# TbMgNi4–xCox–(H,D) 2 System. II: Correlation between Structural and Magnetic Properties

Valérie Paul-Bcour, Premysl Beran, Charles Hervoches, Vitalii Shtender

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Valérie Paul-Bcour, Premysl Beran, Charles Hervoches, Vitalii Shtender. TbMgNi4–xCox–(H,D) 2 System. II: Correlation between Structural and Magnetic Properties. ACS Omega, 2023, 8 (33), pp.30727-30735. 10.1021/acsomega.3c04879. hal-04282043

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Submitted on 13 Nov 2023

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# TbMgNi₄-xCoₓ-(H,D)₂ System. II: Correlation between Structural and Magnetic Properties

Valérie Paul-Boncour, Premysl Beran, Charles Hervoches, and Vitalii Shtender*

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Cite This: ACS Omega 2023, 8, 30727–30735

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**ABSTRACT:** The magnetic properties of TbMgNi₄-xCoₓ intermetallic compounds and selected hydrides and deuterides of this system have been studied by various techniques, including magnetic measurements, in situ X-ray and neutron powder diffraction. The intermetallic compounds crystallize in a SnMgCu₄-type structure and magnetically order below a Curie temperature (T_C), which increases exponentially with the Co content. This can be due to the ordering of the Co sublattice. On the other hand, the insertion of D or H in TbMgNiCo₃ strongly decreases T_C. The X-ray diffraction measurements versus temperature reveal cell volume minima at T_C for the compounds with x = 1–3 without any hints of the structure change. The analysis of the neutron diffraction patterns for the intermetallics with x = 2 and 3 indicates a slightly canted ferrimagnetic structure below T_C. The Tb moments refined at 16 K are 4.1(2) µB/Tb for x = 2, and 6.2(1) µB/Tb for x = 3, which are smaller than the free ion value (9.5 µB/Tb). This reduction can be due to the influence of temperature but also reveals the crystal field effect. As Ni and Co occupy statistically the same Wyckoff site, an average Ni/Co moment was refined, leading to 1.7(2) µB/atom for x = 2 and 1.8(1) µB/atom for x = 3 at 16 K. This moment is slightly canted compared to the Tb moment.

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## 1. INTRODUCTION

Many alloys and intermetallic compounds (IMCs) are considered for their properties in various energy-related applications such as hydrogen storage. This is dictated by the need for a sustainable future. Since IMCs are often termed functional materials owing to their superior properties in different fields, it makes such materials of great importance for investigation.¹

In general, the formation of an extended homogeneity range for RMgNi₄-xCoₓ (R = rare earth) compounds is defined by (i) the existence of binary RT₂ compounds (T = Ni or Co), which is a key point in the formation of RMgT₄ = R₀.₅Mg₀.₅T₂ IMCs, and (ii) the ability of the Ni and Co to replace each other in a homogeneity range, which depends on the nature of the R atom (the lighter R atom, the less Co substitution is possible). These compounds crystallize in a SnMgCu₄-type structure, an ordered derivative of AuBe₅. The last one is closely related to the MgCu₂-type structure (C15) that is common for RT₂ compounds.²

The hydrogenation properties of the R₁-γMgγNi₄-xCoₓ compounds can be modified by changing the concentration of a specific element in the formula (Mg and Co) while keeping the same structure as the parent compound. The increase in hydrogen capacity and kinetics during solid–gas hydrogenation by Co substitution was first reported for YMgNi₄-xCoₓ (x = 0, 2, and 4) compounds.³ Similar results were obtained for RMgNi₄-xCoₓ (R = Nd⁴ or Tb,⁵ with x = 0–

3 for Nd, and up to 4 for Tb), La₁-γRγMgNi₄-xCoₓ (R = Pr⁶ or Nd,⁷ y = 0 or 0.5, x = 0–3), La₁-γRγMgNi₄-xCoₓ (R = Y or Ce, y = 0 or 0.5, x = 0–2),⁸ and (R, R')₂-γMgγNi₄-xCoₓ (R, R' = Pr, Nd; y = 0.8–1.2; x = 0–2)⁹ compounds. As for the Mg content in (R, R')₂-γMgγNi₄-xCoₓ compounds, it should be larger than y = 0.8 to avoid amorphization. Also, lowering the Mg content decreases the equilibrium pressure.⁹,¹⁰ The studies of the electrochemical properties of such R₁-γMgγNi₄-xCoₓ compounds did not demonstrate such an outstanding improvement of the hydrogen capacity versus the Co content. Only a small amount of Co (x = 0.5 for La₁-γRγMgNi₄-xCoₓ (R = Pr or Nd, y = 0 or 0.5);⁶,⁷ x = 1 for La₁-γRγMgNi₄-xCoₓ (R = Y or Ce, y = 0 or 0.5);⁸ x = 0.33 for LaMgNi₄-xCoₓ¹¹) slightly increases the discharge capacity while further increasing the Co content leads to the deterioration of the electrochemical properties. Additionally, Pr or Nd for La substitution improves the cyclic stability of the corresponding electrodes.⁶,⁷ On the other hand, electrode materials with a larger Mg content (y = 1.2) are characterized by improved

Received: July 7, 2023

Accepted: July 28, 2023

Published: August 9, 2023

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electrochemical capacity due to both weight lowering and
enhanced solid–gas H capacity.⁹

Hydrogen storage properties of TbMgNi₄₋ₓCoₓ (x = 0-4) IMCs have been previously studied.⁵ It was shown that Co for Ni substitution allows: (i) a substantial increase of hydrogen capacity by at least 40% (TbMgNi₄H₄ vs TbMgCo₄H₆); (ii) a lowering of the equilibrium plateau of hydrogen pressure (from 1.1 down to 0.1 MPa H₂, respectively); (iii) an improvement of the kinetic of hydride formation (reaction rate constant changes from ln(k) = -9.38 up to -6.12). Furthermore, it was found that the hydrogenation process of TbMgNi₄₋ₓCoₓ goes through two equilibrium plateaus for the concentration range x = 2-4, and presumably at higher pressures for x = 0 and 1. For the Ni-containing compounds, the TbMgNi₄₋ₓCoₓH₂ hydrides crystallize with orthorhombic (3.7 ≤ z ≤ 4.1) and cubic (5.2 ≤ z ≤ 6) structures, while for TbMgCo₄H₂, the monoclinic and cubic structures were found for the same range of H content, respectively. The structural stability of the hydrides increases with Co content and upon deuterium for hydrogen substitution. A decreasing enthalpy of formation of the alloys upon Co for Ni substitution and the inverse effect on the corresponding hydrides has been observed by DFT calculations (for x = 0, 2, 4) as well.⁵

However, there are only a few studies of the magnetic
properties of RMgNi₄₋ₓCoₓ IMCs. The RMgNi₄ (R = La, Ce,
Gd, Dy, Ho, Tm, Yb) compounds display a paramagnetic
Curie–Weiss behavior, which is driven by the rare earth
moments.<sup>12,13</sup> NdMgNi₄ and its hydride<sup>4</sup> together with
CeMgNi₄<sup>13</sup> and CeMgNi₂Co₂<sup>14</sup> display a Pauli paramagnet
behavior. Gd<sub>1.12</sub>Mg<sub>0.88</sub>Ni₄ orders antiferromagnetically below a
Néel temperature T<sub>N</sub>= 4.6(S) K.<sup>13</sup> NdMgNi₂Co₂ orders
magnetically below 50 K, whereas its hydride shows a Pauli
paramagnet behavior.<sup>4</sup>

The present study is a continuation of our previous work on
the hydrogenation and the structural and electronic properties
of the TbMgNi₄₋ₓCoₓ-(H/D)₂ system.⁵ Herein, our purpose
is to elucidate the magnetic changes that are induced by Co for
Ni substitution and hydrogen/deuterium insertion. The
experimental results of magnetometry, X-ray powder diffrac-
tion (XRPD), and neutron powder diffraction (NPD) of
selected compounds will be presented and discussed. To better
understand the magnetic properties of the TbMgNi₄₋ₓCoₓ
pseudobinary compounds, and the influence of hydrogen/
deuterium insertion, the new experimental results will be
analyzed and compared with the literature data for similar
compounds.

## 2. EXPERIMENTAL METHODS

Starting materials for the preparation of TbMgNi₄₋ₓCoₓ (x = 0-4) intermetallic compounds (IMCs) were ingots of Tb, Ni, and Co (all with purity ≥99.9%), and Mg powder (325 mesh, 99.8%). All TbNi₄₋ₓCoₓ (x = 0-4) alloy precursors were prepared by arc melting under a purified argon atmosphere, then ground, mixed with Mg powder, pressed into pellets, and annealed. More details on synthesis can be found in our previous work.⁵ Compared with previous work, new batches of TbMgNi₂Co₂ and TbMgNiCo₃ samples have been prepared for neutron diffraction with a slightly modified procedure. In the first step, a TbNiCo alloy precursor was prepared by arc melting in a purified argon atmosphere. The as-cast TbNiCo buttons were ground in an agate mortar and mixed with mixed NiCo-powder or Co-powder (all with purity ≥99.9% and 325 mesh) and Mg powder in specific proportions. 3 wt % excess of

Mg was added to compensate for the evaporation loss at high
temperatures. The NiCo powder was used to ensure the
absence of magnetic impurities as it was noticed that using
Tb(NiCo)₄ precursor induces more magnetic impurities
compared to the TbNiCo + NiCo precursor. The powder
mixtures were pressed into pellets and placed into tantalum
containers, which were further loaded into a stainless-steel
autoclave and sealed under an Ar atmosphere. Then, the
samples were heated to 1273 K and then cooled to 773 K
(heating and cooling performed within 24 h). The final
temperature was kept for 100 h, after which samples were
quenched in cold water. Hydrogenation of the selected alloys
was performed using a Sievert-type apparatus as in the previous
work.⁵

Phase-structural analysis of the samples was carried out by powder X-ray diffraction using Bruker D8 diffractometers (Cu Kα radiation). The collected XRPD patterns were analyzed by the Rietveld method¹⁵ using FullProf software.¹⁶ For the low-temperature XRPD (LTXRPD), the powders were mounted on single-crystal Si sample holders and X-ray diffraction patterns were collected using a Bruker D8 Advance with monochromatized (Cu Kα₁) radiation between 20 and 300 K. Sequential refinement of LTXRPD data has been done with the Topas 6 software.¹⁷

Inductively coupled plasma optical emission spectrometry (ICP-OES) was used to estimate the chemical concentration of each element in the alloys. The mass of 16 ± 2 mg of each sample was dissolved in 1 mL of nitric acid (nitric acid 65%, VWR) over 5 h, diluted 50 times with Milli-Q water containing 5% HNO₃, and filtered with 0.2 µm syringe filters (Whatman) before measurement. Avio 500 Scott/Cross-Flow Configuration instrument was used for the ICP measurements. A calibration curve was formed for the measurements using a Multielement Calibration Standard (CPAchem). Concentrations of 0 (blank), 0.1, 1, and 10 ppm of the elements Tb, Mg, Ni, and Co were used to create a 4-point linear regression. All measured values are within a relative standard deviation (RSD) of 5%.

Magnetization measurements were carried out using an
MPMS-5S Quantum Design SQUID magnetometer and a
PPMS09 from Quantum Design using the ACMS option. The
samples were placed in a gelatin capsule and fixed with glass
wool. The known diamagnetic contribution of the gelatin
capsule (−2.8 × 10⁻¹² emu/T) is considered negligible
compared to the sample magnetization. Isofield magnetization
curves were recorded between 2 and 300 K with applied fields
of 0.03T. The measurements were generally performed with
decreasing temperature. Isotherm magnetization curves were
measured with decreasing field from 9 to −0.02 T for selected
temperatures between 2 and 300 K.

The neutron powder diffraction (NPD) data for TbMgNi₂Co₂ and TbMgNiCo₃ compounds were collected at different temperatures above and below the magnetic transitions. The experiment was performed on the MEREDIT instrument at the Nuclear Physics Institute (NPI, Czech Republic). A mosaic Cu monochromator (reflection 220) providing neutrons with a wavelength of 1.46 Å was used. FullProf suite software¹⁶ has been used to refine the nuclear and magnetic structure of the measured neutron diffraction patterns. The symmetry analysis to determine the possible magnetic structures was performed using ISODISTORT¹⁸,¹⁹ and Bilbao Crystallographic Server.²⁰ Finally, the magnetic structure was visualized using VESTA.²¹
<table><caption>Table 1. Crystallographic Parameters from Rietveld Refinements of XRPD Data Collected at RT Together with Curie Temperature ($T_C$) and Saturation Magnetization ($M_S$) at 10 K for TbMgNi$_{4-x}$Co$_x$ Compounds and Deuterides</caption><thead><tr><th rowspan="2">no.</th><th rowspan="2">compound</th><th rowspan="2">space group</th><th colspan="3">unit cell parameters [Å]</th><th rowspan="2">V [Å<sup>3</sup>]</th><th rowspan="2">composition from ICP</th><th rowspan="2">T<sub>C</sub> [K]</th><th rowspan="2">M<sub>S</sub> [μ<sub>B</sub>/f.u.] @10 K</th></tr><tr><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td>s1</td><td>TbMgNi<sub>4</sub></td><td>F̄43m</td><td>7.0205(1)</td><td></td><td></td><td>346.02(1)</td><td>Tb<sub>1.03</sub>Mg<sub>1.00</sub>Ni<sub>3.97</sub></td><td></td><td>4.4(1)</td></tr><tr><td>s2</td><td>TbMgNi<sub>3</sub>Co</td><td>F̄43m</td><td>7.0333(1)</td><td></td><td></td><td>347.92(1)</td><td>Tb<sub>1.04</sub>Mg<sub>0.94</sub>Ni<sub>3.08</sub>Co<sub>0.94</sub></td><td>55</td><td>5.96(2)</td></tr><tr><td>s3</td><td>TbMgNi<sub>3</sub>CoD<sub>4.3</sub></td><td>Pmn<sub>2</sub>1</td><td>5.0088(3)</td><td>5.3969(3)</td><td>7.3194(4)</td><td>197.86(2)</td><td></td><td></td><td></td></tr><tr><td>s4</td><td>TbMgNi<sub>2</sub>Co<sub>2</sub></td><td>F̄43m</td><td>7.0452(1)</td><td></td><td></td><td>349.69(1)</td><td>Tb<sub>1.06</sub>Mg<sub>0.81</sub>Ni<sub>2.04</sub>Co<sub>2.09</sub></td><td>64</td><td>6.97(2)<sup>d</sup></td></tr><tr><td>s5<sup>a</sup></td><td>TbMgNi<sub>2</sub>Co<sub>2</sub></td><td>F̄43m</td><td>7.0603(1)</td><td></td><td></td><td>351.94(1)</td><td>Tb<sub>0.99</sub>Mg<sub>0.92</sub>Ni<sub>1.96</sub>Co<sub>2.13</sub></td><td>70</td><td>6.14(2)</td></tr><tr><td>s6</td><td>TbMgNiCo<sub>3</sub></td><td>F̄43m</td><td>7.0500(1)</td><td></td><td></td><td>350.45(1)</td><td>Tb<sub>0.99</sub>Mg<sub>0.85</sub>Ni<sub>1.03</sub>Co<sub>3.13</sub></td><td>194(5)</td><td>4.14(1)</td></tr><tr><td>s7<sup>a</sup></td><td>TbMgNiCo<sub>3</sub></td><td>F̄43m</td><td>7.0731(1)</td><td></td><td></td><td>353.86(1)</td><td>Tb<sub>1.04</sub>Mg<sub>1.01</sub>Ni<sub>1.10</sub>Co<sub>2.85</sub></td><td>169(5)</td><td>5.30(1)</td></tr><tr><td>s8<sup>b</sup></td><td>TbMgNiCo<sub>3</sub>H<sub>4.2</sub></td><td>Pmn<sub>2</sub>1</td><td>5.006(2)</td><td>5.430(2)</td><td>7.3985(2)</td><td>201.14(1)</td><td></td><td>65</td><td></td></tr><tr><td></td><td></td><td>F̄43m</td><td>7.5062(5)</td><td></td><td></td><td>422.92(5)</td><td></td><td>15</td><td></td></tr><tr><td>s9<sup>c</sup></td><td>TbMgNiCo<sub>3</sub>D<sub>5.4</sub></td><td>F̄43m</td><td>7.4785(3)</td><td></td><td></td><td>418.26(3)</td><td></td><td>75/15</td><td>3.60(4)</td></tr><tr><td>s10</td><td>TbMgCo<sub>4</sub></td><td>F̄43m</td><td>7.0763(1)</td><td></td><td></td><td>354.33(1)</td><td>Tb<sub>1.01</sub>Mg<sub>1.08</sub>Co<sub>3.91</sub></td><td>472</td><td>2.80(1)</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>**Figure 1.** Magnetic data of TbMgNi$_{4-x}$Co$_x$ ($x$ = 0–4) compounds. (a) $M(T)$ at 0.03 T, (b) $\log(T_C)$ versus Co content, (c) $M(H)$ at 10 K, and (d) $M_S(x)$ at 10 K.</figcaption></figure>

### 3. RESULTS AND DISCUSSION

**3.1. X-ray Diffraction at Room Temperature.** All of the studied IMCs crystallize in the cubic SnMgCu$_4$-type structure, and their cell parameters increase with Co content (Table 1). However, the two new samples prepared for the NPD experiment present larger cell parameters (0.33%) than the previously studied alloys with the same nominal compositions (TbMgNi$_2$Co$_2$ s4 and s5, TbMgNiCo$_3$ s6 and s7). This can be explained as follows: (i) the final Mg content can vary as a small excess of Mg has been introduced to compensate for the evaporation loss; (ii) different synthesis protocols have been used to obtain single-phase compounds. To determine the final chemical composition, we have conducted ICP measurements for all samples (energy-dispersive X-ray spectroscopy was discarded due to the serious peak overlap of Mg and Tb, as

shown before$^{22}$). From the ICP results, we can clearly observe that the Mg content in the two published samples (TbMgNi$_2$Co$_2$ s4 and TbMgNiCo$_3$ s6) is notably lower than for new samples prepared for NPD (s5 and s7), which is closer to the nominal composition (Table 1). The lack of Mg is mainly compensated by Ni/Co excess, which has a smaller atomic size. As a result, we have rather reduced cell parameters for the previously published samples compared to the NPD samples.

Results of the crystallographic and magnetic properties of the studied compounds are gathered in Table 1. The TbMgNi$_3$CoD$_{4.3}$ deuteride was synthesized in terms of magnetic properties; however, it undergoes rapid decomposition to the parent compound. The results for the TbMgCo$_4$ compound were added for comparison. More results for this compound, including magnetization and

<footnote><sup>a</sup>New batch of samples for neutron diffraction. <sup>b</sup>Prepared with s7. <sup>c</sup>Prepared with s6. <sup>d</sup>2 K.</footnote>
<figure><img src="image_10.png" /><figcaption>Figure 2. Comparison of (a) M(T) and (b) M(H) curves for TbMgNiCo₃(H,D)ₓ.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 3. Rietveld refinement of the NPD patterns of TbMgNi₂Co₂ (s5) and TbMgNiCo₃ (s7) compounds in the paramagnetic and ferrimagnetic state (a) at 300 and 50 K and (b) at 295 and 110 K, respectively.</figcaption></figure>

neutron diffraction experiments at high temperatures, will be presented in a separate publication.

**3.2. Magnetic Properties of TbMgNi₄-xCoₓ Compounds.** The magnetization curves of the TbMgNi₄-xCoₓ (x = 0–4) compounds as a function of temperature and an applied field of 0.03 T are compared in Figure 1a. The M(T) curve TbMgNi₄ compound shows a paramagnetic behavior, while others demonstrate magnetic transitions which depend on Co concentration. The paramagnetic state of the TbMgNi₄ compound agrees with a band structure calculation⁵ and with the results for other RMgNi₄ compounds.¹⁰,¹¹

The Curie temperature ($T_C$), determined as the minimum of the $M(T)$ first derivative, slowly grows versus Co concentration up to $x = 2$. A sharper increase is observed for $x > 2$, which can be fitted by a $\log(T) = f(x)$ linear variation ($\log(T) = 0.88 + 0.46x$), indicating a strengthening of the magnetic interactions versus Co content (Figure 1b). Indeed, $T_C$ is very sensitive to small Co variation: it is larger for sample TbMgNi₂Co₂ s5 versus s4 and for TbMgNiCo₃ s6 versus s7

as they contain more Co. The magnetization of TbMgNi₄ at 10 K increases progressively with the magnetic field and does not reach saturation at 9 T. On the contrary, for Co-containing compounds, the saturation is almost reached at 9 T, indicating a ferro- or ferrimagnetic behavior (Figure 1c). The saturation magnetization at 10 K also varies versus Co content in TbMgNi₄-xCoₓ compounds: at the beginning, it increases with a maximum at $x = 2$ and then decreases for a larger Co content (Figure 1d). This can be expected for a ferrimagnetic structure where Co moments are antiparallel to the Tb ones. Still, the magnetic structure needs to be fully solved by NPD to explain this variation. At 300 K, the magnetization of TbMgNi₄-xCoₓ ($x = 0$ and $1$) shows linear behavior characteristic of a paramagnetic state. In contrast, the magnetization curves of the other compounds ($x = 2–4$), i.e., above their $T_C$, contain a weak ferromagnetic contribution, possibly due to the segregation of magnetic impurities.

As the next step, the influence of hydrogen or deuterium insertion on the magnetic properties of the TbMgNiCo₃
<figure><img src="image_12.png" /><figcaption>**Figure 4.** Evolution of the neutron diffraction patterns of (a) TbMgNi₂Co₂ (s5) and (b) TbMgNiCo₃ (s7) compounds at different temperatures. Vertical bars denote the Bragg peak positions. Indexed *hkl* peaks show the most pronounced magnetic contributions.</figcaption></figure>

compound has been investigated. The magnetization curves M(T) of TbMgNiCo₃H₄.₂ and TbMgNiCo₃D₅.₄ are compared with those of their parent compounds in Figure 2a. Both hydride and deuteride display similar curves, with a reduction of T<sub>C</sub> around 70 K compared to that of the pristine alloys. The hydride contains a mixture of orthorhombic and cubic hydrides, and for the deuteride, we expect a partial desorption of the cubic deuteride as the equilibrium pressure is around 7 bar. We can therefore attribute the transition at 65 K to the orthorhombic phase, whereas the increase of the magnetization below 30 K can be attributed to the cubic phase. For the deuteride, we also observed an increase in coercivity. It was observed that there is an increase in magnetization for hydrogenated samples compared to the parent compound, which can be related to the anisotropy induced by the orthorhombic distortion (Figure 2b). In any case, we can conclude that H/D absorption significantly reduces the magnetization, as it is often observed due to cell volume increase, which reduces the indirect Tb–Tb and Tb–T (T= d-transition metal) interactions. The modification of the density of states (DOS) by large H insertion was also shown to modify the DOS at E<sub>F</sub> and, therefore, the magnetic moment of Co.

**3.3. Neutron Diffraction for TbMgNi₂Co₂ and TbMgNiCo₃ Compounds.** To determine the magnetic structure of the IMCs, neutron powder diffraction (NPD) experiments were performed for TbMgNi₂Co₂ and TbMgNi-Co₃ compounds at different temperatures. As already mentioned, these new samples are single phase with unit cell parameters larger than those of the first batch of samples (Table 1). Their NPD patterns were measured in both paramagnetic and magnetically ordered states to solve the magnetic structure of the studied compounds. The evolution of the NPD patterns of TbMgNi₂Co₂ and TbMgNiCo₃ at different temperatures between 16 and 300 K is presented in Figures 3a and 3b, respectively. At 300 K, the patterns can be indexed using the *F*̅43*m* space group (Figure 3) with the ordered Tb and Mg atoms in 4a and 4c sites, respectively, and a random distribution of Ni and Co atoms in the 16*e* site forming the pyrochlore lattice. The presence of at least two types of magnetic atoms in the cubic structure triggers questions on how they coexist within the magnetic structure.

For both compounds, we observe below T<sub>C</sub> an increase in the intensity of several Bragg peaks attributed to the contribution of the magnetic structure (Figure 4). These magnetic reflections can be indexed in the same cell as the nuclear structure, indicating that the magnetic propagation vector *k* is (0 0 0). The symmetry analysis suggested several

possible magnetic space groups to describe the intensity
changes of the magnetic Bragg peaks. The best fit was obtained
with the magnetic space group *I*4*m*′2′ (BNS 119.319) with the
following relation to the parent structure: 1/2*a* − 1/2*b*, 1/2*a* +
1/2*b*, *c*. The refinement was performed within the parent unit
cell setting, as displayed in Figure 3 for both compounds. The
magnetic structure can be described as a quasi-colinear
ferrimagnetic structure with Tb moments along the *c*-axis
and antiparallel with the canted Ni/Co moments (Figure 5).

<figure><img src="image_13.png" /><figcaption>**Figure 5.** Magnetic structure of TbMgNi₂Co₂ at 50 K, with Tb atoms in violet, (Ni/Co) in blue/gray, and Mg in orange.</figcaption></figure>

As Ni and Co occupy the same crystallographic 16e site, the
magnetic moments of both atoms were constrained to have the
same values during refinement. The Tb moments in
TbMgNi₂Co₂ (4.1(2) µB/Tb at 16 K) are two times smaller
compared to the Tb free ion value of 9.5 µB. The average
moment on the Co/Ni site is 1.7(2) µB at 16 K that is similar
to 1.72 µB for Co-crystal.²³ The Tb and Co/Ni moments in
TbMgNiCo₃ at 16 K are 6.2(1) and 1.8(1) µB/atom,
respectively. Assuming that the cobalt moment is near 2 µB/
Co and that of Ni, 0.6 µB/Ni for both samples, we obtain
M(Co/Ni) = 1.3 µB for *x* = 2 and 1.65 µB for *x* = 3 for a
collinear arrangement. As a canting of the (Ni/Co) moment is
<table><caption>Table 2. Rietveld Refinement Results of the Crystal and Magnetic Structures of Cubic TbMgNi₂Co₂ (s5) and TbMgNiCo₃ (s7) Compounds at Different Temperaturesᵃ</caption><thead><tr><th colspan="7">TbMgNi₂Co₂ (s5)</th></tr><tr><th>T [K]</th><th>16</th><th>50</th><th>70</th><th>75</th><th>80</th><th>300</th></tr></thead><tbody><tr><td>a [Å]</td><td>7.0417(2)</td><td>7.0411(1)</td><td>7.0406(1)</td><td>7.0403(1)</td><td>7.0407(1)</td><td>7.0582(2)</td></tr><tr><td>V [Å³]</td><td>349.17(2)</td><td>349.07(1)</td><td>349.00(1)</td><td>348.96(1)</td><td>349.02(1)</td><td>351.63(1)</td></tr><tr><td>B<sub>iso</sub> (Tb) [Å²]</td><td>0.74(2)</td><td>0.69(2)</td><td>0.85(2)</td><td>0.43(5)</td><td>0.45(2)</td><td>1.41(6)</td></tr><tr><td>M<sub>Tb</sub> [μ<sub>B</sub>]</td><td>4.1(2)</td><td>4.4(1)</td><td>2.6(2)</td><td>2.2(2)</td><td>2.0(2)</td><td>-</td></tr><tr><td>B<sub>iso</sub> (Mg) [Å²]</td><td>0.1(−)</td><td>0.1(−)</td><td>0.11(1)</td><td>0.57(7)</td><td>0.57(7)</td><td>0.46(1)</td></tr><tr><td>Co/Ni x</td><td>0.6209(5)</td><td>0.6219(5)</td><td>0.6208(4)</td><td>0.6228(7)</td><td>0.6228(6)</td><td>0.6290(5)</td></tr><tr><td>M<sub>Co/Ni</sub> [μ<sub>B</sub>]</td><td>1.7(2)</td><td>1.2(1)</td><td>0.8(1)</td><td>0.60(10)</td><td>0.65(11)</td><td>-</td></tr><tr><td>B<sub>iso</sub> (Co/Ni) [Å²]</td><td>0.1(−)</td><td>0.1(−)</td><td>0.11(1)</td><td>0.11(1)</td><td>0.11(1)</td><td>0.30(1)</td></tr><tr><td>R<sub>p</sub> [%]</td><td>4.93</td><td>4.26</td><td>4.17</td><td>4.25</td><td>4.28</td><td>4.13</td></tr><tr><td>R<sub>wp</sub> [%]</td><td>6.51</td><td>5.42</td><td>5.28</td><td>5.40</td><td>5.37</td><td>5.21</td></tr><tr><td>χ²</td><td>2.14</td><td>1.5</td><td>1.43</td><td>1.49</td><td>1.47</td><td>1.37</td></tr></tbody><thead><tr><th colspan="7">TbMgNiCo₃ (s7)</th></tr><tr><th>T [K]</th><th>16</th><th>110</th><th>200</th><th>250</th><th>270</th><th>295</th></tr></thead><tbody><tr><td>a [Å]</td><td>7.0603(2)</td><td>7.0603(2)</td><td>7.0613(2)</td><td>7.0661(2)</td><td>7.0677(2)</td><td>7.0713(2)</td></tr><tr><td>V [Å³]</td><td>351.95(2)</td><td>351.95(2)</td><td>352.09(2)</td><td>352.82(2)</td><td>353.05(2)</td><td>353.58(2)</td></tr><tr><td>B<sub>iso</sub> (Tb) [Å²]</td><td>0.35(1)</td><td>0.49(1)</td><td>0.54(1)</td><td>0.54(4)</td><td>0.59(3)</td><td>1.07(9)</td></tr><tr><td>M<sub>Tb</sub> [μ<sub>B</sub>]</td><td>6.2(1)</td><td>5.2(1)</td><td>1.3(3)</td><td>-</td><td>-</td><td>-</td></tr><tr><td>B<sub>iso</sub> (Mg) [Å²]</td><td>0.35(1)</td><td>0.49(1)</td><td>0.54(1)</td><td>1.34(6)</td><td>1.39(6)</td><td>0.67(9)</td></tr><tr><td>Co/Ni x</td><td>0.626(2)</td><td>0.626(2)</td><td>0.625(2)</td><td>0.627(1)</td><td>0.625(1)</td><td>0.627(2)</td></tr><tr><td>M<sub>Co/Ni</sub> [μ<sub>B</sub>]</td><td>1.8(1)</td><td>1.1(1)</td><td>0.7(1)</td><td>-</td><td>-</td><td>-</td></tr><tr><td>B<sub>iso</sub> (Co/Ni) [Å²]</td><td>0.35(1)</td><td>0.49(1)</td><td>0.54(1)</td><td>0.46(1)</td><td>0.48(1)</td><td>0.51(2)</td></tr><tr><td>R<sub>p</sub> [%]</td><td>4.91</td><td>4.27</td><td>4.29</td><td>4.15</td><td>4.05</td><td>4.04</td></tr><tr><td>R<sub>wp</sub> [%]</td><td>6.34</td><td>5.42</td><td>5.41</td><td>5.26</td><td>5.07</td><td>5.14</td></tr><tr><td>χ²</td><td>1.99</td><td>1.47</td><td>1.48</td><td>1.39</td><td>1.30</td><td>1.33</td></tr></tbody></table>

observed, the values can vary. These results can also be summarized with the first principle calculations.⁵ The total calculated moments for TbMgNi₄, TbMgNi₂Co₂, and TbMgCo₄ were 0, 2.7, and 5 μB/f.u., respectively. TbMgNi₄ is paramagnetic as the nonpolarized configuration is more stable. The total moment increases for x = 2 and 4, and it shows the influence of Co substitution.

The evolution of the Tb and Co/Ni magnetic moments versus temperature for both compounds is depicted in Table 2, as well as the other refined parameters. For each compound, both magnetic sublattices order at the same temperature. The Tb and (Ni/Co) moments still observed at 200 K for TbMgNiCo₃ can reflect a small variation of the transition temperature.

To explain the values of magnetic moments measured by NPD, a comparison can be made with previous work on R₃⁻MgₓCo₉ compounds.²⁴ It was found that the Tb₂MgCo₉ compound is ferrimagnetic with antiparallel and colinear alignment of Tb and Co moments. For the latter compound, the mean value for the Co moment is 1.67 μB/Co, and Tb is assumed to be 9.5 μB/Tb. Other compounds from the same series with light rare earth elements (R = Pr and Nd) have, as expected, a ferromagnetic behavior. The cobalt was estimated to have 1.67 μB in Tb₂MgCo₉, contrary to 0.9 μB in R₃⁻MgₓCo₉ (R = Y, Pr, Nd) compounds, meaning that the molecular field induced by the Tb moment reinforces the Co moment. A similar trend was observed for the binary compounds in R⁻Co (R = rare earth metals) systems, where higher magnetic moments for the Co and lower for the heavy R were reported from magnetic measurements.²⁵ Interestingly, for TbCo₂ at 50 K, which displays a rhombohedral structure

below T<sub>C</sub> due to magnetostriction, the values obtained from NPD refinement were 8.30(5) μB for the Tb moment and 1.30(4), and 1.19(3) μB for Co1 and Co2 moments, respectively.²⁶ The moments of the magnetic atoms in TbCo₂ were assumed to be collinear and antiparallel. They are set to be along the c-axis of the rhombohedral structure, corresponding to the direction (1 1 1) in the cubic structure.²⁶ For the TbCo₅ compound, it was reported that the magnetic moments of Tb and Co atoms are antiparallel.²⁷ These moments are aligned along the a-axis below 365 K, and along the c-axis above 450 K. Between these two temperatures, the magnetization axis rotates continuously. The cobalt atoms of the two crystallographic sites of this compound have slightly different magnetic moments, like the TbCo₂ compound, but the actual value is around 1.7 μB.

Notably, below T<sub>C</sub>, a small increase of unit cell parameter was observed for the TbMgNi₂Co₂ compound, while for TbMgNiCo₃, it was nearly constant according to the calculation of the neutron data sets (see Table 2). To eliminate the effect of any structural changes in TbMgNi₂Co₂ and TbMgNiCo₃ compounds, which could influence the observed values of the magnetic moments, low-temperature X-ray diffraction experiments were conducted.

**3.4. Low-Temperature X-ray Diffraction for TbMgNi₄-xCoₓ Compounds.** For the low-temperature X-ray powder diffraction (LTXRPD), the samples from the previous study⁵ were used. As a result, very intriguing behaviors of the lattices were observed, which are consistent with NPD results. Namely, for all Co-containing specimens, an anomalous increase in the unit cell was noticed at low temperatures. The strong upturn of the unit cell volumes starts

<footnote>ᵃBoth compounds have the space group F̅43m, Tb at (0 0 0), Mg at (1/4 1/4 1/4), and Co/Ni at (x x x).</footnote>
<figure><img src="image_14.png" /><figcaption>**Figure 6.** (a) Thermal evolution of unit cell volumes for TbMgNi<sub>4-x</sub>Co<sub>x</sub> (x = 0–3) compounds (s1, s2, s4, s6). The general error bars of the calculated unit cell volumes are 0.02 Å<sup>3</sup>. Values of T<sub>C</sub> coincide with the beginning of the increase of the unit cell volumes of the Co-based IMCs. (b) Comparison of the evolution of the 440 peaks for TbMgNi<sub>4</sub> (s1) and TbMgNiCo<sub>3</sub> (s6) compounds versus temperature (dashed lines are for the visual comparison).</figcaption></figure>

<table><caption>**Table 3.** Structural Parameters of TbMgNi<sub>4-x</sub>Co<sub>x</sub> (x = 0–3) Compounds at LTXRPD</caption><thead><tr><th>no.</th><th>compound</th><th>V<sub>20</sub> [Å<sup>3</sup>]</th><th>V<sub>T</sub> [Å<sup>3</sup>]</th><th>V<sub>0</sub> [Å<sup>3</sup>]</th><th>I<sub>C</sub></th><th>θ<sub>D</sub> [K]</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>s1</td><td>TbMgNi<sub>4</sub></td><td>343.09(1)</td><td></td><td>343.11(1)</td><td>0.0384(4)</td><td>347(7)</td><td>0.9998</td></tr><tr><td>s2</td><td>TbMgNi<sub>3</sub>Co</td><td>344.97(3)</td><td>344.85(3)</td><td>344.84(3)</td><td>0.0428(19)</td><td>382(32)</td><td>0.9988</td></tr><tr><td>s4</td><td>TbMgNi<sub>2</sub>Co<sub>2</sub></td><td>346.80(1)</td><td>346.23(1)</td><td>346.15(2)</td><td>0.0474(16)</td><td>424(24)</td><td>0.9995</td></tr><tr><td>s6</td><td>TbMgNiCo<sub>3</sub></td><td>348.42(2)</td><td>348.56(2)</td><td></td><td></td><td></td><td></td></tr></tbody></table>

The V<sub>T</sub> (unit cell volume at 0 and 20 K and at the temperature at which an increase of cell parameter is observed) (basically, at this temperature, we have the lowest value of V). T(TbMgNi<sub>3</sub>Co) = 40 K, T(TbMgNi<sub>2</sub>Co<sub>2</sub>) = 70 K, T(TbMgNiCo<sub>3</sub>) = 200 K. I<sub>C</sub>, and θ<sub>D</sub> are refined parameters of eq 1.

to appear exactly at the temperature of magnetic transition (T<sub>C</sub>). However, no crystal symmetry changes were detected, neither from XRPD (no splitting of the peaks through the entire temperature range) nor from the DSC experiment (any peaks were detected for TbMgNiCo<sub>3</sub> in the range of 125–300 K). Dependences of the unit cell volumes as a function of temperature are presented in Figure 6a and can be analyzed using the Debye formula:<sup>28</sup>

$$V = V_0 + I_C \frac{T^4}{\theta_D^3} \int_0^{\theta_D/T} \frac{x^3}{e^x - 1} dx \quad (1)$$

where V<sub>0</sub> is the unit cell volume at 0 K, I<sub>C</sub> is the coefficient including the Grüneisen and compressibility parameters (for higher temperatures, the coefficient is the slope of V(T) dependence), and θ<sub>D</sub> is the Debye temperature. Notably, all parameters expand with the increase of Co content (see Table 3).

LTXRPD data for the Co-free sample were fully described in eq 1, while for the others, the Debye formula was applied just above the deviation of cell parameters. For the TbMgNiCo<sub>3</sub> compound, it was not possible to fit the data with this equation. The first thing which was noted is a coincidence of the cell volume jump at low temperatures with T<sub>C</sub> for Co-containing samples, which can be due to magnetoelastic coupling (see Figure 6a). A comparison can be made with TbNi<sub>2</sub> and TbCo<sub>2</sub> compounds, as TbMgT<sub>4</sub> compounds form a

solid solution based on these compounds, for instance, TbCo<sub>2</sub>–TbMgCo<sub>4</sub>.<sup>22</sup> For both binaries (TbNi<sub>2</sub> and TbCo<sub>2</sub>), rhombohedral distortion was observed below T<sub>C</sub>.<sup>29</sup> Changes of the unit cell volume with temperature were also observed for TbCo<sub>2</sub>,<sup>26</sup> similar to what we observed for TbMgNiCo<sub>3</sub>. However, we could not identify any structural changes in the studied samples (see Figure 6b; LTXRPD data for the TbMgCo<sub>4</sub> compound will be presented in a future paper). This can be somehow explained by the low resolution of the used X-ray diffraction technique, like in one of the studying related to Terfenol-D.<sup>30</sup> Interestingly, the magnitude of the lattice distortion is proportional to the magnetoelastic coupling coefficients, which are usually very small. Thus, the structure change is often too small to be detected by the conventional XRD technique.<sup>30</sup> However, the LTXRPD study for the Tb<sub>3</sub>Ga<sub>5</sub>O<sub>12</sub><sup>31</sup> compound also revealed an increase of unit cell parameters at lower temperatures. Such a thermal anomaly was correlated to the magnetic behavior and explained by the occurrence of a terbium orbital magnetic order for Tb<sup>3+</sup>.<sup>31</sup> Additionally, we performed LTXRPD for the YMgNi<sub>2</sub>Co<sub>2</sub><sup>3</sup> compound and did not see any increase in the cell parameters at lower temperatures [unpublished data]. This confirms that the discontinuous changes of unit cell parameters are related to the nature of rare earth, as found for Tb<sub>3</sub>Ga<sub>5</sub>O<sub>12</sub> vs Y<sub>3</sub>Ga<sub>5</sub>O<sub>12</sub> or Tb<sub>3</sub>Ga<sub>4</sub>FeO<sub>12</sub> vs Y<sub>3</sub>Fe<sub>5</sub>O<sub>12</sub>.<sup>31</sup> In the end, for nonmagnetically ordered compounds (Tb<sub>3</sub>Ga<sub>4</sub>FeO<sub>12</sub>; Tb<sub>3</sub>Ga<sub>5</sub>O<sub>12</sub>; Tb<sub>3</sub>Al<sub>5</sub>O<sub>12</sub>), there was no structural distortion at low
temperature (only abnormal thermal expansion of the unit cell), while cubic to rhombohedral distortion was evidence for magnetically ordered compounds (Tb<sub>3</sub>Fe<sub>5-x</sub>Ga<sub>x</sub>O<sub>12</sub> (x = 0–2)). Considering all of the above statements, it can be concluded that the deviation from thermal expansion in TbMgNi<sub>4-x</sub>Co<sub>x</sub> samples is induced by the Tb magnetic order. Tb is responsible for the increase of the unit cell at lower temperatures, and since TbMgNi<sub>4</sub> is paramagnetic, we do not have such an increase of the unit cell.

## 4. CONCLUSIONS

In this work, the magnetic properties of TbMgNi<sub>4-x</sub>Co<sub>x</sub> compounds have been investigated by combining magnetic measurements with X-ray and neutron powder diffraction measurements at different temperatures. The magnetic ordering temperature T<sub>C</sub> increases versus Co content following a Logarithm law for x ≥ 2, which indicates that the magnetic ordering of Co is very sensitive to the number of Co neighbors. The NPD performed for x = 2 and 3 shows that they order below T<sub>C</sub> in a slightly canted ferrimagnetic structure with the same ordering temperature for both Tb and transition metal sublattices. The Tb and mean (Ni/Co) moments also increase at 16 K versus the Co content. A deviation from linearity is observed in the cell volume variation at T<sub>C</sub> for compounds that contain Co and is attributed to a weak magnetostrictive effect on Tb. H or D insertion significantly decreases the magnetic ordering temperature, as observed for TbMgNiCo<sub>3</sub>(H,D)<sub>x</sub> compounds.

Finally, summarizing all results within the TbMgNi<sub>4-x</sub>Co<sub>x</sub>-(H,D)<sub>2</sub> system, we can say that Co is a lever for the physicochemical properties that acts in a positive way. Co does the following: (i) a substantial increase of hydrogen capacity; (ii) a lowering of the equilibrium plateau of hydrogen pressure; (iii) an improvement of the kinetic of hydride formation; (iv) an increase of T<sub>C</sub>. As for magnetic behaviors, it varies and most probably depends on the statistically distributed Ni/Co atoms within the pyrochlore lattice. Magnetization of the compounds decreases with increasing Co content, which implies stronger Co/Tb competition even though the molecular field induced by the Tb moment reinforces the Co moment. All in all, it triggers the investigation of the magnetic structure of the TbMgCo<sub>4</sub> compound where Co will solely occupy the pyrochlore lattice.

## ■ AUTHOR INFORMATION

### Corresponding Author

Vitalii Shtender – Université Paris-Est Créteil, CNRS, ICMPE, UMR 7182, F-94320 Thiais, France; Department of Chemistry—Ångström Laboratory, Uppsala University, 75121 Uppsala, Sweden; Department of Materials Science and Engineering, Uppsala University, 75103 Uppsala, Sweden; © orcid.org/0000-0002-8690-9957; Email: vitalii.shtender@angstrom.uu.se

### Authors

Valérie Paul-Boncour – Université Paris-Est Créteil, CNRS, ICMPE, UMR 7182, F-94320 Thiais, France

Premysl Beran – Nuclear Physics Institute, Czech Academy of Sciences, 25068 Rez, Czech Republic; European Spallation Source, ESS ERIC, SE-221 00 Lund, Sweden; © orcid.org/0000-0002-1217-3131

Charles Hervoches – Nuclear Physics Institute, Czech Academy of Sciences, 25068 Rez, Czech Republic

Complete contact information is available at: https://pubs.acs.org/10.1021/acsomega.3c04879

## Notes

The authors declare no competing financial interest.

## ■ ACKNOWLEDGMENTS

Financial support from Liljewalch, as well as from Axel Hultgren Foundation, is gratefully acknowledged. Neutron powder diffraction measurements were carried out at the CANAM infrastructure of the NPI CAS Rez. The employment of the CICRR infrastructure supported by MEYS project LM2023041 is acknowledged.

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