crystal parameters a and c are found to markedly change their values in the temperature range 374-384 K. For these compounds, as for the other ones synthesized by induction melting using Fe-P and Mn-Si precursors, a few percent's impurities-if present (e.g., Mn2Fe3Si3 or MnFe2Si type)-were identified using parallel JCPDS files (Joint Committee on Powder Diffraction Standards), thermomagnetic analysis (Curie temperature), and as SEM ZEISS-Ultra (Carl Zeiss, Oberkochen, Germany) + type JEOL JSM-840A (JEOL, Ltd. Akishima, Japan) equipped with Oxford EDX microanalysis (Oxford Instruments plc, Abingdon, UK) The cell parameters at room temperature and the purity level of the phases are shown in Table 2. To investigate the structures behavior versus temperature, a X'PERT PRO MPD PANalytical (PW-3710) θ-2θ diffractometer was used at λK (Cu) = 1,5412 Å with a backscattering graphite (0002) monochromator (Malvern, Almelo, The Netherlands).
Two Anton Paar systems have enabled us to control the temperature of the samples within ±0.5 K. This ancillary equipment, filled with 5N purity Ar gas, are a TTK for temperatures ranging from 90 to 300 K and an HTK for temperatures ranging from 300 to above 500 K. Figure 2 presents a succession of XRD patterns recorded as a function of temperature for MnFeP0.5Si0.5. The crystal parameters a and c are found to markedly change their values in the temperature range 374-384 K. For clarity, only half of the patterns are plotted. The first order magnetic phase transition occurs in the 274-284 K range. Extra small lines belong to the MnFe2Si impurities, as mentioned in Figure 1a and reported in Table 2. For clarity, only half of the patterns are plotted. The first order magnetic phase transition occurs in the 274-284 K range. Extra small lines belong to the MnFe 2 Si impurities, as mentioned in Figure 1a and reported in Table 2.
Using the collection of XRD patterns recorded versus temperature, as shown in Figure 2, the cell parameters a (T), c (T), and the volume V (T) were determined and represented in Figure 3 (e.g., for MnFeP 0.5 Si 0.5 and Figure 4 for Mn 0.7 Fe 1.3 P 0.65 Si 0.35 ). The magnetoelastic effect illustrated here is quite similar to what was earlier reported for the MnFeP 1−y As y system [4,14] and then confirmed later in many works dedicated to Mn 2−x Fe x P 1−y Si y compounds [15][16][17]25].
Additionally, similar magnetoelastic behaviors were observed in the isotype series of Mn 2−x Fe x P 1−y Si y compounds [30]. These are typical characteristics of the deep crystal structure modifications accompanying a first order magnetic phase transition, usually leading to a strong magnetocaloric effect [25]. In all cases, the hexagonal cell compresses abruptly by~1.5% in the basal plane, it expands by~3% along the c-axis, and correspondingly there is almost no change of the cell volume [25,36]. Crystals 2019, 9, 37 7 of 28 Using the collection of XRD patterns recorded versus temperature, as shown in Figure 2, the cell parameters a (T), c (T), and the volume V (T) were determined and represented in Figure 3 (e.g., for MnFeP0.5Si0.5 and Figure 4 for Mn0.7Fe1.3P0.65Si0.35). The magnetoelastic effect illustrated here is quite similar to what was earlier reported for the MnFeP1−yAsy system [4,14] and then confirmed later in many works dedicated to Mn2−xFexP1−ySiy compounds [15][16][17]25].
Additionally, similar magnetoelastic behaviors were observed in the isotype series of Mn2−xFexP1−ySiy compounds [30]. These are typical characteristics of the deep crystal structure modifications accompanying a first order magnetic phase transition, usually leading to a strong magnetocaloric effect [25]. In all cases, the hexagonal cell compresses abruptly by ~1.5% in the basal plane, it expands by ~3% along the c-axis, and correspondingly there is almost no change of the cell volume [25,36].  Using the collection of XRD patterns recorded versus temperature, as shown in Figure 2, the cell parameters a (T), c (T), and the volume V (T) were determined and represented in Figure 3 (e.g., for MnFeP0.5Si0.5 and Figure 4 for Mn0.7Fe1.3P0.65Si0.35). The magnetoelastic effect illustrated here is quite similar to what was earlier reported for the MnFeP1−yAsy system [4,14] and then confirmed later in many works dedicated to Mn2−xFexP1−ySiy compounds [15][16][17]25].
Additionally, similar magnetoelastic behaviors were observed in the isotype series of Mn2−xFexP1−ySiy compounds [30]. These are typical characteristics of the deep crystal structure modifications accompanying a first order magnetic phase transition, usually leading to a strong magnetocaloric effect [25]. In all cases, the hexagonal cell compresses abruptly by ~1.5% in the basal plane, it expands by ~3% along the c-axis, and correspondingly there is almost no change of the cell volume [25,36].

Local Structure Distortion Index and Magnetic Polarization
When studying in details 4 isotypic compounds MnRuP, MnRuAs, MnRhP and MnRhAs, also comparing their crystal and magnetic parameters to the other hexagonal TT'X phosphides and arsenides, several general characteristics have been noticed [7]. Since, and specially for the hexagonal H3 polytype the cell volume is given as: 2 2 When studying in details 4 isotypic compounds MnRuP, MnRuAs, MnRhP and MnRhAs, also comparing their crystal and magnetic parameters to the other hexagonal TT'X phosphides and arsenides, several general characteristics have been noticed [7]. Since, and specially for the hexagonal H3 polytype the cell volume is given as: It was shown [7] that for a given transition metal atom T' (e.g., Ru) occupying the TET site, the relative variation of V TET can reach 14% while for Mn preferentially occuyping the PYR site (according to the general rules depicted in [1,3]) the relative volume variation of V PYR (when changing the metal T') is less, at most 9.5% [7]. In fact, the tetrahedral site is distorted: the in-plane edge joining 2 non-metal neighbors X(2c) being written as d 2c−2c (or p for planar edge) and the axial edge length d 1b−1b (axial edge, equal to the c cell-parameter) allows define a TET-distortion coefficient: The δ (%) measured values in several phosphides and arsenides in ref [7] are as different as +4.07 for MnRuAs (F), +2.43 for MnRuP (AF) and, −2.29 for ZrRuAs (non-magnetic). According to criteria (2), additionally to Figures 3 and 4 quantifying the magnetoelastic phenomenon in the hexagonal Mn 2−x Fe x P 1−y X y (X = As, Si, Ge) known to exhibit large MCEs, we have represented the thermal behavior of δ (otherwise called dp/da − 1) for the two of here studied compounds in Figure 5. If all the calculated interatomic distances exhibit some anomalous but tedious variation at Tc, Figure 5 shows that the δ index involving the distortion of the TET site provides very pertinent information that supports the strong magnetoelastic effect accompanying the magnetic phase transition. As a confirmation, we have verified that in the MnFeP 1−y As y series, a fairly similar anomaly in δ(T) to that measured (e.g., for MnFeP 0.5 Si 0.5 as shown in Figure 5) takes place in the MnFeP 0.65 As 0.35 compound. Appendix A- Table A2 displays some inter-atomic distances at 300 and 465 K for MnFeP 0.5 Si 0.5 where appears that distances related to the tetrahedron are of the most modified. Abrupt changes of the TET site dimensions, here mostly occupied by Fe, should be ascribed to the magnetic polarization instability of the Fe (TET) that consequently affects the strength of the MCE. According to crystal electric field (CEF) considerations [38], the tetrahedral symmetry of the CEF leads to the degeneracy of the d shell to form a doublet (d3z 2 -r 2 ) − (dx 2 -y 2 ) of lower energy and a triplet (dxy) − (dyz) − (dzx) containing the non-appaired electrons [7]. The distortion of the tetrahedral sites raises partly the degeneracy of the later orbital states, which would induce variations of the local (Fe mainly) magnetic moment. The existence of a magnetoelastic effect directly correlated to the degree of distortion of the TET site allows understanding the fundamental mechanisms behind the magnetic polarization of Fe (uniquely or mainly) occupying this site. In the TT'X series, there is no specific metal to non-metal distance, since both the PYR and TET volumes vary with the nature of the T' atom. Consequently, the deformation of the TET site is mainly related to the nature of the T and T' atoms [7].
Recently, the hypothesis of a CEF splitting was re-considered via DOS-partial resolution of S Abrupt changes of the TET site dimensions, here mostly occupied by Fe, should be ascribed to the magnetic polarization instability of the Fe (TET) that consequently affects the strength of the MCE. According to crystal electric field (CEF) considerations [38], the tetrahedral symmetry of the CEF leads to the degeneracy of the d shell to form a doublet (d3z 2 -r 2 ) − (dx 2 -y 2 ) of lower energy and a triplet (dxy) − (dyz) − (dzx) containing the non-appaired electrons [7]. The distortion of the tetrahedral sites raises partly the degeneracy of the later orbital states, which would induce variations of the local (Fe mainly) magnetic moment. The existence of a magnetoelastic effect directly correlated to the degree of distortion of the TET site allows understanding the fundamental mechanisms behind the magnetic polarization of Fe (uniquely or mainly) occupying this site. In the TT'X series, there is no specific metal to non-metal distance, since both the PYR and TET volumes vary with the nature of the T' atom. Consequently, the deformation of the TET site is mainly related to the nature of the T and T' atoms [7].
Recently, the hypothesis of a CEF splitting was re-considered via DOS-partial resolution of S and P-levels, after pointing out the inequivalent distances of Fe-Si and Fe-P around the TET site [12]. In fact, this latest derivation was said to be inconclusive, since the 3d electrons are engaged in different types of bonding-moreover, with the metal neighbors too. However, it is worth recalling that the distortion of the TET site is not specific to phosphide-silicides, but also to phosphide-arsenides, and pure phosphides and arsenides.
In the (ferromagnetic) MnT'X phosphides and arsenides, Mn preferentially occupying the PYR sites shares a markedly high magnetic moment of~3.0 µ B . In contrast, since Fe prefers to occupy the TET site, it shares a much smaller magnetic moment of less than 2 µ B . Upon the magnetoelastic phenomenon occurring at a first order critical temperature, the magnetic moment of Mn appears moderately affected. Conversely, the magnetic moment of Fe can severely drop down (e.g., F to AF transition in MnFeP 1−x As x ) [15]; it can even completely collapse, the same as for the Ferro-Para transitions of MnFeP 1−x As x [14,15], MnFeP 1−x Si x [34], and Fe 2−x Ru x P systems [10,20]. In terms of magnetic correlations, as investigated using neutron diffraction or 57 Fe Mössbauer spectroscopy [14][15][16], it results in long range AF magnetic orderings in the first case, and it evidences in the second case a magnetic scattering up to temperatures far above the so-called Curie temperature [14,40]. For the presently studied compounds, we consider the situation is made somewhat different (1) because of the more metallic character of Si reference to P(As) and (2) because of the preferential occupancy of the 2c sites by Si, when P occupies the 1b site. Consequently, the hexagonal crystal structure appears, forming a 2D stacking of (001) planes, with the Mn-P planes alternating with Si(P)-Fe ones. The main crystallographic and magnetic features corresponding to the cases of Mn 2−x Fe x P 1−y Si y are considered in a following chapter dedicated to their electronic structure calculations.

Magnetization Properties and MCE Characteristics of Bulk Synthesized Mn 2−x Fe x P 1−y Si y Compounds
Magnetization characterizations have been performed using two extraction-type magnetometers by integrating a magnetic flux variation in a series/opposition system of bi-coils. The low temperature equipment allows collection of the magnetization data over a temperature range from 1.5 to 320 K in 0 to 10 T fields generated by a superconducting magnet. The high temperature equipment provides a magnetic field span from 0 to 7 T, enabling us to record magnetization over the temperature range between 200 and 850 K. The resolution of both magnetometers is better than 10 −7 Am 2 . The records that allow determination of the transition temperature were operated under a weak magnetic field (typically 0.05 T), while the saturation magnetization was systematically recorded at 5 K. In order to determine the magnetic entropy variation, a set of magnetic isotherms were recorded by steps of 2 to 5 K (depending on the temperature range) under fields up to 10 T. The data were used to deliver the MCE in terms of the entropy change via a numerical integration of the well-known Maxwell relation given by [52]: The adiabatic temperature change can be evaluated according to the following equation: A Quantum Design PPMS equipped with a 0-9 T superconducting coil was used to determine C p,H at constant pressure. The magnetic contribution to the specific heat (assuming a negligible contribution of the electronic term) was determined by using a non-magnetic reference, the polytype phosphide Co 2 P (assuming a similar phonon contribution). Furthermore, direct measurements of ∆T ad were performed using homemade equipment developed at Néel Institute with the support of the company CoolTech Applications (Holtzheim, France). However, in order to deliver real quantitative comparisons, this type of measurement needs disposal of strictly well shaped and similar sized samples [53].

Tc Determination and Isothermal Magnetization Measurements
Examples of magnetic ordering temperature, as determined by application of a 0.05 T field and plotting the derivative of the magnetization traces, are displayed in Figure 6. It appears that for both Mn-rich and Si-rich compounds, the ordering temperature falls down to room temperature, while for Fe-rich and P-rich formula, the compounds order above room temperature. In fact, the highest ordering temperatures were found occurring with the equi-atomic Mn/Fe and Si/P compositions, being comprised between 365 and 390 K, depending on the stoichiometry and the experienced annealing procedure by the samples.
A Quantum Design PPMS equipped with a 0-9 T superconducting coil was used to determine Cp,H at constant pressure. The magnetic contribution to the specific heat (assuming a negligible contribution of the electronic term) was determined by using a non-magnetic reference, the polytype phosphide Co2P (assuming a similar phonon contribution). Furthermore, direct measurements of ∆Tad were performed using homemade equipment developed at Néel Institute with the support of the company CoolTech Applications (Holtzheim, France). However, in order to deliver real quantitative comparisons, this type of measurement needs disposal of strictly well shaped and similar sized samples [53].

Tc Determination and Isothermal Magnetization Measurements
Examples of magnetic ordering temperature, as determined by application of a 0.05 T field and plotting the derivative of the magnetization traces, are displayed in Figure 6. It appears that for both Mn-rich and Si-rich compounds, the ordering temperature falls down to room temperature, while for Fe-rich and P-rich formula, the compounds order above room temperature. In fact, the highest ordering temperatures were found occurring with the equi-atomic Mn/Fe and Si/P compositions, being comprised between 365 and 390 K, depending on the stoichiometry and the experienced annealing procedure by the samples.

MCE Characterizations
Systematic magnetic isotherms were recorded in the temperature range around the ordering temperature on all the studied compounds. Figure 7 illustrates these records for both Mn-and Si-rich and Fe-and P-rich formula (i.e., Mn 1.4 Fe 0.6 P 0.3 Si 0.7 , Mn 1.3 Fe 0.7 P 0.35 Si 0.65 , and Mn 0.7 Fe 1.3 P 0.65 Si 0.35 ). Interestingly the latter compound exhibits a more pronounced metamagnetic character. The highest saturation level corresponds to the equi-atomic metal and non-metal formula, displaying also the highest Curie temperature, as reported in Table 3. According to Equation (3), the change of magnetic entropy was numerically derived for all the compounds and represented in Figure 8, which is compared to the equi-atomic compound of MnFeP 0.50 Si 0.50 formula. However, for clarity, the entropy change is only reported in Figure 8b for 0 to 1 T and 0 to 5 T field variations.
The mostly ferromagnetic exchange forces issued from the Fe sites and a marked balance between F and AF couplings, leading to a global metamagnetic behavior, was observed and deeply discussed in several papers as one of the main magnetic characteristics of the Mn 2−x Fe x P 1−y X y series (with X = As, Si, Ge) [14][15][16]23,29,30,32,[42][43][44][45][46].
To determine the adiabatic temperature variation ∆T ad using Equation (4), specific heat measurements were undertaken under a zero-magnetic field as well as under magnetic fields by using Quantum Design PPMS facilities. In order to estimate the magnetic field contribution only, the non-magnetic and parent reference pnictide Co 2 P was measured first. Figure 9a shows the three C P measurements under a zero-magnetic field for Mn 1.3 Fe 0.7 P 0.35 Si 0.65 , Mn 0.7 Fe 1.3 P 0.65 Si 0.35 , and Co 2 P (as a reference). The magnetic contributions to the total specific heat are plotted in Figure 9b for the two Mn-Fe phosphide-silicides. Finally, the adiabatic temperature variations were determined for the same samples and shown in Figure 10a. In Figure 10b is displayed the ∆T ad experienced by the MnFeP 0.5 Si 0.5 under several magnetic field variations, for comparison.       The magnetic and magnetocaloric characteristics are displayed in Table 3. According to the latter, it can be seen that from the magnetization analysis at 5 K, Mn 1.30 Fe 0.70 P 0.35 Si 0.65 and Mn 0.70 Fe 1.30 P 0.65 Si 0.35 exhibit reduced Ms values when compared to other members of the series. In fact, a superimposed "susceptibility" (slope) for about 5% in magnetization was found for fields varying from 0 to 10 T. One can anticipate that some AF couplings could have taken place for these two samples, breaking an easy approach to the saturation state. All the values reported in Table 3 agree with those determined earlier by Ou and Dung for Mn 2−x Fe x P 1−y Si y compounds having similar or close compositions (e.g., by the group of Delft) [41,43,49].
For the equi-atomic formula MnFeP 0.50 Si 0.50, the reported values in Table 3 correspond to two "interesting" samples (* and **) that were prepared with little changes in the precursor combination. After the annealing procedure, it appears that this formula could rapidly unveil different magnetic characteristics, as shown in Figure 11 for ∆S m variations. This means that the nominal composition, the effective resulting composition, and the annealing conditions can play a very important and critical role in the real distribution of metal and non-metal elements at their respective crystal sites. These aspects could impact significantly the expected final magnetic characteristics, as reported and discussed in [45,48]. Appendix A- Figure A2 shows for atomized and highly disordered MnFeP 0.50 Si 0.50 samples, no magnetoelastic effect is observed at T C in agreement with that is shown Figure 11.  The magnetic and magnetocaloric characteristics are displayed in Table 3. According to the latter, it can be seen that from the magnetization analysis at 5 K, Mn1.30Fe0.70P0.35Si0.65 and Mn0.70Fe1.30P0.65Si0.35 exhibit reduced Ms values when compared to other members of the series. In fact, a superimposed "susceptibility" (slope) for about 5% in magnetization was found for fields varying from 0 to 10 T. One can anticipate that some AF couplings could have taken place for these two samples, breaking an easy approach to the saturation state. All the values reported in Table 3 agree with those determined earlier by Ou and Dung for Mn2−xFexP1−ySiy compounds having similar or close compositions (e.g., by the group of Delft) [41,43,49].
For the equi-atomic formula MnFeP0.50Si0.50, the reported values in Table 3 correspond to two "interesting" samples (* and **) that were prepared with little changes in the precursor combination. After the annealing procedure, it appears that this formula could rapidly unveil different magnetic characteristics, as shown in Figure 11 for ∆Sm variations. This means that the nominal composition, the effective resulting composition, and the annealing conditions can play a very important and critical role in the real distribution of metal and non-metal elements at their respective crystal sites. These aspects could impact significantly the expected final magnetic characteristics, as reported and discussed in [45,48]. Appendix- Figure A2 shows for atomized and highly disordered MnFeP0.50Si0.50 samples, no magnetoelastic effect is observed at TC in agreement with that is shown Figure 11.
Here, three compounds were selected to probe the local magnetic properties of the Mn 2−x Fe x P 1−y Si y series from Fe-poor to Fe-rich sides (i.e., Mn 1.4 Fe 0.6 P 0.3 Si 0.7 , MnFeP 0.5 Si 0.5 , and Mn 0.7 Fe 1.3 P 0.65 Si 0.35 ) by using 57 Fe Mössbauer spectroscopy. The spectra were recorded in transmission geometry in a bath cryostat at temperatures T = 310, 250, 200, 150, and 84 K. The temperature stabilization was 0.1 K. The obtained spectra were fitted using MOSSMOD or WinNorm programs, assuming two or three local Fe sites, characterized by isomer shift and quadrupole splitting values within each site. A Gaussian distribution of the magnetic hyperfine field was assumed. The spectra recorded between 84 and 310 K exhibited distributions of the hyperfine magnetic fields acting on the Fe located at tetrahedral 3f or pyramidal 3g sites of the hexagonal structure. The impact of the local non-metal (P and Si) and metal (Mn and Fe) neighborhood of Fe in terms of magnetic properties was investigated. At first, the influence of the 50% substitution of Si to P at the 2c position of the Mn 2−x Fe x P 1−y Si y structure on the Fe local magnetic characteristics was examined. For the equi-atomic composition, in principle Fe exclusively occupies the 3f position, while Mn occupies the 3g position [6,[13][14][15][16]36,57]. Then, modifications of the magnetic intra-and inter-atomic correlation of Fe by nearest Fe metal neighbors were studied in Mn 1.4 Fe 0.6 P 0.3 Si 0.7 , where 40% of Mn substitutes to Fe at the 3f position and reciprocally in Mn 0.7 Fe 1.3 P 0.65 Si 0.35 , where 30% of Fe substitutes to Mn at the 3g position.

Results
The recorded spectra and the corresponding distributions of the hyperfine fields for the studied compounds are shown in Figure 12, from Fe-poor to Fe-rich formulas. The hyperfine parameters and the relative contributions of the fractions are collected in Table 4. For MnFeP 0.5 Si 0.5 (equi-atomic composition) the distribution of the magnetic field may be formally reproduced by the sum of two Gaussians with different isomer shifts. However, above 150 K, a small contribution of paramagnetic fraction of~7% can be seen. The spectra of the Fe-poor Mn 1.4 Fe 0.6 P 0.3 Si 0.7 are more complicated. At 84 K the entire distribution of the magnetic field may be reproduced by three Gaussians centered on significantly different values of average magnetic fields. Between 150 and 250 K, the spectra consist of one magnetic and two paramagnetic patterns. At 310 K, all the Fe moments are in a paramagnetic state.

57 Fe Mössbauer Spectroscopy Analysis
Several types of hexagonal and orthorhombic TT'X compounds have been successfully quantified in terms of site occupancy and magnetic polarization by using the 57 Fe Mössbauer spectroscopy [4,6,10,13,15,16,[54][55][56][57]. Here, three compounds were selected to probe the local magnetic properties of the Mn2−xFexP1−ySiy series from Fe-poor to Fe-rich sides (i.e., Mn1.4Fe0.6P0.3Si0.7, MnFeP0.5Si0.5, and Mn0.7Fe1.3 P0.65Si0.35) by using 57 Fe Mössbauer spectroscopy. The spectra were recorded in transmission geometry in a bath cryostat at temperatures T = 310, 250, 200, 150, and 84 K. The temperature stabilization was 0.1 K. The obtained spectra were fitted using MOSSMOD or WinNorm programs, assuming two or three local Fe sites, characterized by isomer shift and quadrupole splitting values within each site. A Gaussian distribution of the magnetic hyperfine field was assumed. The spectra recorded between 84 and 310 K exhibited distributions of the hyperfine magnetic fields acting on the Fe located at tetrahedral 3f or pyramidal 3g sites of the hexagonal structure. The impact of the local non-metal (P and Si) and metal (Mn and Fe) neighborhood of Fe in terms of magnetic properties was investigated. At first, the influence of the 50% substitution of Si to P at the 2c position of the Mn2−xFexP1−ySiy structure on the Fe local magnetic characteristics was examined. For the equi-atomic composition, in principle Fe exclusively occupies the 3f position, while Mn occupies the 3g position [6,[13][14][15][16]36,57]. Then, modifications of the magnetic intra-and inter-atomic correlation of Fe by nearest Fe metal neighbors were studied in Mn1.4Fe0.6P0.3Si0.7, where 40% of Mn substitutes to Fe at The spectra of the Fe-rich Mn 0.7 Fe 1.3 P 0.65 Si 0.35 below room-temperature were fitted by two magnetic sub-spectra with a Gaussian distribution of the magnetic fields with significantly different isomer shifts. At 250 K, one additional paramagnetic component was observed.

Data Analysis
The aim of the present Mössbauer spectra analysis is elucidation of the impact of the local surrounding Fe atoms on their magnetic properties. The analysis is divided into three steps. First, we discuss the role of the different non-metal Si and P configurations (MnFeP 0.5 Si 0.5 ), and next the similar role of d-metal (Fe, Mn,) configurations for the Mn-rich (Mn 1.4 Fe 0.6 P 0.3 Si 0.7, ) and the Fe-rich (Mn 0.7 Fe 1.3 P 0.65 Si 0.35 ) samples. For MnFeP 0.5 Si 0.5 , iron in the tetrahedral position may be coordinated by 2P-2Si, 3P-1Si, and 4P-0Si atoms. In the case of Mn 1.4 Fe 0.6 P 0.3 Si 0.7, the ratio P/Si is very close to 1 2 , and consequently there is almost one type tetrahedron formed by 2P-2Si. For the third studied compound, namely Mn 0.7 Fe 1.3 P 0.65 Si 0.35 , there are three types of tetrahedral sites with co-ordinations 2P-2Si, 3P-1Si, and 4P-0Si. In fact, it is seen that these different non-metal configurations weakly modify the hyperfine magnetic field but influence the s-electron density at the Fe nuclei, causing asymmetry of the Zeeman patterns, formally reproduced in the fitting procedure of the MnFeP 0.5 Si 0.5 spectra by the assumption of two magnetic sub-spectra. A similar result was reported for MnFeP 1−x As x [15,16].
The role of the Fe neighboring d-metal atoms is decisive for its magnetic state and consequently for the resulting exchange forces. For Mn 1.4 Fe 0.6 P 0.3 Si 0.7, Fe located at the 3f site has two nearest metal atoms (3f site) at 2689 Å [36]. Three different local configurations must be distinguished for Fe 3f : two Fe atoms with the probability 0.6 × 0.6 = 0.36, two Mn atoms with the probability 0.4 × 0.4 = 0.16, and one Fe and Mn atom with the probability 2 × 0.6 × 0.4 = 0.48. The next nearest and next-next nearest metal atoms are Mn only, located at 3g site. Such local configurations are seen as the three different magnetic fields observed at 84 K. The fraction with a hyperfine field of about 21 T should be assigned to the Fe-Fe-Fe configuration, as with MnFeP 0.5 Si 0.5 . It is interesting to recall that in the case of Mn 1.4 Fe 0.6 P 0.5 As 0.5 , three similar magnetic sub-spectra were found [6,58].
The Mn atoms at 3f sites weaken the ferromagnetic-mode coupling of the Fe magnetic moments and lowers the Curie point of the system, which is in agreement with the magnetic susceptibility measurements [18,57]. For the iron rich compound Mn 0.7 Fe 1.3 P 0.65 Si 0.35 , the spectra were decomposed into two sextets, assigned to two Fe sites. The component with significantly higher isomer shift and relative intensity of~23% (see Table 4) should be assigned to the Fe at the 3g position. The distribution of the magnetic field in both sites, due to the different local metal atom arrangement, is found weaker than that in the case of Mn 1.4 Fe 0.6 P 0.3 Si 0.7 . The Mössbauer spectroscopy investigations allow pointing out various magnetic states of Fe in the series. This may be explained by the different local metal atom configurations when varying the Mn/Fe ratio. For the equi-atomic compound MnFeP 0.5 Si 0.5 , Mn, and Fe are almost assigned to 3g and 3f positions, respectively, and Si exclusively occupies the 2c position. An almost regular distribution of magnetic interactions leads to support for the highest ordering temperature and the largest hyperfine field on the Fe 3f-site. Besides which, the variation of the P/Si ratio in the range 0.33-1 has a relatively weak impact on the Fe magnetic polarization and exchange couplings comparison made with the direct impact of relative occupation of the 3f and 3g by Fe and Mn respectively, namely when Fe occupies the octahedral 3f site.
According to a rather general relationshi experimentally found in such metal-type compounds formed between 3d and non-metal elements (such as Si, P, As, etc.) [59], one can estimate the local magnetic moment of Fe using the correspondence 1 µ B~1 4 T. The values deduced for Fe 3f are found in good agreement with what is anticipated from electronic structure calculations, as reported in Table 5. Table 6 allows compare the magnetic moments values of Mn and Fe with those found for parent hexagonal MnFeX (X = As; P 0.5 As 0.5 , P 0.7 As 0.3 ). Interestingly, it appears that for the P-Si systems (Table 5), the calculated magnetic polarization on Mn 3g (Fe 3f ) decreases (increases) by 0.2-0.3 µ B . This opposite changes should be related to the change of electronic configuration 3p2 (Si) to 3p3 (P, As) and relative electronegativity and not to a change of size of the non-metal atoms since approximately the radii are as 1, 1.1 and 1.2 Å for P, Si and As respectively. This seems supporting well, the impact of a CEF scheme, leading to a critical increase of the experimental saturation magnetization reported from Table 5 to Table 6. Note: * = non-fully saturated under 7 T should be due by some AF couplings at low temperature. Note: ** = not accounting for the slight polarization levels taking place on non-metals and at inter-sites.
However, the estimate for the Fe 3g magnetic moment in Mn 0.7 Fe 1.3 P 0.65 Si 0.35 appears too weak for 1 µB (see Table 5). In fact, from the saturation magnetization reported Table 3, it appears that this compound could exhibit a more complex magnetic structure than assumed for KKR-CPA calculations. Alternatively, it cannot be excluded that for such complicated structures the value of the hyperfine magnetic field is not strictly proportional to the Fe magnetic moment.

Computational Details
Electronic structure calculations of TT'X compounds and their alloys in relation to phase stability, magnetic, and magneto-caloric properties using the Green function Korringa-Kohn-Rostoker (KKR) method, were frequently discussed in our previous papers [60][61][62][63][64][65][66][67][68][69][70][71][72]. The KKR method belongs to the well-established DFT techniques, as widely operated by many authors [73,74]. However, in our computations, the novel quasi-linear algorithm was implemented [75]. In turn, the KKR technique combined with the coherent potential approximation (CPA) [74] appeared to be a very efficient tool to investigate the electronic properties of chemically disordered magnetic materials. In this paper, KKR-CPA has been applied to study the electronic structure of Mn 1−x Fe x P 1−y Si y solid solutions, aiming to enlighten their magnetic behaviors, as well as other interesting phenomena experimentally evidenced in these materials, such as the selective site substitution (Mn/Fe on 3g/3f sites and P/Si on 2c/1b sites) or the effect of a unit cell volume jump in the vicinity of Ferro-Para transition. Moreover, the spin-polarized KKR-CPA method was employed to calculate the electronic and magnetic behaviors of transition metal atoms (Mn, Fe), not only in the ferromagnetic state, but also in the so-called DLM state (disordered local moments), which can be regarded as a static model of a paramagnetic-like state. The crystal potential of the "muffin-tin" form was used, with l truncation on each atom up to l max = 3. The Perdew-Wang formula describing the exchange-correlation part of the crystal potential was employed [76]. For the crystal potentials converged below 0.1 mRy, spin-polarized total, site-decomposed, and l-decomposed density of states (DOS) were computed. The Fermi level (E F ) was precisely determined from the Lloyd formula [77]. Our experimental values of the cell parameters and the atomic positions [36] were used for KKR-CPA computations (see Tables 1 and 2). More theoretical details on KKR-CPA methodology can be found elsewhere [78].

Site Preference
Mn 0.6 Fe 1.4 P 0.6 Si 0.4 seems to be the right case, allowing the study of the selective occupancy of Fe, substituting Mn either on tetrahedral (3f) or pyramidal (3g) sites. For this purpose, three cases have been considered for the KKR-CPA total energy analysis: The lowest total energy was calculated for (ii) Fe/Mn distribution, while the other models of transition atoms occupancy were found to be less favorable due to the total energy (per atom) of 16 meV and 47 meV higher for (i) and (iii) models, respectively.
The KKR-CPA results remain in excellent agreement with experimental observation, showing that Fe atoms introduced in the hexagonal structure of Mn 2−x Fe x P 1−y Si y first occupy the tetrahedral 3f site, and when the latter are entirely filled (x > 1), the rest of Fe atoms go to the pyramidal 3g site. To some extent, the selectivity of the site occupancy for iron can be explained by comparing the site-decomposed DOS sites, as shown in Figure 13 for Fe and Mn on 3f and 3g. From calculations, it appears that it is energetically more beneficial for Fe atoms to substitute Mn on 3f than on the 3g site, since DOS shapes of Fe and Mn better match on 3f over a wide range of energy (well seen for spin-up electrons).
Also, the spin-down d-Fe DOS peak appearing near the Fermi level is much larger for the 3g site than the corresponding one on the 3f site. The KKR-CPA results remain in excellent agreement with experimental observation, showing that Fe atoms introduced in the hexagonal structure of Mn2−xFexP1−ySiy first occupy the tetrahedral 3f site, and when the latter are entirely filled (x > 1), the rest of Fe atoms go to the pyramidal 3g site. To some extent, the selectivity of the site occupancy for iron can be explained by comparing the site-decomposed DOS sites, as shown in Figure 13 for Fe and Mn on 3f and 3g. From calculations, it appears that it is energetically more beneficial for Fe atoms to substitute Mn on 3f than on the 3g site, since DOS shapes of Fe and Mn better match on 3f over a wide range of energy (well seen for spin-up electrons).
Also, the spin-down d-Fe DOS peak appearing near the Fermi level is much larger for the 3g site than the corresponding one on the 3f site. The latter corresponds to a more favorable situation from an energetic point of view. The site preference of Si substituting P was analyzed in the MnFeP0.5Si0.5 compound by considering three models of atoms distribution: (і) 0.75 P and 0.25 Si on 2c, 1.0 Si on 1b; (іі) 0.25 P and 0.75 Si on 2c, 1.0 P on 1b; (ііі) fully random distribution of both metalloids, i.e., 0.5 P and 0.5 Si on 2c and 1b sites.
The lowest energy was computed for configuration (ii), where Si occupies only the 2c site. The P/Si distribution within models (iii) and (i) are energetically less favorable, since the computed total energy is 16 meV and 36 meV higher, respectively. This KKR-CPA result is also well supported by the XRD refinement of the MnFeP0.5Si0.5 compound, evidencing the fact that Si atoms exclusively occupy the 2c site.

Magnetic Properties of Mn2−xFexP1−ySiy
Spin-polarized KKR-CPA calculations were performed for the following compounds: Mn0.6Fe1.4P0.6Si0.4, Mn0.7Fe1.3P0.65Si0.35, MnFeP0.5Si0.5, Mn1.3Fe0.7P0.35Si0.65, Mn1.4Fe0.6P0.3Si0.7, MnFeP0.5Si0.5. It is worthy to note that due to markedly different magnetic moments carried by the same elements occupying either 3f or 3g sites, it is expected that overall magnetic behaviors should depend on the relative concentration of Fe and Mn elements. On the other hand, the influence of the relative P and Si contents on magnetic behaviors seems to be less obvious. However, we will show that both factors play an important role in the formation of Mn2−xFexP1−ySiy magnetic characteristics, since the It is worthy to note that due to markedly different magnetic moments carried by the same elements occupying either 3f or 3g sites, it is expected that overall magnetic behaviors should depend on the relative concentration of Fe and Mn elements. On the other hand, the influence of the relative P and Si contents on magnetic behaviors seems to be less obvious. However, we will show that both factors play an important role in the formation of Mn 2−x Fe x P 1−y Si y magnetic characteristics, since the phosphorus differs by the number of electrons from the silicon by one, while only the transition metal atoms carry important magnetic moments. Hence, while the substitution of Mn by Fe mainly leads to the replacement of a stronger magnetic moment (~2.9 µ B on 3g) by a slightly weaker one (~2.4 µ B on 3g), the change in the mutual concentration of elements at the non-metal position (P/Si) leads to E F "scanning" on the existing polarized DOS function due to the change in the number of electrons in the system.
In this sense, the valence electron count (VEC) seems to be a useful quantity that enables us to simplify the comparison between the magnetic properties of

Conclusions and Perspectives
Both the parent Mn2−xFexP1−yAsy and Mn2−xFexP1−ySiy series of compounds that exhibit peculiar and various magnetic properties and specific compositions with the hexagonal Fe2P structure-type were demonstrated, sharing high magnetocaloric performances. The present challenges remain as: (1) contribute to fundamental knowledge for both series and (2) optimize the synthesis routes to

Conclusions and Perspectives
Both the parent Mn2−xFexP1−yAsy and Mn2−xFexP1−ySiy series of compounds that exhibit peculiar and various magnetic properties and specific compositions with the hexagonal Fe2P structure-type were demonstrated, sharing high magnetocaloric performances. The present challenges remain as: (1) contribute to fundamental knowledge for both series and (2) optimize the synthesis routes to point, we are aware that the presence of large hysteretic effects, combined with the inappropriate use of the Maxwell relation, would overestimate the entropy change exhibited by some samples [81]. This question will be addressed in a forthcoming communication. On the other hand, if the HF melting process appears a rather easy one, the homogenization procedure via a carefully executed annealing step remains mandatory to expect optimized performances. In support of the more fundamental analyses undertaken here to qualify the crystal and magnetic characteristics of the series, 57 Fe Mössbauer spectroscopy measurements and electronic structure calculations were developed. Three compositions were analyzed by using the 57 Fe Mössbauer spectroscopy: a Mn-rich, the Mn/Fe equi-atomic, and a Fe-rich formula. Interestingly, the local coordination in non-metal elements was found not essentially critical in terms of local polarization. The magnetic interactions with the number of next Fe neighbors played the most important role. In fact, the spectra were fairly decomposed in their different components, allowing allocation to the Fe 3f and Fe 3g well defined values, in agreement with obtained calculations from the electronic structure determination. This approach was used to compare the possible scheme of metal and non-metal crystallographic ordering. Unambiguously, it was confirmed that the Mn/Fe preferential occupations are for the 3g and 3f sites, respectively, while the P and Si preferential occupations are for the 1b and 2c sites, respectively.
The 3g moments on the PYR sites (either Mn only or Mn/Fe occupied) appear weakly decreased by the Si content, de facto up to y = 0.66. A similar situation occurs for the Fe 3f moment of the TET sites, with an increasing tendency. However, if both calculated variations remained rather limited, the values calculated for the Fe magnetic moments that were related to the 3f and 3g sites agree well with those found by Mössbauer spectroscopy, and the as-calculated total magnetization values were in fair agreement with the experimental values deduced from experimental magnetization measurements. Meanwhile, in spite of the large similarities in terms of numerical values for the local and global magnetic characteristics, the density of states calculated for Mn and Fe in MnFeP 0.5 Si 0.5 are significantly different and determine the effective attribution of the metal elements in one (3f) or the other (3g) site. All the fundamental characteristics, either experimentally or theoretically determined in the present analysis for various members of the Mn 2−x Fe x P 1−y Si y series, appear coherent, along with the multiple data from the reported literature.
Author Contributions: D.F. works as a solid state chemist and physicist (e.g., on magnetic and magnetocaloric materials), and participated in the synthesis, crystal structure, and magnetic analyses. He also supervised the work of S.H.-K. as PhD, and has written the original draft manuscript in direct collaboration with all contributors. S.H-K. participated in the synthesis, XRD collection, and bulk magnetic and Cp measurements up to their global analysis. P.d.R. works as a solid state chemist and physicist (e.g., on magnetic materials) and participated in the RT XRD measurements and SEM microscopy analysis. She was actively involved in the management of the S.H.-K. works. M.B. is a specialist of magnetocaloric materials and the analysis of their experimental properties and namely of the formal modeling of transition metal pnictides comprising the series MnFe(P,X). He participated in the evolution of the drafted manuscript. R.Z. is a solid state physicist working on thermodynamics of magnetic metal systems versus temperature and pressure. He validated the crystal structure and magnetic property investigations versus temperature. W.C. works as a PhD of R.Z. and recorded the XRD data and then analyzed the cell parameter behaviors versus temperature by using profile refinements methods. P.F. is a solid state physicist using 57 Fe Mössbauer spectroscopy and other methods for interpreting the bulk and dynamics of systems at micro-to atomic-scales (e.g., he is a specialist of thermal behavior of hyperfine parameters). J.S. is a solid state physicist, specialized in 57 Fe Mössbauer spectroscopy, thus building and managing the used experimental set-up. He has fitted and interpreted the resulting data. S.K. ( †) is a solid state and theoretical physicist, who has for a time developed and continuously improved very powerful codes for KKR-CPA calculations. He was actively associated in the present analysis, leading to clear-cut results. J.T. is a solid state physicist strongly involved in the present and related investigations on theoretical magnetic characterization on intermetallic compounds, allowing establish a relationship between bulk and atomic-scale peculiarities, with nuclear and hyperfine characteristics.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest. Figure A1. The crystal structure of the Mn2−xFexP1−ySiy compounds (Fe2P type, SG P-62m), showing the environments of the two metal sites (3f for TET, 3g for PYR) and the two non-metal sites at 1b and 2c positions. In fact, the index δ = d(2c-2c)/c − 1 is determined from the ratio of planar (p) and axial (a) edges of the tetrahedral site (TET). In fact, a direct and significant comparison is not obvious, because of the two species changing composition, and, moreover, due to the magnet-elastic effect, the changes must be expressed in an absolute temperature scale with reference to the ordering temperature that could higher or lower than RT. With substitution of Fe to Mn, the P-P and P,Si-P distances decrease by less than 1%. However the most marked changes are concerned the tetrahedral site containing iron, as it was found first for the Mn1−xFexP1−yAsy systems [14][15][16].  Figure A1. The crystal structure of the Mn 2−x Fe x P 1−y Si y compounds (Fe 2 P type, SG P-62m), showing the environments of the two metal sites (3f for TET, 3g for PYR) and the two non-metal sites at 1b and 2c positions. In fact, the index δ = d( 2c-2c )/c − 1 is determined from the ratio of planar (p) and axial (a) edges of the tetrahedral site (TET). In fact, a direct and significant comparison is not obvious, because of the two species changing composition, and, moreover, due to the magnet-elastic effect, the changes must be expressed in an absolute temperature scale with reference to the ordering temperature that could higher or lower than RT. With substitution of Fe to Mn, the P-P and P,Si-P distances decrease by less than 1%. However the most marked changes are concerned the tetrahedral site containing iron, as it was found first for the Mn 1−x FexP 1−y As y systems [14][15][16]. Once again, the interatomic distances related to the tetrahedra are revealed as sensitive to the magnetoelastic phenomenon. However, in all cases, the TET site is deformed but its volume varies by less than 2 × 10 −2 Å 3 , similarly to the relative cell volume variation ∆V/V at transition, as shown in the Figure 5. Besides the axial Mn-P distance decrease, the paramagnetic Mn shifts by~0.075 Å towards the apex of the PYR site. Correspondingly, the nearest Mn-Mn distances decrease by symmetry for 0.06 Å. This is fully coherent with the TET deformation expressed by the index δ = d( 2c-2c )/c − 1 as a driving force of the magnetoelastic distortion, with the a-cell parameter dropping down at T C conversely to the drop up of the c-cell parameter.
Crystals 2019, 9, 37 24 of 28 Once again, the interatomic distances related to the tetrahedra are revealed as sensitive to the magnetoelastic phenomenon. However, in all cases, the TET site is deformed but its volume varies by less than 2 × 10 −2 Å 3 , similarly to the relative cell volume variation ∆V/V at transition, as shown in the Figure 5. Besides the axial Mn-P distance decrease, the paramagnetic Mn shifts by ~0.075 Å towards the apex of the PYR site. Correspondingly, the nearest Mn-Mn distances decrease by symmetry for ~0.06 Å. This is fully coherent with the TET deformation expressed by the index δ = d(2c-2c)/c − 1 as a driving force of the magnetoelastic distortion, with the a-cell parameter dropping down at TC conversely to the drop up of the c-cell parameter. Figure A2. Example of a smooth transition in the parent compound MnFeP0.5Si0.5, directly received from atomization and ferromagnetically ordering close to the 390-400 K Plot of the δ = d(2c-2c)/c − 1 index versus temperature shows no noticeable magnetoelastic effect. leading to almost no variation of magnetic entropy at transition as reported in Figure 11. In fact, this atomized material exhibits ~12% of Mn3Fe2Si3 as impurity and some atomic disorders in the Fe2P-type structure, preventing an established collective magnetoelastic phenomenon. bbbbb T C Figure A2. Example of a smooth transition in the parent compound MnFeP 0.5 Si 0.5 , directly received from atomization and ferromagnetically ordering close to the 390-400 K Plot of the δ = d( 2c-2c )/c − 1 index versus temperature shows no noticeable magnetoelastic effect. leading to almost no variation of magnetic entropy at transition as reported in Figure 11. In fact, this atomized material exhibits 12% of Mn 3 Fe 2 Si 3 as impurity and some atomic disorders in the Fe 2 P-type structure, preventing an established collective magnetoelastic phenomenon.