Structure and Magnetic Properties of Bulk Synthesized Mn_2−xFe_xP_1−ySi_y Compounds from Magnetization, ⁵⁷Fe Mössbauer Spectroscopy, and Electronic Structure Calculations

Abstract

The series of Mn_2−xFe_xP_1−ySi_y 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 Mn_2−xFe_xP_1−ySi_y 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 ΔS_m and adiabatic temperature ΔT_ad 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.

1. Introduction

The series of pnictides related to the Fe₂P type, which we have studied for a long time, exhibit very unusual magnetic properties, as detailed in a series of reports [1,2,3]. In fact, these ternary compounds TT’X (T, T’ = transition metals, X = P, As, Si, Ge etc.) crystalize in one of three types of structures: orthorhombic (SG Pnma: O4), hexagonal (SG P-62m: H3), and tetragonal (SG P4₂/nmm: T2). The polytype structures, from the most to the least dense compacting modes of a unique Rhombus (R) block (with 4, 3, and 2 blocks successively), are formed from two X-tetrahedrons and two-X-pyramids coordinating T and T’ [1,4]. The compaction level of the structure directly impacts the magnetic characteristic of the polytypic series when T and T’ share magnetic trends. In fact, the tetragonal compounds, being mostly arsenides (X = As), exhibit antiferromagnetic (AF) characteristics [4,5], while the orthorhombic compounds, being mostly phosphides, exhibit typically non-collinear and long range magnetic ordering [6,7]. For the intermediately dense compounds of hexagonal Fe₂P type structure, ferromagnetic (Ferro) and long-range magnetic structures are observed. These typical behaviors were effectively found with the MnFeP_1−xAs_x [4] system, where in successive orthorhombic, hexagonal, and tetragonal structures, Mn occupies the CN5-coordinated site (pyramid: PYR) and Fe occupies the CN4-coordinated one (tetrahedron: TET). The non-collinear MnFeP AF-type of magnetic structure was solved in a simple orthorhombic AF-2c cell, but from more precise neutron diffraction data, a long-range magnetic ordering was established with M_Mn = 3.07 µ_B and M_Fe ~ 0.13 µ_B [7,8]. Besides, a O4 to H3 process was found occurring versus temperature [9].

The tetragonal, less dense MnFeAs was established early as having a collinear AF structure [5], then confirmed in [10] with M_Mn = 3.36 µ_B and M_Fe ~ 0.0 µ_B. Under high pressure, a denser hexagonal (P-62m) MnFeAs compound was stabilized and parallel experimental and electronic structure investigations revealed that both Mn and Fe share a magnetic moment with M_Mn = 3.14 µ_B and M_Fe = 1.54 µ_B, respectively [10]. Similarly, according to the increasing relative density of polytypes from T2 to H3 to O4, it is worth recalling that under pressure, the ferromagnetic H3 Fe₂P was transformed to a ferromagnetic O4 form [11]. If the Curie temperature was slightly diminished (by ~5 K), the hyperfine fields (~Fe moments) were markedly reduced (0.75 for PYR and 0.5 for TET sites). Obviously, similar transformations were recently found occurring in the Fe₂P_1−ySi_y system under high pressure [12].

For 0.15 < x < 0.66, the MnFeP_1−xAs_x system crystallizes within the hexagonal P-62m symmetry with Mn and Fe in 3g and 3f positions, respectively. X = P, As, occupy 1 and 2c positions [4]. According to size and electronegativity differences [1,13], the site selectivity [14,15,16] is respected and for the equi-atomic Mn/Fe composition, only a very little amount of metal disorder was noticed, but some P to As redistributions were found. A first order AF-F transition accompanied with a marked magnetoelastic effect was evidenced in the hexagonal MnFeP_1−xAs_x system. This transition line (P-rich side), where almost no volume change occurs (∆a/a~−1/2 ∆c/c), was found in the prolongation of the ferromagnetic to paramagnetic (Para) transition line (P-poor side). The long range incommensurate magnetic structure of the AF-type was solved only thanks to information gained both by neutron diffraction and ⁵⁷Fe Mössbauer spectroscopy [14,15,16]. It consists in both Mn-helix and Fe-sine arrangements with M_Mn = 2.40 µ_B and M_Fe = 0.45 µ_B, respectively. Such a complex magnetic structure was confirmed more recently [17]. The magnetic moment of Fe appears highly sensitive to the overall magnetic structure, the same as for the critical Fe₂P [2,16,17,18,19]. In contrast to the large Mn moment of 2.6–3.02 µ_B, that of Fe is found to be more than twice as large in the ferromagnetic state (1.20 µ_B) than in the AF state [13]. Moreover, the Fe moment is expected to depolarize in the paramagnetic state, in fair agreement with DFT-based calculations for Fe₂P and (Fe_2−xRu_x)₂P [20]. Accordingly, the reverse susceptibility markedly deviates from a typical Curie-Weiss law supported by short range ordering [4,14,16,21], suggesting a Moriya spin fluctuation regime [22] that was more recently confirmed by µ⁺SR investigations [23]. It is worth recalling that all hexagonal Fe₂P type magnetic materials forming a 2D stacking mode of Mn/Fe layers exhibit a strong deviation from a linear 1/χ behavior versus temperature, being in contrast with the parent orthorhombic Pnma compounds, which exhibit an overall random Mn-vs.-Fe distribution within a 3D network [4,24]. More interestingly, very outstanding properties were revealed in terms of magnetocaloric (MC) characteristics [25], then promoting the series of Mn_2−xFe_xP_1−yAs_y compounds among the best-known MC materials susceptible of application in magnetic refrigeration at room temperature. Following this discovery, an increasing number of papers have been published [17,26,27]. However, because of the negative aspect of arsenic in such compounds that are considered for domestic application, efforts to substitute this poisoning element (e.g., by silicon or Ge) have been carried out while successfully preserving high magnetocaloric effect (MCE) levels [28,29,30]. Again, a considerable interest was raised for the parent series of Mn_2−xFe_xP_1−ySi(Ge)_y compounds, with both experimental and theoretical knowledge gained on structural and magnetic properties of the novel series [31,32,33,34,35,36,37,38,39,40].

The aim of the present contribution is not to provide an additional review report on the Mn_2−xFe_xP_1−ySi(Ge)_y compounds, for which considerable literature can be found for the last ten years, and exciting fundamental results and potentially high application properties were pointed out and for a part referenced in [41,42,43,44,45,46,47,48,49].

Based on lengthy practice and knowledge of the “generic” phosphide–arsenide series (not only comprising Mn and Fe as d-magnetic metals [3]), we aimed focus on three main aspects to account for better knowledge of the new Mn_2−xFe_xP_1−ySi_y series. These are:

-

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_0.5Si_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.

2. 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−xFe_xP_1−ySi(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 step needs to process very carefully the BM powders. For more details about recent developments regarding the practical aspects of Fe₂P-type materials, we refer to the references [50,51].

Besides taking advantage of the atomization technique [28], several kgs of Mn_2−xFe_xP_1−ySi_y samples were synthesized as nano-crystalline powders using a Fe-P precursor and complementary amounts of Mn, Fe, and Si [35,36]. Unfortunately, some P-rich deposits were found in the condensation chamber, even after various annealing procedures, while it was highly challenging to obtain these materials in a single hexagonal phase. The resulting magnetic characteristics (not described here) were found to be far from those previously reported in the literature (e.g., synthesized by BM).

Next, various Fe-P precursors used as additives in steel metallurgy were tested for their relative stability at high temperature, since their formula is closer to a eutectic composition and contains binary phosphides Fe₂P and FeP. Tiny amounts of Fe₃P can be detected by microanalysis [36]. Tests of P-pressure vapor were conducted using Ta and Nb targets during the HF heating to melt Fe₂P or MnFe(P-Si), unveiling the formation of both TaP and NbP. Conversely, the same targets did not react in similar conditions when using pure Fe₂P [36]. Therefore, the synthesis of a perfect and well crystallized Fe₂P sample can be carried out from the Fe-P precursor and the corresponding addition of cleaned ~20–40 µm Fe-particles, by way of either solid state reaction or induction heating techniques. Next, stoichiometric and well crystallized Mn₃Si and Mn₅Si₃ were easily prepared by induction melting. Finally, combinations of these high-quality primaries Fe₂P, Mn₅Si₅, and Mn₃Si in calculated amounts, with a few complements of pure Fe, Mn, or Si if requested, has led to easy synthesis of the Mn_2−xFe_xP_1−ySi_y compounds, restricting y close to ≤2/3 for the optimum repartition of P and Si at the 1b and 2c sites of the P-62m type structure [36]. A two-step process means that first binary precursors are prepared by induction melting, thus stabilizing their own compositions, and second a ternary material is melted with limited risks of decomposition.

Then, an annealing procedure for 2–3 h at T > 1150 °C allows delivery of pure H3-type materials, provided that cooling was fast enough. Several parent compounds, such as those discussed in the present paper (Mn_1.40Fe_0.60P_0.30Si_0.70, Mn_1.30Fe_0.70P_0.35Si_0.65, MnFeP_0.50Si_0.50, Mn_0.70Fe_1.30P_0.65Si_0.35, and Mn_0.60 Fe_1.40P_0.60Si_0.40), were synthesized, using this easy induction melting procedure of Fe-P and Mn-Si based precursors [36]. Recently, batches of ~12 kg of (Mn-Cr)FeP_1−ySi_y were successfully prepared according to the two steps method, starting with a commercial Fe₈₀P₂₀ and different Mn₅Si₃ and Mn₃Si-type precursors prepared aside. A small amount of Cr was used to tailor the ordering temperature [37].

3. Results

3.1. Structure Analysis

3.1.1. Structure Characterization at Room Temperature

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_0.50Si_0.50 (a) and Mn_0.6 Fe_1.4P_0.6Si_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. Structural parameters of MnFeP_0.5Si_0.5 (I) and Mn_0.6 Fe_1.4P_0.6Si_0.4 (II).

Sites	Sample I	x	y	z	Sample II	x	y	z
3g	100% Mn	0.5967(1)	0.0	0.5	56% Mn + 44% Fe	0.598(8)	0.0	0.5
3f	100% Fe	0.2491(2)	0.0	0.0	100% Fe	0.268(6)	0.0	0.0
2c	P,Si	0.33333	0.66666	0.0	100% P	0.33333	0.66666	0.0
1b	P,Si	0.0	0.0	0.5	33.3% P + 66.6% Si	0.0	0.0	0.5

. Appendix A: Figure A1 shows the structure and

Table A1. A comparison of interatomic distances for two selected parent systems.

Interatomic Distances at 290 K [Å]
	MnFeP0.5Si0.5	Mn0.6Fe1.4P0.6Si0.4
Mn-Mn	3.267  x4	3.233  x4
Mn-Fe	2.716  x2 2.740  x4	2.619  x2 2.737  x2
Mn-P,Si Mn-P	2.509  x4 2.499  x1	2.503  x4 2.461  x1
Fe-P,Si Fe-P	2.371  x2 2.267  x2	2.268  x2 2.339  x2
Fe-Fe	2.673  x2	2.642  x2

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], 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., 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. Extra phases identified in Mn_2−xFe_xP_1−ySi_y synthesized by melting Fe-P and Mn-Si precursors.

Compounds	% Fe2P-Type (P-62m)	% Mn5Si3-Type (P63/mcm)	Cell Parameters (Å)
Mn1.40Fe0.60P0.30Si0.70	91	9	a = 6.139, c = 3.425
Mn1.30Fe0.70P0.35Si0.65	96	4	a = 6.053, c = 3.355
MnFeP0.50Si0.50	96	~4% MnFe2Si	a = 6.196, c = 3.309
Mn0.70Fe1.30P0.65Si0.35	99	<1	a = 6.101, c = 3.347
Mn0.60Fe1.40P0.60Si0.40	99	<1	a = 6.123, b = 3.334

.

3.1.2. Structure Characterization versus Temperature

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_0.5Si_0.5. The crystal parameters a and c are found to markedly change their values in the temperature range 374–384 K.

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_0.5Si_0.5 and Figure 4 for Mn_0.7Fe_1.3P_0.65Si_0.35). The magnetoelastic effect illustrated here is quite similar to what was earlier reported for the MnFeP_1−yAs_y system [4,14] and then confirmed later in many works dedicated to Mn_2−xFe_xP_1−ySi_y compounds [15,16,17,25].

Additionally, similar magnetoelastic behaviors were observed in the isotype series of Mn_2−xFe_xP_1−ySi_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].

3.1.3. 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:

V_Hex = 3V_R = 3(2V_PYR + 2V_TET), where V_PYR = a²·c·√3/18 and V_TET = a²·c·√3/36

(1)

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:

δ = d(_2c−2c)/d(_1b−1b) − 1

(2)

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 Figure 3 and Figure 4 quantifying the magnetoelastic phenomenon in the hexagonal Mn_2−xFe_xP_1−yX_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−yAs_y series, a fairly similar anomaly in δ(T) to that measured (e.g., for MnFeP_0.5Si_0.5 as shown in Figure 5) takes place in the MnFeP_0.65As_0.35 compound. Appendix A—

Table A2. A comparison of interatomic distances for MnFeP_0.5Si_0.at temperatures apart T_C.

	300 K (F)	465 K (P)
Mn-Mn	3.262  x4	3.203  x4
Mn-Fe	2.691  x2 2.758  x4	2.689  x2 2.763  x4
Mn-P	2.505  x2 2.505  x2 2.528  x1	2.533  x2 2.534  x2 2.455  x1
Fe-P	2.371  x2 2.267  x2	2.291  x2 2.335  x2
Fe-Fe	2.689  x2	2.712  x2

displays some inter-atomic distances at 300 and 465 K for MnFeP_0.5Si_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 (d3z²-r²) − (dx²-y²) 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−xAs_x) [15]; it can even completely collapse, the same as for the Ferro-Para transitions of MnFeP_1−xAs_x [14,15], MnFeP_1−xSi_x [34], and Fe_2−xRu_xP systems [10,20]. In terms of magnetic correlations, as investigated using neutron diffraction or ⁵⁷Fe 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−xFe_xP_1−ySi_y are considered in a following chapter dedicated to their electronic structure calculations.

3.2. Magnetization Properties and MCE Characteristics of Bulk Synthesized Mn_2−xFe_xP_1−ySi_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 Am². 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]:

$$\Delta S_m\left(T,H_2-H_1\right)=-{{\displaystyle \int }}_{H_1}^{H_2}{\left(\frac{\partial M}{\partial T}\right)}_{H}dH$$

(3)

The adiabatic temperature change can be evaluated according to the following equation:

$$\Delta T_{ad}\left(T,H2-H1\right)=-\underset{H1}{\overset{H2}{{\displaystyle \int }}}\frac{T}{C_{P,H}}{\mu }_0{\left(\frac{\partial M}{\partial T}\right)}_{H}dH$$

(4)

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 Co₂P (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].

3.2.1. 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.

3.2.2. 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_1.4Fe_0.6P_0.3Si_0.7, Mn_1.3Fe_0.7P_0.35Si_0.65, and Mn_0.7Fe_1.3P_0.65Si_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. Main magnetic and magnetocaloric characteristics measured on six members of the series Mn_2−xFe_xP_1−ySi_y versus decreasing values of the Mn/Fe ratio, * and ** samples are explicated Figure 11.

Compound	Fe/Mn	Si/P	Transition Order	TC (K)	MS (µB)	∆T hys (K)	−∆Smmax (J/kg K) 2 T–5 T	∆Tad (K) 2 T–5 T
Mn1.40Fe0.60P0.30Si0.70	2.333	2.333	F→P 1–2nd (?)	260	4.17	0	4.63–8.3	-
Mn1.30Fe0.70P0.35Si0.65	1.858	1.858	MET 1st	282	>2.87	0	11–15.5	3.6–6.8
MnFeP0.50Si0.50 *	1.0	1.0	MET 1st	365	3.95	18	15–30	7.6–20
MnFeP0.50Si0.50 **	1.0	1.0	MET 1st	382	3.77	18	24–58	8–16.1
Mn0.70Fe1.30P0.65Si0.35	0.538	0.538	MET 1st	318	>3.25	10	18.4–38	7.8–16.4
Mn0.60Fe1.40P0.60Si0.4	0.428	0.666	F→P 1–2nd (?)	394	4.05	6	4.1–8.5	1.1–2.5

. 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_0.50Si_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−xFe_xP_1−yX_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 Co₂P was measured first. Figure 9a shows the three C_P measurements under a zero-magnetic field for Mn_1.3Fe_0.7P_0.35Si_0.65, Mn_0.7Fe_1.3P_0.65Si_0.35, and Co₂P (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_0.5Si_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_1.30Fe_0.70P_0.35Si_0.65 and Mn_0.70Fe_1.30P_0.65Si_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−xFe_xP_1−ySi_y compounds having similar or close compositions (e.g., by the group of Delft) [41,43,49].

For the equi-atomic formula MnFeP_0.50Si_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_0.50Si_0.50 samples, no magnetoelastic effect is observed at T_C in agreement with that is shown Figure 11.

3.3. ⁵⁷Fe 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 ⁵⁷Fe 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 Mn_2−xFe_xP_1−ySi_y series from Fe-poor to Fe-rich sides (i.e., Mn_1.4Fe_0.6P_0.3Si_0.7, MnFeP_0.5Si_0.5, and Mn_0.7Fe_1.3 P_0.65Si_0.35) by using ⁵⁷Fe 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−xFe_xP_1−ySi_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_1.4Fe_0.6P_0.3Si_0.7, where 40% of Mn substitutes to Fe at the 3f position and reciprocally in Mn_0.7Fe_1.3 P_0.65Si_0.35, where 30% of Fe substitutes to Mn at the 3g position.

3.3.1. 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. Results of Mössbauer studies of the Fe-poor Mn_1.4Fe_0.6P_0.3Si_0.7 (columns 2 to 6), the equi-atomic compound MnFeP_0.5Si_{0.5 (}columns 7 to 11), and the Fe-rich Mn_0.7Fe_1.3P_0.65Si_0.35 (columns 12 to 16). Symbols are: T—temperature [K], <B>—average value of hyperfine field in the Gaussian distribution [T], σ—half-width distribution [T], IS—isomer shift vs. metallic iron [mm/s], QS quadrupole splitting [mm/s], and P—contribution [%].

T	<B>	σ	IS	QS	P	<B>	σ	IS	QS	P	<B>	σ	IS	QS	P
310	0 0 0	0 0 0	0.23 0.20 0.17	0.41 0.59 0	49 11 40	21.6 0 19.5	2.3 0 2.8	0.28 0.19 0.32	−0.22 0 −0.13	49 11 40	16.2 13.9 0	3.3 3.6 0	0.29 0.36 0.28	0.25 0.23 0.30	64 18 18
250	15.6 0 0	4.0 0 0	0.29 0.24 0.17	−0.18 0.58 0	50 10 40	22.6 0 20.8	2.4 0 2.6	0.31 0.23 0.37	−0.22 0 −0.12	50 10 40	19.3 16.1 0	3.0 3.6 0	0.37 0.44 0.30	0.06 0.1 0.29	72 21 7
200	19.1 0 0	3.3 0 0	0.33 0.29 0.19	−0.19 0.59 0	40 7 53	23.3 0 21.5	2.1 0 2.5	0.34 0.23 0.39	−0.23 0 −0.14	40 7 53	20.3 18.7	2.9 2.7	0.40 0.47	0.15 0.10	77 23
150	20.6 0 0	3.0 0 0	0.36 0.29 0.19	−0.19 0.59 0	43 10 47	23.8 0 21.9	2.1 0 2.5	0.37 0.29 0.42	−0.23 0 −0.14	43 10 47	19.9 18.6	2.8 2.5	0.41 0.48	0.14 0.07	77 23
84	21.6 9.5 1.9	2.7 3.2 2.5	0.40 0.31 0.21	−0.21 0.25 0.07	45 55	24.2 22.4	2.0 2.6	0.39 0.44	−0.24 −0.14	45 55	21.3 19.5	2.9 2.6	0.45 0.52	−0.15 0.07	77 23

. For MnFeP_0.5Si_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_1.4Fe_0.6P_0.3Si_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.

The spectra of the Fe-rich Mn_0.7Fe_1.3P_0.65Si_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.

3.3.2. 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_0.5Si_0.5), and next the similar role of d-metal (Fe, Mn,) configurations for the Mn-rich (Mn_1.4Fe_0.6P_0.3Si_0.7,) and the Fe-rich (Mn_0.7Fe_1.3 P_0.65Si_0.35) samples. For MnFeP_0.5Si_0.5, iron in the tetrahedral position may be coordinated by 2P-2Si, 3P-1Si, and 4P-0Si atoms. In the case of Mn_1.4Fe_0.6P_0.3Si_0.7, the ratio P/Si is very close to ½, and consequently there is almost one type tetrahedron formed by 2P-2Si. For the third studied compound, namely Mn_0.7Fe_1.3 P_0.65Si_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_0.5Si_0.5 spectra by the assumption of two magnetic sub-spectra. A similar result was reported for MnFeP_1−xAs_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_1.4Fe_0.6P_0.3Si_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_0.5Si_0.5. It is interesting to recall that in the case of Mn_1.4Fe_0.6P_0.5As_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_0.7Fe_1.3 P_0.65Si_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_1.4Fe_0.6P_0.3Si_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_0.5Si_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~14 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. Total (per formula) and site-decomposed magnetic moments (per atom) in selected compounds of Mn_2−xFe_xP_1−ySi_y, as calculated from Korringa Kohn Rostoker Coherent Potential Approximation KKR-CPA. Experimental magnetization is also given in the last column. All values are in μ_B. Valence Electron Concentration VEC is for the number of valence electrons in a compound (see text).

Compound	VEC	Total (cal.)	Mn3f	Fe3f	Mn3g	Fe3g	Magn. (exp.)
Mn1.4Fe0.6P0.3Si0.7	19.0	4.25	1.76	1.48	2.82	-	4.17
Mn1.3Fe0.7P0.35Si0.65	19.05	3.98	1.48	1.40	2.69	-	>2.85 *
MnFeP0.5Si0.5	19.5	4.30	-	1.49	2.97	-	3.77–3.95
Mn0.7Fe1.3P0.65Si0.35	19.95	4.04	-	1.41	2.92	2.44	>3.25 *
Mn0.6Fe1.4P0.6Si0.4	20.0	3.99	-	1.43	2.91	2.42	4.05

Note: * = non-fully saturated under 7 T should be due by some AF couplings at low temperature.

.

Table 6. Values of magnetic moments and magnetization found for the isotype MnFeP_1−yAs_y compounds of Fe₂P type.

Compound	VEC	Total (cal.)	Mn3f	Fe3f	Mn3g	Fe3g	Magn. (exp.)
MnFeAs (HP) [10]	-	>4.23 **	-	1.10	3.13	-	4.50
MnFeP0.5As0.5	-	>3.80 **	-	1.20	2.60	-	4.13
MnFeP0.7As0.3 [14]	-	>4.27 **	-	1.25	3.02	-	4.10

Note: ** = not accounting for the slight polarization levels taking place on non-metals and at inter-sites.

allows compare the magnetic moments values of Mn and Fe with those found for parent hexagonal MnFeX (X = As; P_0.5As_0.5, P_0.7As_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.

However, the estimate for the Fe_3g magnetic moment in Mn_0.7Fe_1.3P_0.65Si_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.

3.4. Electronic Structure Analysis

3.4.1. 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−xFe_xP_1−ySi_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 Table 1 and Table 2). More theoretical details on KKR-CPA methodology can be found elsewhere [78].

3.4.2. Site Preference

Mn_0.6Fe_1.4P_0.6Si_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:

(i)

0.9 Fe and 0.1 Mn on 3f, 0.5 Fe and 0.5 Mn on 3g;

(ii)

1.0 Fe on 3f, 0.4 Fe and 0.6 Mn on 3g;

(iii)

fully random distribution of TM elements, i.e., 0.5 Fe and 0.5 Mn on 3f and 3g sites.

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−xFe_xP_1−ySi_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 latter corresponds to a more favorable situation from an energetic point of view. The site preference of Si substituting P was analyzed in the MnFeP_0.5Si_0.5 compound by considering three models of atoms distribution:

(i)

0.75 P and 0.25 Si on 2c, 1.0 Si on 1b;

(ii)

0.25 P and 0.75 Si on 2c, 1.0 P on 1b;

(iii)

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 MnFeP_0.5Si_0.5 compound, evidencing the fact that Si atoms exclusively occupy the 2c site.

3.4.3. Magnetic Properties of Mn_2−xFe_xP_1−ySi_y

Spin-polarized KKR-CPA calculations were performed for the following compounds: Mn_0.6Fe_1.4P_0.6Si_0.4, Mn_0.7Fe_1.3P_0.65Si_0.35, MnFeP_0.5Si_0.5, Mn_1.3Fe_0.7P_0.35Si_0.65, Mn_1.4Fe_0.6P_0.3Si_0.7, MnFeP_0.5Si_0.5. 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 Mn_2−xFe_xP_1−ySi_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 Mn_2−xFe_xP_1−ySi_y with different concentrations. Consequently, the aforementioned features result in quite complex variations of electronic and magnetic properties, depending on the alloy composition. Although the change of VEC from 19.95 (Mn_0.6Fe_1.4P_0.6Si_0.4) to 20 (Mn_1.3Fe_0.7P_0.35Si_0.65) does not significantly impact the magnetization, nevertheless the behavior of electrons near the Fermi energy is clearly different (see Figure 14 and Figure 15).

4. Conclusions and Perspectives

Both the parent Mn_2−xFe_xP_1−yAs_y and Mn_2−xFe_xP_1−ySi_y 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 deliver materials for magnetic refrigeration applications, namely the second series without the non-friend arsenic element. Here, it is shown that starting from defined proportions of the three base precursors that are Fe-P, Mn₅Si₃, and Mn₃Si, combined with tiny amounts of elements such as Fe, Co, and Ge to refine the balance, the synthesis of the desired magnetocaloric performing formula can be easily achieved using a conventional high frequency melting process. Moreover, such a process can be up-scaled up to 10 kg batches.

The present paper focuses on five selected formula, namely Mn_1.40Fe_0.60P_0.30Si_0.70, Mn_1.30Fe_0.70P_0.35Si_0.65, MnFeP_0.50Si_0.50, Mn_0.70Fe_1.30P_0.65Si_0.35, and Mn_0.60 Fe_1.40P_0.60Si_0.40 from the Mn-rich side to the Fe-rich side. At the same time, the non-metal composition was chosen according to the metal one. Crystalline structure investigations were systematically conducted on the series of Mn-Fe phosphide-silicides, allowing retrieval of the strong magnetoelastic phenomena accompanying the Ferro-Antiferromagnetic and Ferro-Paramagnetic transformations, as pointed out earlier in the hexagonal Mn-Fe phosphide-arsenide series [4,14,15,16], and already pointed out elsewhere [25]. It was confirmed that again in the new series (P-Si), Mn(3g) and Fe(3f) prefer to occupy pyramidal (CN5) and tetrahedral (CN4) sites, respectively [25,36]. At the same time, the Si stoichiometry cannot overpass the ratio Si/P = ½, since the non-metal have to be repatriated into 2c and 1b positions of the hexagonal P-62m space group. This selective occupancy of Si results from steric consideration, since as mentioned above, PYR volume = 2 TET volume. In this context, it is worthy to remember that for the isotype Mn_2−xFe_xP_1−yAs_y system [4,14], the hexagonal domain composition is limited to y = 0.66.

Systematic studies devoted to the TT’X series (T and T’ = transition metals, X = P, As, Si, Ge), have enabled characterization of most of the hexagonal-type compounds exhibiting ferromagnetic characteristics, where magnetoelastic phenomena [4,14,15,16,25,26,27,28,29,34], up to a change in the crystal structure [79,80], accompany the change or the loss of magnetic exchange couplings. Three causes can be considered: (1) the preferential presence of Fe in the “smaller” TET site with rather short Fe-X distances; (2) the sensibility of the Fe moment (discussed in [42,44]) as a magnetic element at the limit of weak to strong ferromagnetic behavior; and (3) the layered metal/non-metal disposition in the successive [001]-planes, with Mn-P alternating to Fe-Si containing layers. The combination of these three factors leads to certain instability in the local magnetic polarization of Fe, and then in the Fe–Fe (and Fe–Mn) long- and short-range exchange couplings. Therefore, here it is proposed to consider a new index of local striction effect, expressed as δ = dp/da − 1, to be directly related to the strength of the magnetoelastic effect accompanying the change or the loss of Fe–Fe ferromagnetic correlations. Specifically, this concerns the tetrahedral site only, Fe dominantly occupying the 3f position, where dp expresses the variation in the 1b–1b distance (here only occupied by P atoms), and da expresses the variation in the 2c–2c distance (occupied by Si and P, in reference to the y value). In fact, the δ index refers to the relative elongation/contraction of the CN4 tetrahedral environment of the Fe planar/axial, according to the main axis of the structure. As a consequence, recalling Figure 3, Figure 4 and Figure 5, the thermal variation δ(T) leads to anticipation of the behavior of (T) and c (T) cell parameters at the first order magnetic transition. Since in these metal-type materials, the ionicity degree of the elements is not particularly marked, there are no specific reference T-X (T’-X) distances as there are for oxides and halides. Consequently, the full lattice relaxes smoothly at the transition when no marked magneto-volume phenomenon is observed. No abrupt changes, such as the measured d(T) along the magnetic transition in the parent orthorhombic series of TT’X compounds, were noted.

The induction melting synthesized compounds exhibit a well-defined magnetocaloric performance, as determined from ∆S_m and ∆T_ad measurements, which are the magnetic entropy and adiabatic temperature variations over the first order magnetic transition region. Concerning this 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, ⁵⁷Fe Mössbauer spectroscopy measurements and electronic structure calculations were developed. Three compositions were analyzed by using the ⁵⁷Fe 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_0.5Si_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−xFe_xP_1−ySi_y series, appear coherent, along with the multiple data from the reported literature.