# A structural study and some magnetic properties of Hf1-xMoxFe2 Laves phase materials

I. Sarr, O. Isnard, A. Vernière, L.V.B. Diop

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## To cite this version:

I. Sarr, O. Isnard, A. Vernière, L.V.B. Diop. A structural study and some magnetic properties of Hf1-xMoxFe2 Laves phase materials. Journal of Alloys and Compounds, 2025, 1037, pp.182354. 10.1016/j.jallcom.2025.182354. hal-05219809

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# A structural study and some magnetic properties of Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> Laves phase materials

I. Sarr<sup>a</sup>, O. Isnard<sup>b</sup>, A. Verniere<sup>a</sup>, L.V.B. Diop<sup>a,*</sup>

## ARTICLE INFO

**Keywords:**

Transition metal intermetallics

X-ray diffraction

Crystal structure

Magnetic properties

## ABSTRACT

The effects of molybdenum substitution on the structural and magnetic properties of the Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> (0 ≤ x ≤ 0.25) transition metal based Laves phase materials have been studied by means of x-ray powder diffraction, scanning electron microscopy, energy dispersive x-ray microanalysis, and magnetization measurements. All of the intermetallic compounds form in the hexagonal MgZn<sub>2</sub>-type crystal structure (space-group symmetry *P*6<sub>3</sub>/<i>mmc</i>) and exhibit ferromagnetic ground state. For the *x* = 0.1–0.25 alloys, microstructural analysis and diffraction data reveal that there are two hexagonal phases with different chemical compositions sharing the same *P*6<sub>3</sub>/<i>mmc</i> lattice symmetry but having slightly different unit-cell parameters. This phenomenon in turn is rooted in partial segregation of hafnium and molybdenum, and a peculiar microstructure. Mo for Hf substitution in Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> induces an anisotropic shrinkage of the hexagonal cell: the initial contraction in the *ab* basal plane is more rapid than that along the high-symmetry direction *c*. It is further shown that the intrinsic magnetic properties, Curie temperature *T*<sub>C</sub> and spontaneous magnetization *M*<sub>s</sub>, are extremely sensitive to Mo content: a strong decrease of *T*<sub>C</sub> and a significant reduction of *M*<sub>s</sub> are observed. The ferromagnetic ordering temperature changes from 600 K for *x* = 0 to 178 K for *x* = 0.25.

## 1. Introduction

Laves phases with the formula *AB*₂ are known for almost 100 years and form the largest group of intermetallic compounds. This binary system *AB*₂ constitutes a huge class of materials and the compositions are highly diverse. Usually, the *B* element corresponds to a smaller, less electropositive metal (mid-to-late *d*-block atom and, rarely, *p*-block atom or metalloid) whereas the *A* component stands for a larger electropositive atom (early *d*-block metal, rare-earth, alkali, and alkaline earth). Laves phase compounds have long been important in metallurgy owing mainly to their high melting temperatures and high strength.

Iron-based Laves type intermetallic compounds AFe₂ (A being a 3d, 4d, 5d, or rare-earth atom) have been the matter of extensive experimental and theoretical studies [1]. They continue to attract abundant interest from the fundamental research viewpoint as well as from the modern technological applications side, offering a plethora of tunable physical (magnetic, electronic, and structural) properties. Laves phase alloys are successfully used as functional materials in an unexpectedly broad range in applications including efficient electrocatalyst for hydrogen evolution, coatings resistant to wear and corrosion, hydrogen

storage, magnetostriction (e.g., Terfenol used in magneto-mechanical sensors and actuators), magnetocalorics (for solid-state magnetic refrigeration), negative thermal expansion (e.g., high-precision optics and aerospace), superconductors, to name but a few [2–4]. Such a huge variety of different functional properties makes Laves family of intermetallic compounds outstanding.

The binary compounds AFe₂ display diverse types of magnetic ordering and crystal structure depending upon the species at the *A* site. In other words, these intermetallic systems exhibit a strong coupling between lattice and spin degrees of freedom. There are three major classes of Laves phases, namely, C14 hexagonal MgZn₂-type (space group *P*6<sub>3</sub>/<i>mmc</i>, Pearson symbol *hP*12), C15 cubic MgCu₂-type (*Fd*-3*m*, *c*F24), and C36 hexagonal MgNi₂-type (*P*6<sub>3</sub>/<i>mmc</i>, *hP*24). These crystallographic structures are derived from three kinds of nets in different stacked sequences and belong to the group of Frank-Kasper phases featured by tetrahedrally close packed atomic arrangements. Among the compounds adopting the hexagonal C14 Laves structure, ScFe₂ and HhFe₂ are ferromagnetic materials [5,6], by contrast, TiFe₂ and TaFe₂ alloys show an antiferromagnetic ground state [7–9]. MoFe₂ is a paramagnet [10]. Interestingly, NbFe₂ is a remarkable itinerant system

<footnote><sup>a</sup> Université de Lorraine, CNRS, LIL, Nancy F-54000, France</footnote>

<footnote><sup>b</sup> Université Grenoble Alpes, Institut Néel, CNRS, BP166X, Grenoble Cédex 9 38042, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: leopold.diop@univ-lorraine.fr (L.V.B. Diop).</footnote>
displaying a quantum critical point (QCP) which is chemically mediated [11–17]. Three distinct ground state phases near the QCP are traversed across a narrow compositional range upon varying the Nb/Fe stoichiometry (the non-thermal control parameter) in Nb₁_yFe₂+y.

The pseudo-binary Laves phase materials (Hf,Ta)Fe₂ and (Hf,Nb)Fe₂ undergo multiple temperature-induced phase transitions from ferromagnetism (FM) to paramagnetism (PM) via an antiferromagnetic (AFM) state upon heating [9,18,19]. A competition between ferromagnetic and antiferromagnetic interactions is evidenced in these series of compounds, as the Fe magnetic moment depends sensitively on the local atomic environment [9,19]. They present a complex and fascinating magnetic phase diagram in which the ground state can easily be tuned by chemical composition or hydrostatic pressure [9,18,19]. Due to the extreme sensitivity of their physical properties to reasonably weak external stimuli or to chemical pressure, the itinerant-electron systems (Hf,Ta)Fe₂ and (Hf,Nb)Fe₂ manifest an exceptional playground for materials physics. The cross over between FM and AFM order in (Hf,Ta)Fe₂ have been investigated by electronic band structure calculations [20]. The interatomic Fe-Fe exchange coupling parameters and their lattice dependence demonstrated that the FM interaction with the first shell is considerably decreased upon contraction of the *a* lattice constant [20]. It is noteworthy that the Fe6h-Fe6h exchange coupling is always positive denoting that these interactions promote a FM spin configuration within the atomic plane containing the Fe6h crystal sites with Fe6h as near neighbors [20]. Unconventional thermal phenomena associated with the FM-AFM first-order magnetic phase transformation have been discovered in Ta-doped HfFe₂ intermetallic [21]. Such unusual thermal behavior causes heating (cooling) when heat is extracted from (provided to) the system, thus yielding indisputable evidence of metastable superheated FM and supercooled AFM states [21].

In the present study, we concentrate our work on AFe₂ Laves phase alloys based on non-magnetic *A* component so as to get a deeper understanding of the magnetic behavior of the Fe-sublattice in the purposefully selected (Hf,Mo)Fe₂ pseudo-binary system. A further aim is to investigate the solubility of molybdenum in HfFe₂ crystal lattice, as well as the effects of Mo for Hf substitution on the structural and magnetic properties.

## 2. Experimental techniques

Polycrystalline Hf₁ₓMoₓFe₂ alloys with nominal compositions ranging from x = 0 up to x = 1 (x = 0; 0.05; 0.1; 0.125; 0.15; 0.175; 0.2; 0.22; 0.25; 0.3; 0.4; 0.5; 0.6; 0.7; 0.75; 1) were synthesized by comelting appropriate amounts of the high-purity constituting metals (Hf—99.95 %, Mo—99.95 %, Fe—99.99 %) in a high frequency induction furnace under a protective atmosphere of argon. To promote homogeneity, each sample (total mass of 5 g) was melted several times with the button being flipped over after each re-melting. The weight losses after induction melting were very low (< 0.25 wt% of the initial mass). Pieces of the so-obtained ingots were introduced in alumina cylindrical crucibles and loaded in fused quartz tubes, which were thoroughly rinsed with pure argon and sealed off in a partial Ar pressure of 300 mbar. The silica ampoules were placed into a resistive vertical tube furnace for annealing at 1000 °C for one week, and finally quenched in water. Unless noted otherwise, the results reported below are obtained on as-cast samples.

The crystal structure and crystallographic phase purity of all the samples were analyzed at room temperature by standard x-ray diffraction using a Bruker D8 Advance powder diffractometer in the classical Bragg-Brentano reflection geometry (θ-2θ), with a copper anticathode and Ge(111) monochromator (λ<sub>Kα1</sub> = 1.54056 Å). Diffraction patterns were recorded over an angular 2θ range from 10° to 100° and a scan step of 0.02°. Rietveld refinements of the diffractograms were carried out using the FullProf suite software package [22]. Structural parameters and phase fractions were determined. Following the x-ray powder diffraction analysis, the samples purity was also checked by

scanning electron microscopy (SEM). The microstructure and the elemental composition were analyzed with SEM in backscattered electron (BSE) contrast using a Zeiss GeminiSEM 500 microscope equipped with an Oxford Instruments Aztec energy dispersive x-ray spectroscopy (EDS) system. SEM micrography and EDS microanalysis were performed at an accelerating voltage of 30 kV.

DC magnetic measurements were carried out on powder samples in steady magnetic fields of up to 9 T at temperatures ranging from 4 to 400 K using a vibrating-sample magnetometer (PPMS-14 of Quantum Design). Both magnetic-field and temperature dependences of the magnetization have been recorded. The magnetic measurements were extended up to 800 K using an extraction-type magnetometer that has been described elsewhere [23]. At this point, it is worth emphasizing that all magnetic data were corrected for the presence of traces of the ferromagnetic α-Fe secondary phase – Honda-Owen's correction [24] – to get the intrinsic magnetic properties of (Hf,Mo)Fe₂. Two different methods were used to estimate the amount of secondary phase: x-ray powder diffraction analysis and magnetic measurements. The latter measurements were undertaken just above the magnetic ordering temperature of the (Hf,Mo)Fe₂ alloys studied here in order to remain far below the Curie point of α-Fe, which is 1043 K.

## 3. Results and discussion

Selected x-ray powder diffraction patterns of Hf₁ₓMoₓFe₂ alloys are compared in Fig. 1a. Upon increasing Mo content, the Bragg peaks become broader as it can be seen from the enlarged region in Fig. 1b. Despite the observed broadening of the Bragg reflections, the diffractograms remain qualitatively identical. The Bragg lines shift toward higher diffraction angles due to lattice shrinkage. The diffraction peaks could be identified to arise from the C14 hexagonal MgZn₂-type crystal structure with *P*6₃/*mmc* symmetry group (#194). A Rietveld refinement of the diagram recorded at room temperature for the sample with nominal composition x = 0.05 is presented in Fig. 2a. The analysis of the diffraction pattern indicates that the sample is mainly single phase. The main phase, identified as Hf₀.95Mo₀.05Fe₂, adopts the C14 Laves phase structure and corresponds to 96.1 wt% of the sample. The obtained lattice constants are *a* = 4.965(1) Å and *c* = 8.098(1) Å. A careful look at the diffractogram reveals the presence of residual traces of α-Fe (1.9 wt %) and Hf₂Fe (2.0 wt%) secondary phases.

Rietveld refinement results of the x = 0.175 x-ray diagram – Fig. 2b – confirm the presence of the *P*6₃/*mmc* structure as the majority phase with traces of α-Fe. Yet, the best refinement of the x = 0.175 x-ray diffraction pattern is achieved considering a two-phases model, in which there are two hexagonal lattices sharing the same *P*6₃/*mmc* crystal symmetry group but having slightly different unit-cell dimensions. The x-ray diagrams of the samples with x ≥ 0.1 are well fitted by the two-hexagonal-phases model, i.e., two phases with the same crystal structure. This indicates that these alloys have phase segregation. As a result, a good refinement with the two-hexagonal-phases model is illustrated in Fig. 2b. The Rietveld-refined structural parameters and reliability factors derived from the fit are given in Table 1. The mass proportion of each phase was extracted from the structural refinements (the two-phases model for x ≥ 0.1 and the one-phase model for x < 0.1). The corresponding results are plotted against nominal composition x in Fig. 3. The fraction of the Mo-rich C14 Laves phase, P2, increases upon increasing Mo content while the concentration of the Mo-poor C14 Laves phase, P1, shows the opposite trend. As can be seen from Fig. 3, the C14 hexagonal Laves type compounds are by far the major phases.

In (Hf,Mo)Fe₂ alloys, the broadening of the diffraction peaks observed in Fig. 1 upon increasing Mo concentration is attributed to the coexistence of two hexagonal Laves phases, i.e., to chemical inhomogeneities in the materials (phase separation). It is worthwhile to notice that similar Bragg lines broadening was also seen in (Hf,Ti)Fe₂ Laves phase materials due to compositional fluctuations [25].

Following the phase identification from x-ray diffraction, the
<figure><img src="image_4.png" /><figcaption>Fig. 1. (a) X-ray powder diffraction patterns recorded at room temperature (λ<sub>Ka1</sub> = 1.54056 Å) for Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> alloys. (b) Only the diffraction angle range from 35° to 50° is shown to better illustrate the broadening of the Bragg peaks.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. (a) Rietveld refinement of the diffraction pattern recorded at room temperature (λ<sub>Ka1</sub> = 1.54056 Å) for Hf<sub>0.95</sub>Mo<sub>0.05</sub>Fe<sub>2</sub>. The top row of the Bragg markers is for the Hf<sub>0.95</sub>Mo<sub>0.05</sub>Fe<sub>2</sub> majority phase. The second and third rows are corresponding to the contribution from the Hf<sub>2</sub>Fe and the α-Fe minority phases, respectively. (b) Rietveld refinement of the diffraction pattern recorded at room temperature for Hf<sub>0.825</sub>Mo<sub>0.175</sub>Fe<sub>2</sub>. The first and second rows of bars represent the positions of the Bragg peaks for the two C14 hexagonal phases, P1 and P2, respectively (see text). The third row of the Bragg markers is for the α-Fe minority phase.</figcaption></figure>

**Table 1**

Structural parameters deduced from Rietveld refinement of the x-ray diffraction patterns for H<sub>0.95</sub>Mo<sub>0.05</sub>Fe<sub>2</sub> and Hf<sub>0.825</sub>Mo<sub>0.175</sub>Fe<sub>2</sub>. Crystallographic space group, lattice parameters, unit cell volume, fractional atomic coordinates, and reliability factors are indicated.

<table><thead><tr><th rowspan="2"></th><th rowspan="2">Hf<sub>0.95</sub>Mo<sub>0.05</sub>Fe<sub>2</sub></th><th colspan="2">Hf<sub>0.825</sub>Mo<sub>0.175</sub>Fe<sub>2</sub></th></tr><tr><th>P1</th><th>P2</th></tr></thead><tbody><tr><td>Space group</td><td>P6<sub>3</sub>/mmc</td><td>P6<sub>3</sub>/mmc</td><td>P6<sub>3</sub>/mmc</td></tr><tr><td>a (Å)</td><td>4.965 (1)</td><td>4.948 (1)</td><td>4.921 (2)</td></tr><tr><td>c (Å)</td><td>8.098 (1)</td><td>8.080 (3)</td><td>8.053 (3)</td></tr><tr><td>V (Å<sup>3</sup>)</td><td>172.9 (1)</td><td>171.3 (1)</td><td>168.9 (1)</td></tr><tr><td>z<sub>Hf(f)</sub></td><td>0.0633 (2)</td><td>0.0636 (3)</td><td>0.0622 (3)</td></tr><tr><td>x<sub>Fe(6h)</sub></td><td>0.8326 (7)</td><td>0.8294 (10)</td><td>0.8316 (15)</td></tr><tr><td>y<sub>Fe(6h)</sub> = 2x<sub>Fe(6h)</sub></td><td>1.6653 (15)</td><td>1.6588 (20)</td><td>1.6633 (30)</td></tr><tr><td>χ<sup>2</sup></td><td>5.66</td><td>1.78</td><td>1.78</td></tr><tr><td>R<sub>Bragg (%)</sub></td><td>7.21</td><td>5.34</td><td>7.85</td></tr><tr><td>R<sub>wp (%)</sub></td><td>17.3</td><td>11.5</td><td>11.5</td></tr><tr><td>R<sub>p (%)</sub></td><td>29.5</td><td>20.2</td><td>20.2</td></tr><tr><td>R<sub>exp (%)</sub></td><td>7.29</td><td>8.58</td><td>8.58</td></tr></tbody></table>

existence of phase segregation was confirmed by backscattered electron Scanning Electron Microscopy images shown in Fig. 4. The electron microscopy results corroborate the above discussed x-ray diffraction data. This SEM study shows the presence of traces of a minority phase which is much richer in hafnium and appears in white in the BSE images of Fig. 4, corresponding to the Hf<sub>2</sub>Fe compound. In black one has the light phase, i.e., α-Fe. The matrix phase (grey) corresponds to the Mo-poor Laves phase compound, P1. The dark grey regions refer to the Mo-rich Laves phase, P2. The chemical compositions of the matrix phase P1 and the Mo-rich phase P2 are determined by EDS microanalysis and are found to be Hf<sub>26.54</sub>Mo<sub>6.12</sub>Fe<sub>67.34</sub> and Hf<sub>18.83</sub>Mo<sub>14.54</sub>Fe<sub>68.41</sub>, respectively, for the sample with nominal composition x = 0.175 (Fig. 4c). The EDS results for the as-cast samples are reported in Table 2.

Surprisingly, the annealed samples – 1000°C for one week – show clearly phase segregation (see Fig. 4d). Usually, it is anticipated that a long heat treatment at high temperature would favor grain growth and recrystallization, and promote better chemical homogeneity. In these (Hf,Mo)Fe<sub>2</sub> materials, it is found that the phase segregation is hard to avoid by annealing. This observation proves that in Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub>, Mo and Hf tend towards segregation. Tendency towards chemical phase
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Mass fraction of the different phases versus nominal Mo content as derived from Rietveld refinements of the x-ray powder diffraction patterns for $Hf_{1-x}Mo_xFe_2$ series.</figcaption></figure>

segregation in both annealed and as-cast samples was also reported for $(Hf,Ti)Fe_2$ and $(Hf,Nb)Fe_2$ pseudo-binary systems [19,25]. In $(Hf,Mo)Fe_2$ series of compounds, the big difference in atom size between Hf and Mo (large size mismatch of ≈ 11 %) is likely responsible for the phase segregation. This phase separation phenomenon constitutes a way to relieve local stress owing to a size mismatch.

It is important to emphasize that samples with higher molybdenum concentrations $x > 0.25$ were prepared, however, a more pronounced phase separation occurs and they were found to contain much larger amounts of the extra phases. This likely reflects the vicinity of Mo solubility limit in the crystal lattice of $HfFe_2$. Therefore, those samples with nominal composition $x > 0.25$ were not considered further in the present investigation. Combining the SEM results with x-ray powder diffraction data discussed above, we conclude that the solubility limit of Mo in $Hf_{1-x}Mo_xFe_2$ series of compounds is about $x = 0.25$. For comparison purposes we note that in the isotype compounds $(Hf,Nb)Fe_2$ the Nb solubility limit is reached around $x = 0.3$ [19].

The $Hf_{1-x}Mo_xFe_2$ intermetallic compounds crystallize in the C14 hexagonal $MgZn_2$-type variant of the Laves phases and the corresponding atomic arrangement is depicted in Fig. 5. In such crystal structure, Hf/Mo atoms reside on one single Wyckoff site 4$f$ (1/3, 2/3, z) with an axial symmetry 3*m*. The Fe atoms occupy two crystallographically inequivalent positions: 6*h* with the point symmetry $mm2$,

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Backscattered electron SEM images of (a) as-cast $Hf_{0.95}Mo_{0.05}Fe_2$ sample, (b) annealed $Hf_{0.95}Mo_{0.05}Fe_2$ sample, (c) as-cast $Hf_{0.825}Mo_{0.175}Fe_2$ sample, (d) annealed $Hf_{0.825}Mo_{0.175}Fe_2$ sample, (e) as-cast $Hf_{0.5}Mo_{0.5}Fe_2$ sample and (f) as-cast $Hf_{0.3}Mo_{0.7}Fe_2$ sample.</figcaption></figure>
<table><caption>**Table 2**

Chemical compositions obtained by EDS analysis for P1 and P2 phases in Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> alloys.</caption><thead><tr><th rowspan="3">Nominal x</th><th colspan="6">P1</th><th colspan="6">P2</th></tr><tr><th colspan="3">Composition (at%)</th><th colspan="2">Mo/Hf ratio</th><th colspan="3">Composition (at%)</th><th colspan="3">Composition (at%)</th></tr><tr><th>Hf</th><th>Mo</th><th>Fe</th><th>Measured</th><th>Ideal</th><th>Hf</th><th>Mo</th><th>Fe</th><th>Hf</th><th>Mo</th><th>Fe</th></tr></thead><tbody><tr><td>0.05</td><td>31.51(10)</td><td>1.65(03)</td><td>66.84(12)</td><td>0.052(1)</td><td>0.053</td><td>-</td><td>-</td><td>-</td><td>28.19(11)</td><td>3.67(06)</td><td>68.13(04)</td></tr><tr><td>0.10</td><td>30.49(07)</td><td>3.27(09)</td><td>66.24(06)</td><td>0.107(3)</td><td>0.111</td><td>27.54(28)</td><td>4.39(11)</td><td>68.06(18)</td><td>27.54(28)</td><td>4.39(11)</td><td>68.06(18)</td></tr><tr><td>0.125</td><td>28.98(06)</td><td>4.02(05)</td><td>67.00(05)</td><td>0.139(2)</td><td>0.143</td><td>24.61(01)</td><td>5.62(02)</td><td>69.77(04)</td><td>24.61(01)</td><td>5.62(02)</td><td>69.77(04)</td></tr><tr><td>0.15</td><td>28.06(11)</td><td>4.65(09)</td><td>67.69(09)</td><td>0.166(4)</td><td>0.176</td><td>24.18(42)</td><td>6.79(12)</td><td>69.10(29)</td><td>24.18(42)</td><td>6.79(12)</td><td>69.10(29)</td></tr><tr><td>0.175</td><td>26.54(11)</td><td>6.12(06)</td><td>67.34(07)</td><td>0.231(3)</td><td>0.212</td><td>24.57(15)</td><td>7.24(06)</td><td>68.18(08)</td><td>24.57(15)</td><td>7.24(06)</td><td>68.18(08)</td></tr><tr><td>0.20</td><td>25.55(22)</td><td>6.56(11)</td><td>67.90(14)</td><td>0.257(7)</td><td>0.250</td><td>17.50(48)</td><td>10.08(26)</td><td>72.42(29)</td><td>17.50(48)</td><td>10.08(26)</td><td>72.42(29)</td></tr><tr><td>0.22</td><td>25.56(35)</td><td>7.42(07)</td><td>67.02(34)</td><td>0.290(7)</td><td>0.282</td><td>16.41(01)</td><td>11.26(15)</td><td>72.32(17)</td><td>16.41(01)</td><td>11.26(15)</td><td>72.32(17)</td></tr><tr><td>0.25</td><td>23.03(33)</td><td>8.43(15)</td><td>68.53(21)</td><td>0.366(12)</td><td>0.333</td><td>15.64(50)</td><td>13.01(36)</td><td>71.35(14)</td><td>15.64(50)</td><td>13.01(36)</td><td>71.35(14)</td></tr><tr><td>0.30</td><td>22.16(22)</td><td>10.35(08)</td><td>67.48(27)</td><td>0.467(8)</td><td>0.429</td><td>19.62(10)</td><td>13.88(03)</td><td>66.50(07)</td><td>19.62(10)</td><td>13.88(03)</td><td>66.50(07)</td></tr><tr><td>0.40</td><td>26.67(14)</td><td>10.65(14)</td><td>62.67(25)</td><td>0.399(7)</td><td>0.666</td><td>18.25(35)</td><td>15.93(18)</td><td>65.81(17)</td><td>18.25(35)</td><td>15.93(18)</td><td>65.81(17)</td></tr><tr><td>0.50</td><td>24.33(08)</td><td>12.39(04)</td><td>63.28(11)</td><td>0.509(3)</td><td>1.000</td><td>10.25(32)</td><td>22.11(21)</td><td>67.63(11)</td><td>10.25(32)</td><td>22.11(21)</td><td>67.63(11)</td></tr><tr><td>0.60</td><td>19.83(16)</td><td>16.14(16)</td><td>64.02(30)</td><td>0.814(15)</td><td>1.500</td><td>12.18(49)</td><td>21.53(21)</td><td>66.28(29)</td><td>12.18(49)</td><td>21.53(21)</td><td>66.28(29)</td></tr><tr><td>0.70</td><td>18.23(20)</td><td>18.20(16)</td><td>63.57(29)</td><td>0.998(20)</td><td>2.330</td><td>3.36(14)</td><td>30.97(10)</td><td>65.68(23)</td><td>3.36(14)</td><td>30.97(10)</td><td>65.68(23)</td></tr><tr><td>0.75</td><td>14.15(14)</td><td>20.91(36)</td><td>64.94(46)</td><td>1.478(40)</td><td>3.000</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** MgZn<sub>2</sub>-type crystal structure of the Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> system. The Hf or Mo (4f) atoms are plotted in blue. The 2a-Fe atoms are represented by green balls and the 6h-Fe atoms in red ones.</figcaption></figure>

generated by (x, 2x, 1/4) and 2a (0, 0, 0) with an axial symmetry $\bar{3}m$. The atomic arrangement has a layered structure which consists of Kagomé and triangular lattice sheets stacked along the six-fold symmetry axis c. One layer hosts the 2a Fe sites and the Hf/Mo atoms at 4f position. Another layer (two Kagomé networks) is exclusively formed by Fe atoms at 6h Wykoff position. The triangular lattice layer made by Fe atoms occupying the 2a crystal sites and the double layer of Kagomé lattice sheets formed by Fe atoms located at 6h sites alternate along the

high-symmetry direction c. The Hf/Mo atoms reside in Fe cages and the 2a crystal site constitutes an inversion center for the 6h sub-lattice. With regard to crystallography, there are two distinct types of Fe sites which exhibit different local chemical environments and may display different magnetic behavior. Notwithstanding their distinct local symmetry, the Fe-2a and Fe-6h atomic positions possess the same number of near neighbors. The Fe-2a site is surrounded by 12 near neighbors, half of which are Fe-6h in addition to 6 Hf/Mo atoms. The local atomic environment of the Fe-6h position is composed of 2a type, 6h Mo neighbors and 4 Fe-6h atoms. The Hf/Mo atoms at 4f position are surrounded by 16 near neighbors: 9 Fe located at 6h, 4 of which are Hf/Mo ones and 3 Fe-2a neighbors.

The lattice parameters a and c, and unit-cell volume V of the hexagonal P1 phase are displayed as a function of Mo concentration in Fig. 6. The unit-cell parameters for the entire series of samples studied here were deduced from the Rietveld analysis of the diffractograms collected at room temperature and are summarized in Table 3. The lattice constants a = 4.973(2) Å and c = 8.101(3) Å of the parent undoped compound HfFe<sub>2</sub> are consistent with previous studies on polycrystalline materials [9,20,26–30]. Partial substitution of Mo for Hf leads to a continuous diminution of the unit-cell volume (Fig. 6b). The observed volume shrinkage reflects the smaller atomic size of Mo (metallic radius of 1.40 Å) compared to that of Hf (1.58 Å) according to the calculations of Teatum et al. [31]. Even though the cell volume decreases almost linearly as the larger hafnium is replaced by molybdenum, it is immediately apparent from a visual inspection of Fig. 6a that the lattice does not shrinks isotropically. The initial contraction in the ab

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** (a) Lattice parameters, a and c, and (b) unit-cell volume, V, for P1 phase as a function of Mo concentration in Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> series of compounds.</figcaption></figure>
<caption>**Table 3**</caption>

Unit cell parameters (for P1 phase) as obtained from Rietveld refinement of the x-ray powder diffraction patterns, spontaneous magnetization at 4 K, and magnetic ordering temperature of the Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> compounds.

<table><thead><tr><th>x</th><th>a (Å)</th><th>c (Å)</th><th>V (Å<sup>3</sup>)</th><th>M<sub>s</sub> (µ<sub>B</sub>/f.u.)</th><th>T<sub>C</sub> (K)</th></tr></thead><tbody><tr><td>0</td><td>4.973 (2)</td><td>8.101 (3)</td><td>173.5 (1)</td><td>3.19 (3)</td><td>600 (3)</td></tr><tr><td>0.05</td><td>4.965 (1)</td><td>8.098 (1)</td><td>172.9 (1)</td><td>3.08 (2)</td><td>392 (2)</td></tr><tr><td>0.10</td><td>4.960 (1)</td><td>8.097 (1)</td><td>172.5 (1)</td><td>2.91 (3)</td><td>339 (3)</td></tr><tr><td>0.125</td><td>4.956 (1)</td><td>8.096 (2)</td><td>172.2 (1)</td><td>2.68 (3)</td><td>312 (3)</td></tr><tr><td>0.15</td><td>4.951 (2)</td><td>8.087 (3)</td><td>171.7 (1)</td><td>2.32 (3)</td><td>288 (3)</td></tr><tr><td>0.175</td><td>4.948 (1)</td><td>8.080 (3)</td><td>171.3 (1)</td><td>1.84 (2)</td><td>260 (3)</td></tr><tr><td>0.20</td><td>4.943 (1)</td><td>8.074 (2)</td><td>170.9 (1)</td><td>1.35 (3)</td><td>233 (4)</td></tr><tr><td>0.22</td><td>4.942 (1)</td><td>8.072 (3)</td><td>170.8 (1)</td><td>1.03 (4)</td><td>212 (4)</td></tr><tr><td>0.25</td><td>4.940 (1)</td><td>8.070 (2)</td><td>170.5 (1)</td><td>0.64 (6)</td><td>178 (4)</td></tr></tbody></table>

basal plane of the hexagonal structure is unmistakably more rapid than that along the six-fold symmetry axis c. The composition dependence of the lattice constant a follows a practically linear behavior and the contraction rate amounts to $\Delta a/a = -2.75\%$. This anisotropic contraction of the unit cell yields an overall volume shrinkage rate of $\approx 12.5 \AA^3$ per Mo atom ($\Delta V/V = -7.2\%$) along the Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> series of intermetallic compounds. The substitution of Mo for Hf in these Fe-based Laves phase alloys has significant effect on the cell parameters and produces the phenomenon of “chemical pressure” on the hexagonal crystal lattice. Mo for Hf substitution induces a systematic contraction of the unit cell, affecting interatomic distances within the crystal lattice. The big difference in atom size between Hf and Mo could cause a coherent lattice mismatch that produces elastic deformation that can be observed in strain maps. Since the crystal symmetry is fixed and each newly added Mo atom has a size different from Hf (large size mismatch of $\approx 11\%$), the cell can gradually distort as a result of the substitution. The unit-cell dimensions of the P2 phase decrease with Mo content. For the Mo-rich C14 Laves phase, P2, the contraction of the hexagonal lattice is also anisotropic and more pronounced along the a-axis direction (in the basal plane).

Fig. 7a presents the low-field thermomagnetic curves, $M(T)$, of the field-cooled Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> polycrystalline samples, measured in an applied magnetic field of 0.05 T. The isofield magnetization curves of Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> compounds indicate that the magnetic ground state is ferromagnetic. The Curie point temperatures ($T_C$) were determined from the temperature dependence of the square of the magnetization $M^2(T)$ – Fig. 7b. $T_C$ was taken as the point of intersection of the tangents to the sharply descending portions of the $M^2(T)$ plots with the extended baselines observed at high temperature (the lines to which the curves

tended in the paramagnetic regime). Besides the ferromagnetic character evidenced in the temperature dependence of the magnetization, one can point out the strong reduction of the magnetic ordering temperature upon increasing Mo content. $T_C$ values are given in Table 3. The variation of the Curie temperature with composition is plotted in Fig. 8. In the concentration range $x = 0.05-0.25$, a linear behavior is observed with a rate of $1.065 \times 10^3$ K per Mo atom. This evolution can be related to the quasi-linear contraction of the unit-cell volume occurring upon Mo for Hf substitution. The Curie temperature $T_C = 600$ K obtained here for the parent compound HfFe<sub>2</sub> is in excellent agreement with the results reported earlier $T_C = 595-602$ K [6,9,29,32,33].

As it can be clearly seen from Fig. 8 and Table 3, the partial substitution of Mo for Hf induces a substantial decrease of the Curie point temperature down to 178 K for Hf<sub>0.75</sub>Mo<sub>0.25</sub>Fe<sub>2</sub> corresponding to a huge drop by nearly a factor of 3.4. For as much as neither Hf nor Mo are expected to be magnetically ordered, we can attribute this change to the Fe-sublattice only. Such variation of $T_C$ with Mo concentration in Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> is reminiscent of the behavior found for the itinerant-electron magnets Hf<sub>1-x</sub>Ta<sub>x</sub>Fe<sub>2</sub> [9,33,34]. In the latter system, the tremendous decrease of the ferromagnetic ordering temperature leads to the collapse of the FM order and the magnetic ground state becomes AFM at a Ta concentration of about $x = 0.25$ [9,33–35].

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Concentration dependence of the Curie temperature $T_C$ for Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> compounds.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** (a) Temperature dependence of the magnetization for Hf<sub>1-x</sub>Mo<sub>x</sub>Fe<sub>2</sub> compounds. (b) Temperature dependence of the square of the magnetization showing the determination of the Curie temperature $T_C$ for Hf<sub>0.95</sub>Mo<sub>0.05</sub>Fe<sub>2</sub>.</figcaption></figure>
In Fig. 9a we compare the isothermal magnetization curves, $M(H)$, recorded at 4 K for the thermally demagnetized $Hf_{1-x}Mo_xFe_2$ compounds. For each magnetization isotherm, the external applied magnetic field was cycled between 0 and 9 T. The spontaneous magnetization $M_S$ was deduced from the isothermal magnetization curves by linear extrapolation to zero internal field, i.e., the ordinate of the crossing point of the linearly extrapolated low- and high-field parts of the $M(H)$ curves [41,42]. The corresponding values are summarized in Table 3 and reported as a function of Mo concentration in Fig. 9b. For $HfFe_2$ intermetallic compound the spontaneous magnetization is found to be $M_S = 3.19 \ \mu_B$/f.u. which matches very well with previous reports [6,9, 29]. The obtained $M_S$ is converted to a mean magnetic moment of $\approx 1.6 \ \mu_B$/Fe atom. This value is remarkably reduced when compared to 2.22 $\mu_B$/Fe of elemental iron. It is noteworthy that the spontaneous magnetization for $HfFe_2$ is significantly higher than that of $ScFe_2$, for which 2.32 $\mu_B$/f.u. (1.16 $\mu_B$/Fe) has been reported [36,37]. The average magnetic moment for $HfFe_2$ is comparable in magnitude to the value obtained for $YFe_2$. Indeed, a saturation moment of 1.45 $\mu_B$/Fe was observed in the Laves type intermetallic compound $YFe_2$ [38–40].

The spontaneous magnetization at 4 K (Fig. 9b) decreases upon increasing Mo content and the most salient feature is the large drop of $M_S$ above $x = 0.1$. In the Hf-rich side $x < 0.1$, the spontaneous magnetization is barely sensitive to Mo content, however, in the composition range $0.1 \le x \le 0.25 \ M_S$ is strongly dependent on Mo concentration. The spontaneous magnetization varies from 3.19 to 0.64 $\mu_B$/f.u. as $x$ changes from 0 to 0.25. This denotes a huge influence of the Mo for Hf substitution on the 3d electron magnetism of Fe-sublattice. In the $Hf_{1-x}Mo_xFe_2$ series of compounds, the intrinsic magnetic properties $M_S$ and $T_C$ display different behavior of the composition dependence; demonstrating that the trend of the ferromagnetic ordering temperature is not uniquely driven by the change of the spontaneous magnetization. The observed evolution of $M_S$ versus $x$ most likely reflects the importance of the electronic structure on the 3d transition metal (Fe) sites. That is to say, $T_C$ does not only depend on $M_S$ evolution, yet reflects the variation of the crystal lattice change which triggers alteration of the Fe-Fe exchange interactions. Further theoretical investigations and electronic band-structure calculations could be interesting to explore the origin of the composition dependence of the intrinsic magnetic characteristics $M_S$ and $T_C$ along the (Hf,Mo)Fe$_2$ intermetallic compounds.

To clarify the magnetic states at different magnetic fields and temperatures, we exemplify in Fig. 10 the magnetization isotherms for $Hf_{0.9}Mo_{0.1}Fe_2$ in the temperature range from 10 to 400 K. In the low temperature regime, the magnetization saturates at low applied magnetic field. The spontaneous magnetization decreases upon heating and

<figure><img src="image_12.png" /><figcaption>Fig. 10. Isothermal magnetization curves recorded at various temperatures for $Hf_{0.9}Mo_{0.1}Fe_2$.</figcaption></figure>

the observed magnetic behavior proves that the ferromagnetic ordering temperature lies between 325 and 350 K consistent with the Curie point temperature of 339 K (see Table 3) derived from the low-field thermomagnetic $M(T)$ plot.

## 4. Conclusions

In summary, we have carried out a systematic study of the crystal structure, microstructure, and magnetic properties of $Hf_{1-x}Mo_xFe_2$ Laves phase alloys combining microscopic and macroscopic experimental techniques. The C14 hexagonal crystal structure of the $Hf_{1-x}Mo_xFe_2$ intermetallic compounds is preserved at least as far as $x = 0.25$. The substitution of Mo for Hf leads to a pronounced lattice shrinkage. Unexpectedly, a phase segregation is observed in the alloys with nominal composition $x = 0.1–0.25$, which is ascribed to the large size difference between Hf and Mo atoms. Magnetization measurements demonstrate that a very low Mo content is sufficient to induce a huge effect on the ferromagnetic ordering temperature $T_C$. Moreover, a strong decrease of the spontaneous magnetization $M_S$ is found upon increasing Mo concentration.

Further experiments such as Mössbauer spectroscopy or neutron powder diffraction may be interesting to study these intermetallics at the local scale and establish their magnetic structures in order to gain a

<figure><img src="image_13.png" /><figcaption>Fig. 9. (a) Isothermal magnetization curves recorded at 4 K for $Hf_{1-x}Mo_xFe_2$ compounds. (b) Concentration dependence of the spontaneous magnetization $M_S$.</figcaption></figure>
deeper insight into the coupling between the magnetic and crystal lattices in these compounds.

## CRediT authorship contribution statement

I. Sarr: Writing – review & editing, Visualization, Resources, Investigation, Formal analysis, Data curation. O. Isnard: Writing – review & editing, Resources, Investigation. A. Verniere: Writing – review & editing, Supervision, Project administration, Funding acquisition. L. V.B. Diop: Writing – review & editing, Writing – original draft, Visualization, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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