# Phase formation, structure and magnetic properties of Ge substituted Fe2P compounds

L.L. Bao, H. Yibole, S. Erdmann, H.İ. Sözen, T. Klüner, F. Guillou

► To cite this version:

L.L. Bao, H. Yibole, S. Erdmann, H.İ. Sözen, T. Klüner, et al. Phase formation, structure and magnetic properties of Ge substituted Fe2P compounds. Solid State Sciences, 2025, 173, pp.108183. 10.1016/j.solidstatesciences.2025.108183. hal-05508681

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Submitted on 13 Feb 2026

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# Phase formation, structure and magnetic properties of Ge substituted Fe₂P compounds

L.L. Bao¹, H. Yibole¹, S. Erdmann², H. İ. Sözen²,³, T. Klüner², F. Guillou¹,⁴,*

1- College of Physics and Electronic Information, Inner Mongolia Key Laboratory of Applied Condensed Matter Physics, Inner Mongolia Normal University, 81 Zhaowuda Rd, Hohhot 010022, China

2- Institute of Chemistry, Carl-Von-Ossietzky University of Oldenburg, Oldenburg 26129, Germany

3- Mercedes-Benz Turk A.S., Orhan Gazi Mahallesi, Mercedes Bulvarı No 17/1, Esenyurt, Istanbul 34519, Turkey

4- Normandie University, ENSICAEN, UNICAEN, CNRS, CRISMAT, Caen 14000, France

*francoisguillou@unicaen.fr

## Abstract

Compounds crystallizing in the Fe₂P-type hexagonal structure are attracting interest as functional magnetic materials, including for the giant magnetocaloric effect displayed by Mn-rich (Mn,Fe)₂(P,Ge) quaternary compounds. In this work, we systematically investigate the structural and magnetic phase diagrams of *ternary* compounds Fe₂P₁-xGex (0 ≤ x ≤ 1.0) through both theoretical calculations and experiments, aiming to isolate and clarifying the consequences of Ge for P metalloid substitutions. Ge can substitute P within the hexagonal Fe₂P-type structure up to x ≈ 0.175. Beyond this limit, the hexagonal Fe₅Ge₃ phase forms, limiting the Ge content entering the Fe₂P phase and thereby defining the solubility limit. The appearance of secondary phases is associated with a predicted reduced formation energy of the Fe₂P-phase upon Ge substitutions. Theoretical calculations indicate that Ge for P substitution stabilizes a higher moment on Fe at the 3f site, leading to an increase in saturation magnetization, which is experimentally confirmed. Within the solubility range, the Curie temperature increases sharply up to ~550 K as the Ge content rises, while simultaneously inducing a magnetocrystalline anisotropy at room temperature. Powder X-ray diffraction on oriented samples indicates that Fe₁.₉₅P₁-xGex (0 ≤ x ≤ 0.1) exhibits a c-axis easy magnetic axis.

**Keywords:** Magnetism, Structure-property relationship, first-principles calculation, Hard magnets.
# I. Introduction

Transition metal (Mn,Fe)₂(P,X) compounds, with X = As, Ge, or Si, have attracted significant attention due to their large magnetocaloric effect, which positions them as competitive candidates for near room temperature magnetic cooling, along with other promising materials such as FeRh, Gd₅(Si,Ge)₄, La(Fe,Si)₁₃, Heusler, or MnMX alloys [1-9]. This interest stems from the quite unique first-order ferromagnetic transition of the Fe₂P binary parent, which is accompanied by discontinuous changes in lattice parameters while maintaining the hexagonal crystal symmetry (P-62m) [10]. Fe₂P is also of particular interest due to its substantial saturation magnetization (μ₀Mₛ ~ 1.03 T) and an exceptionally large uniaxial magnetocrystalline anisotropy for a transition metal compound (K₁ ~ 2.3 MJm⁻³) [11-12]. This renders Fe₂P-materials potentially competitive as rare-earth-free permanent magnets [13-19], and could be an alternative to more commonly considered Mn-based (MnBi, MnAl), Co-based, ordered Fe-Ni or Fe-N alloys [20-26]. The Curie temperature of the Fe₂P binary compound (T_c ≈ 211 K) is however too low for applications. In the 60's and 70's, increasing T_c was mainly achieved by Co or Ni for Fe substitutions [27-28]. The Fe₂P-type structure is formed from two inequivalent iron sites, 3f and 3g, forming layers stacked along the c axis and corresponding to tetrahedron and pyramidal environment of metalloid atoms, respectively. The metalloid elements also occupy two inequivalent sites, 2c and 1b, located in the 3f and 3g layers, respectively [10]. Recent investigations have shown that metalloid substitutions on P (or simultaneous Fe and P substitutions) offer a more promising approach to tuning the properties of Fe₂P compounds [13-19].

To develop magnetocaloric (Mn,Fe)₂(P,X) compounds, the optimization primarily consists in having a first-order ferromagnetic phase transition at the targeted operating temperature. In contrast, for Fe₂P permanent magnets, the primary concern is to maximize the Curie temperature and achieve a significant uniaxial anisotropy. Developing quaternary compounds based on Fe₂P for permanent magnets or magnetic cooling, therefore necessitates tailored strategies, which in turn requires preliminary knowledge of the influence of the substituting elements.

The structural and magnetic phase diagram of the Fe₂(P,As), Fe₂(P,B) or Fe₂(P,Si) ternary compounds have been studied and metalloid-substitutions systematically led to increased Curie temperature [19,29-30]. In contrast, the structure and properties of Fe₂(P,Ge) ternary compounds
remain vastly unexplored. Ge is classified as a critical supply element and is at first consideration, often regarded as undesirable for technological applications. Nevertheless, a detailed investigation of Ge substitutions is indispensable for drawing a comprehensive understanding of the structure-property relationships in Fe₂P-based compounds.

So far, studies of Ge as a substitute for P in Fe₂P have primarily focused on the magnetocaloric (Mn,Fe)₂(P,Ge) compounds. Ge was initially considered as a partial substitute for As in Mn₁.₁Fe₀.₉P₀.₇As₀.₃_yGe_y (y ≤ 0.3) and was found to be effective in raising the Curie temperature while preserving the hexagonal crystal structure [31]. Higher Ge substitutions, up to y = 0.5, further increase T_c, but also cause the phase transition to become second-order, thereby reducing the isothermal entropy change [32]. Temperature-dependent XRD confirmed a magnetoelastic phase transition, evidenced by discontinuities in a and c lattice parameters in the MnFe(P₀.₈₅Ge₀.₁₅) compound [33]. A first-order transition was also observed from temperature dependent Mössbauer data in Mn₁.₁Fe₀.₉P₁-yGe_y compounds, with the spectra being fitted by a random distribution of Ge on the non-equivalent 2c and 1b sites of the Fe₂P-type crystal structure [34]. Neutron powder diffraction on the quaternary Mn₁.₁Fe₀.₉P₀.₈Ge₀.₂ compound shows that Mn and Fe magnetic moments lay in the a-b plane, with Ge preferentially occupying the 2c site [35-36]. Neutron powder diffraction also pointed out the contribution of a long period antiferromagnetic order on the irreversible changes that occur during the first cooling process across the phase transition [37]. Finally, attempts were made to reduce the Ge content in magnetocaloric quaternary (Mn,Fe)₂(P,Ge) compounds to reduce the material cost [38].

All these studies concentrated on quaternary compounds exhibiting a giant magnetocaloric effect and did not provide a comprehensive understanding of Ge for P metalloid substitutions in Fe₂P. We therefore studied the phase formation, transition temperatures and evolution of the magnetism in ternary compounds Fe₂(P,Ge). Such a systematic exploration is actually necessary given that the final compound, Fe₂Ge, with a metal-to-metalloid ratio of 2:1, does not exist in bulk form, instead leading to the coexistence of the hexagonal Fe₅Ge₃ and Fe₃Ge alloys [39]. This situation can be anticipated to favor the appearance of competing crystal structures and to results in a limited solubility range.
## II. Experimental and theoretical methods

Sixteen Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub> (0 ≤ x ≤ 1.0) polycrystalline samples were prepared by solid state reaction in quartz ampule. First, stoichiometric quantities of elemental starting materials Fe (99.9%) and P (97.3%) powders, and Ge (99.99%) lumps are weighted and ball-milled in Ar filled stainless steel jars, by using a planetary ball mill at a speed of 360 rpm for 10 hours and a ball: material ratio of 5:1. The resulting powders were pressed into 10 mm-diameter pellets and sealed in Ar-filled quartz tubes (200 mbar). The samples were annealed at 900°C for 24 hours and furnace-cooled to room temperature.

For powder of X-ray diffraction and for magnetic orientation, the bulk samples were hand-crushed into fine particles and sieved to < 36 µm. For magnetic-field alignment, the powders were mixed with epoxy in a 1:1 mass ratio and poured into a flat-plate mold. The sample was then placed in a μ<sub>0</sub>H = 1.1 T magnetic field (Halbach array) at room temperature until the epoxy had fully cured.

Powder XRD patterns were collected on a PANalytical Empyrean diffractometer using Cu-Kα radiation in the 2θ range 20–90° and Rietveld refinements performed using the Fullprof software [40]. Scanning electron microscopy (SEM) coupled with x-ray fluorescence analysis (EDX) were carried out using a Hitachi SU8010 microscope equipped with an Oxford Instruments Energy Dispersive X-ray Spectroscopy System (using an acceleration voltage of 15 keV). Differential scanning calorimetry measurements were carried out on a TA instruments DSC2500. Magnetic measurements at 5 K and 300 K were conducted using the vibrating sample magnetometer option of a Quantum Design Physical Property Measurement System 9 T. High-temperature magnetic measurements (T > 400 K) were performed in a Lakeshore VSM equipped with a high-temperature furnace.

First principles calculations were conducted within the framework of spin-polarized density functional theory (DFT) using the Vienna ab initio Simulation Package (VASP) [41-42]. The projector-augmented wave method was utilized as implemented in VASP. The exchange-correlation effects were treated within the generalized gradient approximation (GGA) as proposed by Perdew-Burke-Ernzerhof (PBE) [43]. The Brillouin zone was sampled using a Γ-centered grid k-point mesh with a 6×6×6 grid for supercells containing 72 atoms. The supercells were built by enlarging the primitive unit cell of Fe<sub>2</sub>P by 2×2×2 and a stepwise substitution of P atoms with Ge.
For each substitution, all possible Wykoff sites were considered, and the atom positions and cell volumes were optimized self-consistently in our calculations. The energetically most favorable configuration was then chosen for each subsequent substitution. The cut-off energy for the plane wave basis was set to be 400 eV, and the width of the smearing parameter was set to $10^{-5}$ eV. The input parameters ensured an energy convergence with an error $\le 1$ meV/atom.

To calculate the Curie temperatures, the exchange interaction energies $J_{ij}$ for the converged ferromagnetic (FM) state of the hexagonal structures were evaluated via the Liechtenstein method [44], based on the magnetic force theorem approach. In this approach, the exchange energies are derived from the total energy variations for small deviations of some magnetic moments from the ground state magnetic configuration. Magnetic couplings were calculated using DFT, following the Korringa-Kohn-Rostoker (KKR) [45-46] method and Green's function method, implemented in the AkaiKKR [47] code- also known as MACHIKANEYAMA – within the atomic sphere approximation (ASA) incorporating the coherent potential approximation (CPA) [48-49]. The atomic sphere radii were based on the Wigner-Seitz radii of each atom [50]. Continuous concentration changes for the P sublattices were considered based on KKR-CPA. All KKR calculations are based on the local density approximation (LDA) [51-52], taking the exchange correlation function as parametrized by Moruzzi, Janak and Williams [53]. In this work, scattering was considered up to d scattering ($l_{max} = 2$) in the systems. For the Brillouin zone quality, 448 k-points in the irreducible Brillouin zone were chosen together with an edelt value (an imaginary energy attached to the Fermi energy) of 0.001 Ry to achieve a convergence of the Curie temperature up to a variation of only 5 K. As an input structure for each KKR calculation, the theoretically relaxed (VASP, GGA-PBE) values are considered to include cell volume and c/a ratio changes caused by Ge substitution.

### III. Results and Discussion

#### III.1. First-principles calculations on hexagonal Fe<sub>2</sub>(P,Ge)
<figure><img src="image_2.png" /><figcaption>**Figure 1:** Crystal structure of hexagonal Fe₂P₁-xGeₓ compounds. Left hand side, representation of the Fe₂P-type crystal structure highlighting the tetrahedron and pyramidal environments for Fe in 3f and 3g sites, respectively. Right hand side, panel a) Theoretical calculations of the formation energies relative to elemental reference states with Ge in 2c or 1b sites; panel b) cell volume and c/a ratio as a function of Ge concentration (Ge in 2c site).</figcaption></figure>

Table I and Figure 1 summarize the calculated lattice parameters for Fe₂P₁-xGeₓ compounds with hexagonal Fe₂P-type structure in the range of 0 ≤ x ≤ 0.21. The formation energies are calculated with the following equation (Eq. 1) using the elements as reference states to evaluate the preferred site (2c or 1b) for Ge substitution.

$$E_{Form} = E(Fe_2P_{1-x}Ge_x) - 2E(Fe) - xE(Ge) - (1-x)E(P) \quad (1)$$

In both cases, the formation energy increases with Ge content, indicating a reduced stability of the Fe₂P structure upon Ge substitution. For x < 0.21, Ge substitutions preferentially occur at the 2c site. This prediction is in agreement with the size rule usually governing the metalloid site occupancy in Fe₂P-type compounds, which states that the largest atom will occupy the largest 2c site, and in line with neutron diffraction in quaternary (Mn,Fe)₂(P,Ge) showing a preferential Ge occupancy in 2c site [35-36]. As expected from their respective radii, Ge for P substitutions trigger a unit cell expansion. However, this
expansion is strongly anisotropic: the lattice parameter *a* increases while *c* decreases, leading to a most pronounced distortion of the *c/a* ratio compared to the binary Fe₂P parent.

Figure 2 illustrates the predicted evolution of magnetic properties in Fe₂(P,Ge). The total magnetization increases with Ge substitution, driven exclusively by the enhancement of the Fe moment in 3f site. Meanwhile, the Curie temperature (*T*<sub>C</sub>) rises significantly, mainly driven by stronger 3f-3g interlayer exchange interactions. These evolutions align with established trends among Fe₂P-type compounds. Prior studies on Fe₂(P,Si), Fe₂(P,As), and (Mn,Fe)₂(P,Si) have shown that a reduction in *c/a* shortens the 3f-3g interlayer spacing, strengthening the ferromagnetic 3f-3g interaction, stabilizing higher moments on 3f site, and increasing *T*<sub>C</sub> [40,54-57]. The evolution with Ge substitutions is steeper than that with Si or As, and the predicted increase in *T*<sub>C</sub> is comparable to that observed for B substitutions [40,54-57]. We can note that the preferential Ge site occupancy does not significantly influence the total saturation magnetization, but may affect the estimated Curie temperature through notably different *c/a* ratios.

<table><caption>**Table 1:** Theoretical structural parameters, magnetic moments and ordering temperature for Fe₂P₁-xGeₓ compounds (Ge in 2c site being the most stable configuration except for *x* = 0.21)</caption><thead><tr><th>Ge</th><th>a [Å]</th><th>c [Å]</th><th>c/a</th><th>V [Å³]</th><th>M<sub>S</sub> (μ<sub>B</sub>)</th><th>3f (μ<sub>B</sub>)</th><th>3g (μ<sub>B</sub>)</th><th>T<sub>C</sub> [K]</th></tr></thead><tbody><tr><td>0</td><td>5.809</td><td>3.425</td><td>0.590</td><td>100.090</td><td>3.02</td><td>0.83</td><td>2.24</td><td>340</td></tr><tr><td>0.04</td><td>5.833</td><td>3.413</td><td>0.585</td><td>100.562</td><td>3.07</td><td>0.87</td><td>2.25</td><td>410</td></tr><tr><td>0.08</td><td>5.864</td><td>3.396</td><td>0.579</td><td>101.132</td><td>3.12</td><td>0.94</td><td>2.23</td><td>520</td></tr><tr><td>0.125</td><td>5.895</td><td>3.384</td><td>0.574</td><td>101.790</td><td>3.18</td><td>0.99</td><td>2.24</td><td>586</td></tr><tr><td>0.16</td><td>5.934</td><td>3.360</td><td>0.566</td><td>102.391</td><td>3.24</td><td>1.07</td><td>2.23</td><td>650</td></tr><tr><td>0.21 (2c)</td><td>5.966</td><td>3.338</td><td>0.559</td><td>103.019</td><td>3.31</td><td>1.14</td><td>2.23</td><td>667</td></tr><tr><td>0.21 (1b)</td><td>6.022</td><td>3.269</td><td>0.543</td><td>102.520</td><td>3.29</td><td>1.24</td><td>2.12</td><td>732</td></tr></tbody></table>
<figure><img src="image_3.png" /><figcaption>**Figure 2:** Calculated magnetic properties of Fe<sub>2</sub>(P,Ge) compounds (Ge in 2c site). a) Magnetic moments on 3f and 3g sites and total magnetization; b) Curie temperatures, intralayer 3f-3f, 3g-3g and interlayer 3f-3g J<sub>ij</sub> interaction energies.</figcaption></figure>

### III.2. Crystal structure of Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub> compounds

Figure 3 presents the room temperature powder X-ray diffraction patterns of Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub> (0 ≤ x ≤ 1.0) compounds and their analysis. For 0 ≤ x ≤ 0.175, the diffraction patterns correspond predominantly to the hexagonal Fe<sub>2</sub>P-type structure (space group P-62m) with small additional peaks revealing the presence of secondary phases (limited to ~ 5 wt.%). The nature of the secondary phase depends on the nominal composition. When x ≤ 0.1, the secondary phase presents a Fe<sub>3</sub>P-type tetragonal structure (space group I-4), while hexagonal Fe<sub>3</sub>Ge (space group P63/mmc) appears at higher Ge content. For the experimental investigations, the metal:metalloid ratio was reduced to 1.95 in order to limit —though not completely prevent— the formation of secondary phases with a 3:1 metal:metalloid ratio. Metal-deficient compositions have been shown to reduce the formation of such 3:1 phases in Si-based Fe<sub>2</sub>P compounds [14], although rapid quenching is generally more effective [58]. Since metal vacancies in Fe<sub>2</sub>P-based compounds are known to influence both the structure and the magnetic properties, we avoid a direct comparison between the theoretical results for Fe<sub>2</sub>P<sub>1-x</sub>Ge<sub>x</sub> and the experimental ones for Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub>. Instead,
we focus hereafter on the evolution of the properties as a function of Ge content within each respective series. At $x \ge 0.175$, a Fe₅Ge₃-type phase (hexagonal, space group P63/mmc) emerges and becomes dominant as $x$ approaches 1.0. It is interesting to note that the Fe₅Ge₃ phase fraction shows a linear increase with the Ge content above $x = 0.175$. This composition therefore marks out the solubility limit where Ge no longer enter the Fe₂P-type phase and rather segregate into the Fe₅Ge₃ phase.

<figure><img src="image_4.png" /><figcaption>**Figure 3:** a) Room temperature XRD patterns of Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub> ($0 \le x \le 1.0$) compounds. b) Secondary phase fraction, unit cell volume, and c/a ratio for the main Fe<sub>2</sub>P-type phase at $x \le 0.5$.</figcaption></figure>

Table 2 summarizes the phase fractions, as well as the lattice parameters and cell volume for the Fe<sub>2</sub>P-type phase at $x \le 0.6$ and for the Fe<sub>5</sub>Ge<sub>3</sub>-type phase at $x > 0.6$. For $x = 0$, the observed lattice parameters present a slight offset compared to that of stoichiometric Fe<sub>2</sub>P (<i>a</i> = 5.8677 Å, <i>c</i> = 3.4584
Å [10]) due to Fe-deficient nominal compositions. For $x \le 0.175$, a increases while c decreases, leading to a nearly linear volume expansion; except at $x \approx 0.10$, where a change in the nature of the secondary phase reduces the effective Ge incorporation. The c/a ratio decreases similarly, with a broad hump near $x = 0.10$. Above $x > 0.175$, the solubility limit is reached and the Fe₂P-type phase hardly shows any structural evolution.

<table><caption>**Table II:** Powder x-ray diffraction data for Fe₁.₉₅P₁-xGeₓ. Secondary phase fraction, lattice parameters and unit cell volume for the main Fe₂P-type structure at $x \le 0.6$ and for Fe₅Ge₃ at $x > 0.6$.</caption><thead><tr><th>x<br>per f.u.</th><th>Fe<sub>3</sub>P<br>wt%</th><th>Fe<sub>3</sub>Ge<br>wt%</th><th>Fe<sub>5</sub>Ge<sub>3</sub><br>wt%</th><th>a<br>(Å)</th><th>c<br>(Å)</th><th>V<br>(Å<sup>3</sup>)</th></tr></thead><tbody><tr><td>0</td><td>5.4(2)</td><td>--</td><td>--</td><td>5.8695(2)</td><td>3.4560(1)</td><td>103.115(5)</td></tr><tr><td>0.05</td><td>6.1(2)</td><td>--</td><td>--</td><td>5.9294(1)</td><td>3.4196(1)</td><td>104.121 (5)</td></tr><tr><td>0.075</td><td>6.8(2)</td><td>--</td><td>--</td><td>5.9518(1)</td><td>3.4061(1)</td><td>104.493(5)</td></tr><tr><td>0.1</td><td>3.6(2)</td><td>2.5(1)</td><td>--</td><td>5.9596(2)</td><td>3.4017(1)</td><td>104.629(6)</td></tr><tr><td>0.125</td><td>--</td><td>4.4(1)</td><td>--</td><td>5.9712(2)</td><td>3.3937(2)</td><td>104.793(7)</td></tr><tr><td>0.15</td><td>--</td><td>4.4(1)</td><td>--</td><td>5.9955(2)</td><td>3.3788(2)</td><td>105.182(7)</td></tr><tr><td>0.175</td><td>--</td><td>4.6(2)</td><td>3.0(1)</td><td>6.0067(3)</td><td>3.3737(2)</td><td>105.42(1)</td></tr><tr><td>0.2</td><td>--</td><td>4.5(1)</td><td>5.3(1)</td><td>6.0029(4)</td><td>3.3755(2)</td><td>105.34(1)</td></tr><tr><td>0.3</td><td>--</td><td>6.3(1)</td><td>17.0(1)</td><td>6.0011(4)</td><td>3.3778 (3)</td><td>105.35(2)</td></tr><tr><td>0.4</td><td>--</td><td>7.7(1)</td><td>26.9(1)</td><td>5.9984(4)</td><td>3.3788 (3)</td><td>105.28(1)</td></tr><tr><td>0.5</td><td>--</td><td>8.3(1)</td><td>37.3(2)</td><td>6.0021(5)</td><td>3.3781(4)</td><td>105.39(1)</td></tr><tr><td>0.6</td><td>--</td><td>9.7(2)</td><td>46.2(2)</td><td>6.0008(5)</td><td>3.3781(4)</td><td>105.35(2)</td></tr><tr><td>0.7</td><td>--</td><td>8.8(1)</td><td>58.5(3)</td><td>4.0222(3)</td><td>5.0241(5)</td><td>70.39(1)</td></tr><tr><td>0.8</td><td>--</td><td>9.9(1)</td><td>68.5(3)</td><td>4.0216(3)</td><td>5.0240(4)</td><td>70.37(1)</td></tr><tr><td>0.9</td><td>--</td><td>11.4(2)</td><td>77.6 (4)</td><td>4.0219(3)</td><td>5.0247(4)</td><td>70.37(1)</td></tr><tr><td>1.0</td><td>--</td><td>16.9(2)</td><td>83.1(4)</td><td>4.0192(3)</td><td>5.0203(4)</td><td>70.23(1)</td></tr></tbody></table>
Electron microscopy and local chemical analysis by energy dispersive X-ray analysis were carried out to confirm the interpretation of the powder x-ray diffraction patterns. Figure 4 illustrates SEM and EDX imaging and their analysis for a composition, x = 0.2, just above the solubility limit. The picture reveals a significant porosity and an elemental contrast with three regions presenting different shades. Elemental mapping indicates that the bright regions correspond to Ge-rich P-poor phases. The effective compositions of the three regions were calculated as Fe<sub>2.00</sub>P<sub>0.85</sub>Ge<sub>0.15</sub> for the darkest main phase, Fe<sub>2.99</sub>P<sub>0.03</sub>Ge<sub>0.98</sub> and Fe<sub>5.08</sub>P<sub>0.08</sub>Ge<sub>2.84</sub> for the secondary phases, thereby confirming the XRD analysis involving Fe<sub>2</sub>P, Fe<sub>3</sub>Ge and Fe<sub>5</sub>Ge<sub>3</sub>-structure types.

<figure><img src="image_5.png" /><figcaption>**Figure 4:** SEM and EDX analysis for the Fe<sub>1.95</sub>P<sub>0.80</sub>Ge<sub>0.20</sub> sample (above solubility limit).</figcaption></figure>

Figure 5 summarizes the evolution of the crystal structure in Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub> series and compare it to that of other ternary compounds derived from Fe<sub>2</sub>P [19,29,30]. First, we would like to highlight the overall qualitative agreement between theory and experiment regarding the strongly anisotropic nature of the unit cell expansion along the Ge series. Due to the limitations of each approach, the exact lattice parameter values differ between the experimental results and the calculations in
subsection III.1. Nevertheless, there is remarkable agreement on the trends. Within the solubility range ($x \le 0.175$), Ge substitutions are found to induce structural evolution of the hexagonal cell, $dV/V \sim 13$ Å$^3$(at.%Ge)$^{-1}$ and $d(c/a)/(c/a) \sim -0.15$ (at.%Ge)$^{-1}$, pronounced compared to As, Si or B substitutions. However, this comparison also highlights that each element that substitutes for P leads to a unique structural response. The evolution of the unit cell volume is primarily influenced by a size factor (volume reduction for B, expansion for As and Ge). The lattice parameter ratio $c/a$ is likely sensitive to electronic count. For instance, B substitutions lead to the most pronounced $c$ decrease. Ge and Si decrease $c$ to a lesser extent, whereas As, which is isoelectronic with P, has the weakest influence on $c$.

In other respects, no general rule governs the solubility limits. It appears that each $Fe_2P_{1-x}X_x$ ternary series involves a unique origin. For $X$ = As, the solubility ends at $x \approx 0.65$, when the 2c site is fully occupied [29]. For $X$ = Si, one encounters first a transformation towards a body centered orthorhombic structure between $x = 0.20$ and $0.25$ at room temperature. The solubility limit is observed at $x \approx 0.5$, with phases forming that have different metal-to-metalloid ratios [19]. The case $X$ = B is the closest to that presently observed, since the solubility limit at around $x = 0.08$ produces a multiphase coexistence of $Fe_5PB_2$, $\varepsilon$(Fe-P-B) and $Fe_2(P,B)$ [30]. For $X$ = Ge, the mixed-phase region beyond $x = 0.175$ likely results from reduced $Fe_2(P,Ge)$ formation energy. In particular, it is unlikely that a volume limit is preventing Ge substitutions, since larger unit cell volumes are observed along the $Fe_2(P,As)$ series. Interestingly, in $(Mn,Fe)_2P_{1-x}Ge_x$, the $Fe_2P$ structure persists up to $x \approx 0.30$ despite the additional volume expansion induced by Mn.
<figure><img src="image_6.png" /><figcaption>**Figure 5:** Comparison of the evolution of the lattice parameters and cell volume for Fe<sub>2</sub>P<sub>1-x</sub>X<sub>x</sub> or Fe<sub>1.95</sub>P<sub>1-x</sub>X<sub>x</sub> compounds with X = As, Ge, Si and B [19,29,30].</figcaption></figure>

### III.3. Magnetic properties of Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub> compounds

Figure 6 shows the magnetization data for the Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub> ternary compounds. The transition from ferromagnetic to paramagnetic of the main Fe<sub>2</sub>P-type phase is indicated by the significant drop in magnetization. Additional magnetic anomalies are also noticeable due to the secondary phases: near the T<sub>C</sub> of Fe<sub>3</sub>P around 716 K for x < 0.1 [59]; near the T<sub>C</sub> ≈ 640 K of Fe<sub>3</sub>Ge for x ≥ 0.10 [60]; and above the solubility limit (x > 0.175) an additional anomaly marks the T<sub>C</sub> at 485 K of Fe<sub>5</sub>Ge<sub>3</sub> [39]. The T<sub>C</sub> of the Fe<sub>2</sub>P phase increases rapidly with increasing Ge content until T<sub>C</sub> reaches 550 K at x = 0.175. Above the solubility limit, the T<sub>C</sub> of the Fe<sub>2</sub>P phase does not increase further. DSC measurements were carried out for all compounds. The thermograms (not shown) exhibit broad
thermal anomalies, which are characteristic of second-order transitions, occurring at temperatures
that correspond to the magnetic transitions.

Magnetization curves at T = 5 K are presented for various Ge contents. For x = 0, a large applied
field of at least 7 T is required to start saturating, highlighting the particularly large anisotropy field
and strong magnetocrystalline anisotropy of the Fe₂P binary parent compound [11,12]. Increasing
the Ge content decreases the anisotropy field, indicating a weakening of the anisotropy at low
temperatures. Meanwhile, it can be seen that the saturation magnetization increases progressively
with increasing Ge. Therefore, the experimental data provide support for the theoretical calculations
presented in subsection III.1. While the theoretical Curie temperatures are overestimated (as is
usually observed when magnetic exchange interactions are used to estimate T_c), an overall
increase in T_c with Ge is clearly observed. Experimentally, the rate at which T_c increases, dT_c/dx ~
+ 19 K/at.% is significantly higher than that observed for As (~ + 5 K/at.% not linear [29]), Si (~ +10
K/at% Si [19]) and is comparable to that of B (~ +19 K/at% [30]). This high sensitivity of T_c mimics
the swift evolution of c/a upon Ge substitutions, confirming the primary role of structural deformation
in increasing exchange interactions, particularly by reducing 3f-3g interlayer distances due to the
c/a decrease.

Similarly, although there is a slight discrepancy between theory and practice, most likely due to the
experimental off-stoichiometry and the presence of secondary phases, the evolution of the
saturation magnetization estimated from M(H) curves at 5 K is remarkably consistent with that
predicted in subsection III.1. Experimentally, a significant increase in saturation magnetization of
+0.26 μ<sub>B</sub> is observed before reaching the solubility limit. This is quantitatively comparable to the
increase predicted by theory and attributed to higher moments developing on the Fe 3f site only.
<figure><img src="image_7.png" /><figcaption>**Figure 6:** Magnetization of Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub> compounds. a) Magnetization versus temperature curves; b) Magnetization versus field curves at T = 5 K on bulk samples with saturation magnetization (M<sub>sat</sub>) in inset.
The dash line marks out the solubility limit.</figcaption></figure>

While the weakening of the anisotropy is, in principle, undesirable, the sharp rise in Curie
temperature in Fe<sub>2</sub>(P,Ge) ternary compounds leads to a situation similar to that in the ternary
Fe<sub>2</sub>(P,Si) or quaternary (Fe,Co)<sub>2</sub>(P,Si) compounds, with finite anisotropy emerging at room
temperature. Compared to the binary parent Fe<sub>2</sub>P which is paramagnetic at room temperature, Ge
substituted samples show ferromagnetic magnetization curves at T = 300 K, see Figure 7. The
second order derivative of the magnetization curves d<sup>2</sup>M/dH<sup>2</sup> reveals a singularity in the form of a
cuspy minimum which we interpret as the anisotropy field detected by singular point detection (SPD)
[61]. The anisotropy field develops noteworthy values with Ge substitutions, reaching μ<sub>0</sub>Ha ≈ 2.5
T for x ≈ 0.10; above this, further substitutions lead to a decrease. The maximum anisotropy field
is reached before the solubility limit, which can be ascribed to the balance between the opposing
effects of Ge substitutions: weakening the maximum anisotropy and increasing T~C~, resulting in an optimum found around x ≈ 0.10 at room temperature.

Powder oriented in magnetic field of µ₀H = 1.1 T were measured for the Fe<sub>1.95</sub>P<sub>0.9</sub>Ge<sub>0.1</sub> sample.
The XRD pattern shows strongly enhanced [001] and [002] diffraction peaks compared to the
random powder presented in Fig. 3. This indicates a uniaxial easy magnetic direction along the
c-axis. However, the orientation is not as complete as that observed in the Fe<sub>2</sub>(P,Si) ternary
compounds [14,19]. At this stage, it is unclear whether this originates from imperfect powder
alignment or canting of the moment with respect to the c-axis. Further investigations would be
needed to resolve the magnetic structure and accurately quantify the anisotropy.

<figure><img src="image_8.png" /><figcaption>**Figure 7 :** Room temperature magnetic properties of Fe<sub>1.95</sub>P<sub>1-x</sub>Ge<sub>x</sub> compounds. a) Magnetization curves recorded at room temperature on bulk polycrystalline samples. In inset, anisotropy field estimated by SPD. b) Powder XRD on magnetically oriented and bounded powder for x = 0.1.</figcaption></figure>
## IV. Conclusion

The structure and magnetic properties of Fe$_{2}$P$_{1-x}$Ge$_x$ ternary compounds were investigated through combined theoretical (on Fe$_2$P$_{1-x}$Ge$_x$) and experimental (on Fe$_{1.95}$P$_{1-x}$Ge$_x$) approaches. The solubility range of Ge within the Fe$_2$P-type hexagonal structure is found to be limited, with the Fe$_5$Ge$_3$ alloy preferably forming for $x > 0.175$. Within the limited compositional window, Ge for P substitutions reveal a pronounced evolution of the crystal structure, characterized by a strong contraction of the c/a lattice parameter ratio and a consequent swift increase in Curie temperature. First-principles calculations revealed a structural evolution consistent with experimental observations and predicted an enhanced moment for Fe at the 3f site, thereby increasing the total magnetization—an effect that was experimentally confirmed.

Regarding the potential application of Fe$_2$(P,Ge) compounds as rare-earth-free magnets, Ge substitution significantly increases $T_c$ above room temperature and preserves the easy c-axis uniaxial anisotropy, which is favorable for developing permanent magnets. However, as with Si for P substitutions, there is a trade-off between increasing $T_c$ and weakening the low temperature anisotropy upon Ge substitutions. Future work, particularly on single crystals, is needed to assess more quantitatively the anisotropy.

## Acknowledgments

This work was supported by the National Natural Science Foundation of China (grant no 52461036 and 12464015) and the program for young talents of science and technology in the Universities of Inner Mongolia autonomous region (grant number NJYT23107). The work of F. Guillou at Caen University was supported by the French government, managed by the Agence Nationale de la Recherche under the France 2030 programme, under the reference ANR-23-EXES-0001, by the Normandy region and a CPJ project. The theoretical calculations were performed at the HPC Cluster ROSA, located at the University of Oldenburg (Germany) and funded by the DFG through its Major Research Instrumentation Program (INST 184/225-1 FUGG) and the Ministry of Science and Culture (MWK) of the Lower Saxony State.

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