# Conical incommensurate magnetic ordering in the transition metal-rich YCo12B6 ternary boride

B. Vallet-Simond, O. Isnard, L.V.B. Diop

► To cite this version:

B. Vallet-Simond, O. Isnard, L.V.B. Diop. Conical incommensurate magnetic ordering in the transition metal-rich YCo12B6 ternary boride. Journal of Alloys and Compounds, 2025, 1037, pp.182379. 10.1016/j.jallcom.2025.182379. hal-05219795

HAL Id: hal-05219795

https://hal.science/hal-05219795v1

Submitted on 22 Aug 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Conical incommensurate magnetic ordering in the transition metal-rich YCo₁₂B₆ ternary boride

B. Vallet-Simond<sup>a</sup>, O. Isnard<sup>a</sup>, L.V.B. Diop<sup>b,*</sup>

## ARTICLE INFO

**Keywords:**

Rare-earth intermetallic

Neutron diffraction

Magnetic structure

Hopkinson effect

## ABSTRACT

The ternary boride YCo₁₂B₆ was investigated by means of ac susceptibility, magnetization, and neutron powder diffraction experiments over the temperature range 1.5–300 K. The crystal structure was refined and the spin configuration determined. This intermetallic compound crystalizes in a rhombohedral (R$\overline{3}$m) structure. In the ground state, its magnetic structure is characterized by a short incommensurate propagation vector $k = (0, 0, \pm0.0432)$, i.e., a long incommensurate period along the c-axis. Substantially different magnetic moments have been observed on the two crystallographically inequivalent Co sites (18g and 18h), a larger moment being refined on the Co-18h position. The Co spins arrange themselves into a conical magnetic structure with a tilt angle of about 57° with respect to the threefold symmetry axis c. Furthermore, a highly anisotropic lattice expansion is observed.

## 1. Introduction

One of the most important classes among the solid materials is that of intermetallics characterized by a great diversity both in their crystal chemistry and their physical properties. Rare-earth (R) and transition metal (T) based intermetallic compounds are currently of significant interest from the viewpoints of fundamental research and technological applications. Since the discovery of the Nd-Fe-B high-performance permanent magnets, extensive studies have focused on intermetallic borides combining two different types of magnetic behavior, i.e., the localized magnetism of the 4f electronic shells of the rare-earth atoms and the itinerant electron magnetism of the 3d transition metals. The huge amount of interest is mainly stimulated by the technological significance of these magnetic systems. Yet, there are several fundamental issues which need to be investigated for a better understanding of the physical properties of the R-T-B materials. The present work is devoted to the RCo₁₂B₆ borides which, although are known for almost 50 years, continue to attract much attention owing to their complex and not completely understood structural [1–4], magnetic [5–25] and electronic properties [13,26–30].

The transition metal-rich intermetallic compounds RCo₁₂B₆ were first identified by Niihara and Yajima [1] during a survey of the R-Co-B phase diagram. They form with essentially all the rare-earths (not yet

reported for Yb, Eu and Pm) and crystallize in the rhombohedral SrNi₁₂B₆-type structure (space-group symmetry R$\overline{3}$m). In the crystal lattice, the Co atoms are located on two inequivalent sites 18g and 18h, the R atoms occupy the 3a crystallographic positions, and the B atoms reside on the 18h crystal sites, in the standard Wyckoff notation. The evolution of the unit-cell parameters within this 1:12:6 family of compounds follows the conventional lanthanide contraction. Earlier reported magnetic investigations show that the Co-based RCo₁₂B₆ phases are ferro- (R = Y, La-Sm) or ferri- (R = Gd-Tm) magnets with rather modest Curie temperatures ($T_C$ =134–162 K) and a remarkably low mean Co magnetic moment (0.44 µB) in the ground state. Furthermore, the magnetic ordering temperature is found to be weakly dependent on the R element. The low intrinsic magnetic properties of the RCo₁₂B₆ borides are ascribed to the hybridization of B(p) and Co(d) electrons bands as a consequence of short interatomic distances between B and Co atoms (≈ 2.05 Å) and to the relatively small number of Co with respect to B (factor of 2). The Co magnetic behavior has been investigated in detail in both magnetically ordered and paramagnetic states. The average Co magnetic moment in the ordered state is four times smaller than the effective paramagnetic moment. This leads to a Rhodes-Wohlfarth ratio of ≈ 2.32 and reveals the itinerant character of the Co-sublattice magnetism in these materials. According to neutron powder diffraction analyses, the magnetic ground state of LaCo₁₂B₆ is

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

<footnote><sup>b</sup> Université de Lorraine, CNRS, IJL, Nancy F-54000, France</footnote>

<footnote>* Corresponding author.
E-mail address: leopold.diop@univ-lorraine.fr (L.V.B. Diop).</footnote>
characterized by a short propagation vector and incommensurate spin conical modulations, i.e., a ground state spin configuration where the Co ordered magnetic moments arrange themselves into a periodical conical structure tilted 60° away from the threefold symmetry axis *c* [23]. The spin canting in the Co sublattice of some RCo₁₂B₆ alloys was previously observed in Mössbauer spectroscopy [11,19] and Nuclear magnetic resonance NMR [14] experiments. It is important to emphasize that Nd and Ho containing RCo₁₂B₆ compounds undergo a temperature-induced spin reorientation transition [11,21,22,31–33]. This change of the easy axis with temperature is due to the competition between the Co and Nd/Ho sublattice magnetocrystalline anisotropies which exhibit different preferred directions. The influence of applied hydrostatic pressure on the intrinsic magnetic properties of RCo₁₂B₆ series of compounds has been examined by magnetization measurements up to 1 GPa [12,15,23,34]. Only a moderate pressure sensitivity has been observed for all investigated compounds. An unusually large Hopkinson effect was discovered near T~C~ in YCo₁₂B₆ [28]. Most recently, remarkable electrical magneto-transport properties have been reported for RCo₁₂B₆ (R = Y, Ho, and Gd) systems [29]. Magnetoresistance and Hall effect results unveiled the crucial role of magnetic scattering in two spin-polarized channels, however, relevant phenomena originating from spin textures entailing the Co sublattice must be considered to fully describe the anomalous Hall contribution [29].

Despite the huge interest in the 1:12:6 family of materials, the extraordinary research effort and accordingly extensive literature noted above, only the magnetic structure of La-, Gd-, and Ho-based RCo₁₂B₆ intermetallics [19,22,23] has been reported, so far. For the other members of this series of compounds, there appear to have been no direct measurements of the spin configuration, possibly as a result of the perceived difficulties in performing neutron diffraction on materials that contain heavy absorber like natural boron ($\sigma_{abs} = 767$ barn). The only reliable source of information on the magnetic ordering directions is a ⁵⁷Fe Mössbauer spectroscopy study performed on Fe-doped samples of the RCo₁₂B₆ compounds [11,33,35,36]. However, it is hard to say to what extent the results of this study are representative of pure RCo₁₂B₆ since the magnetic properties of RCo₁₂-xFeₓB₆ were found to vary rapidly at low Fe concentrations [19,37]. Particularly, the extreme sensitivity of the magnetic ordering direction to Fe content has been evidenced in Gd (Co,Fe)₁₂B₆ pseudo-ternary system [19,37], i.e., only very little Fe substitution is sufficient to alter the magnetic anisotropy from easy-axis to easy-plane. The dramatic effect of Fe for Co substitution on the magnetic ordering in R(Co,Fe)₁₂B₆ is attributed to the strong preference Fe has to occupy the 18h and denotes competing anisotropies of the 18g and 18h Co sites [19]. In the R(Co,Fe)₁₂B₆ structure, Fe exhibits a distinct site occupancy preference [9,19].

We are unaware of any neutron diffraction study of YCo₁₂B₆ intermetallic compound. The precise magnetic structure, and the true easy magnetization direction remain unknown. The present paper aims at answering the open questions on the basis of neutron powder diffraction study performed on purposefully prepared YCo₁₂B₆ alloy by using ¹¹B isotope.

## 2. Experimental techniques

The polycrystalline sample of YCo₁₂B₆ was prepared by arc melting the mixture of appropriate amounts of high-purity metals under a protective argon gas atmosphere. ¹¹B isotope was used for the sample synthesis in order to overcome the large thermal neutron absorption of natural boron. To promote compositional homogeneity, the sample was melted several times with the ingot being turned over after each remelting. The so-obtained button was wrapped in tantalum foil and subsequently annealed in a sealed evacuated quartz tube at 900 °C for 21 days. The crystallographic phase purity was checked at room temperature by standard x-ray diffractometry using a Bruker D8 Endeavour powder diffractometer in reflection mode with the Bragg-Brentano geometry using Cu Kα radiation. DC magnetization measurements were

undertaken on powder sample in steady magnetic fields of up to 10 T over a wide temperature range from 4 to 300 K. Both temperature and magnetic-field dependences of the magnetization were recorded. The ac magnetic susceptibility was measured at a frequency of 10 kHz down to 4 K in a magnetic field of 3 mT.

Neutron diffraction experiments were carried out on the high-intensity two-axis powder diffractometer D1B at the Institut Laue-Langevin in Grenoble, France. The powder was contained in a cylindrical vanadium sample holder ($D = 6$ mm, $H = 5$ cm) and mounted on the stick of a He cryostat, whose contribution to the diffractograms was get rid of using a radial oscillating collimator. Neutron powder diffraction (NPD) patterns were collected at temperatures ranging from 1.5 to 300 K over a detector angular range coverage 5° ≤ 2θ ≤ 128° which is especially suited for magnetic structure determination. The data were recorded using a ³He/CF4 multicounter with a step of 0.1° between each of the 1280 detection cells. We employed neutron incident wavelengths of 2.52 Å and 1.28 Å that were selected by a (002) reflection of a pyrolytic graphite monochromator and a Bragg (311) line of a germanium crystal, respectively. All full-pattern structural and magnetic refinements of the diffractograms employed the FullProf suite software package [38] using the Rietveld method.

## 3. Results and discussion

The temperature dependence of the ac magnetic susceptibility ($\chi'$) of the transition metal-rich YCo₁₂B₆ ternary boride (Fig. 1) shows a sharp Hopkinson peak just below the Curie point temperature T~C~ [28,29]. According to the magnetoimpedance studies [28], the characteristic Hopkinson effect observed in YCo₁₂B₆ ensues from a critical phenomenon associated with the initial permeability. In addition, a bump and a plateau are found in the temperature intervals 70–105 K and 110–132 K, respectively. Upon increasing the external applied magnetic field, the Hopkinson peak is smeared out and the anomalies (bump and plateau) disappear [6,39]. Curie temperature of T~C~ = 152 (3) K is derived from the thermal evolution of the square of the magnetic susceptibility $\chi^2(T)$. T~C~ was taken as the point of intersection of the tangents to the sharply descending portion of the $\chi^2(T)$ curve with the extended baseline observed at high temperature (paramagnetic regime). At this point, it is important to emphasize that the magnetic structure is conical, as the neutron powder diffraction data will show.

To clarify the magnetic states at different temperatures and fields, the isothermal magnetization curves, $M(H)$, for YCo₁₂B₆ are plotted in Fig. 2. In the low temperature regime, the magnetization isotherms saturate at low field. The observed magnetic behavior proves that the ferromagnetic ordering temperature lies between 150 and 175 K, and the spontaneous magnetization $M_S$ decreases upon heating. $M_S$ was

<figure><img src="image_3.png" /><figcaption>Fig. 1. AC magnetic susceptibility ($\chi'$) for YCo₁₂B₆.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2. Magnetization isotherms of YCo₁₂B₆ measured between 4 and 300 K.</figcaption></figure>

deduced from the magnetization isotherms 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*) plots. At *T* = 4 K, *M*<sub>S</sub> amounts to 5.30 µ<sub>B</sub>/f.u. which matches very well with previous studies [5,6,23,24]. This value is converted to a mean magnetic moment of ≈ 0.44 µ<sub>B</sub>/Co atom.

For a better understanding of the physical properties of YCo₁₂B₆ ternary boride, a precise knowledge of both magnetic and crystalline structure and their thermal dependence is prerequisite. On account of that, neutron diffraction patterns have been recorded at selected temperatures so as to refine the crystal structure and to establish the magnetic ordering of this system. A Rietveld refinement of the NPD pattern obtained at 300 K in the paramagnetic state is illustrated in Fig. 3. The 300 K neutron diagram is representative of the nuclear Bragg scattering and the diffraction peaks could be identified to originate from the SrNi₁₂B₆-type phase (space-group symmetry R3m). A careful look at the neutron diffractogram indicates the presence of residual traces of the γ-Co extra phase in the studied sample. Fitting the 300 K diffractogram leads to the results presented in Table 1.

At high temperature, that is above the magnetic ordering temperature, for instance at *T* = 200 K (Fig. 4) the neutron diffraction pattern

<figure><img src="image_5.png" /><figcaption>Fig. 3. Rietveld refinement of the neutron diffraction pattern for YCo₁₂B₆ collected at 300 K. The top row of Bragg markers is for the YCo₁₂B₆ main phase, with a second row shown for the γ-Co minority phase.</figcaption></figure>

<caption>Table 1</caption>

Rietveld refinement results deduced from the analysis of the neutron diffraction patterns recorded for YCo₁₂B₆ at 300 and 1.5 K. Lattice parameters, fractional atomic coordinates, magnetic moments, moment orientations, propagation vector, and reliability factors are indicated.

<table><thead><tr><th>Temperature (K)</th><th>300</th><th>1.5</th></tr></thead><tbody><tr><td>a (Å)</td><td>9.4381(6)</td><td>9.4265(6)</td></tr><tr><td>c (Å)</td><td>7.4379(6)</td><td>7.4372(6)</td></tr><tr><td>Co (18g)</td><td></td><td></td></tr><tr><td>x</td><td>0.3673(12)</td><td>0.3670(6)</td></tr><tr><td>Co (18h)</td><td></td><td></td></tr><tr><td>x</td><td>0.4227(6)</td><td>0.4241(12)</td></tr><tr><td>z</td><td>0.0311 (15)</td><td>0.0298(15)</td></tr><tr><td>B (18h)</td><td></td><td></td></tr><tr><td>x</td><td>0.4830(2)</td><td>0.4829(2)</td></tr><tr><td>z</td><td>0.2848(6)</td><td>0.2850(6)</td></tr><tr><td>Co (18g) moment (μ<sub>B</sub>)</td><td>–</td><td>0.52 (7)</td></tr><tr><td>Co (18h) moment (μ<sub>B</sub>)</td><td>–</td><td>0.84 (9)</td></tr><tr><td>Cone angle – away from c-axis (deg)</td><td>–</td><td>57(6)</td></tr><tr><td>Propagation vector</td><td>–</td><td>0, 0, ±0.0432(18)</td></tr><tr><td>χ<sup>2</sup></td><td>1.48</td><td>2.66</td></tr><tr><td>R<sub>B</sub> (%)</td><td>2.82</td><td>2.44</td></tr><tr><td>R<sub>mag</sub> (%)</td><td>–</td><td>17.8</td></tr><tr><td>R<sub>wp</sub> (%)</td><td>12.5</td><td>8.01</td></tr><tr><td>R<sub>p</sub> (%)</td><td>11.1</td><td>9.6</td></tr><tr><td>R<sub>exp</sub> (%)</td><td>10.3</td><td>4.91</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Rietveld refinement of the neutron diffraction pattern for YCo₁₂B₆ collected at 200 K. The top row of Bragg markers is for the YCo₁₂B₆ main phase. The second and third rows are corresponding to the nuclear contribution from the vanadium sample environment and the γ-Co minority phase, respectively.</figcaption></figure>

can be fitted from the nuclear contribution only. The neutron pattern of YCo₁₂B₆ at 1.5 K is shown in Fig. 5a. For the sake of clarity, the angular 2θ range 20–35° is displayed in Fig. 5b. When YCo₁₂B₆ is cooled from room temperature down to 1.5 K, the nuclear Bragg reflections remain identical apart from a shift toward higher diffraction angles due to thermal contraction. According to the Rietveld analyses of the NPD patterns, the intermetallic possesses the rhombohedral SrNi₁₂B₆-type crystal structure over the investigated temperature interval. No signature of temperature-induced structure transformations was perceived down to the lowest temperature of the neutron powder diffraction experiment. That is, the trigonal crystal symmetry of the atomic arrangement is preserved down to 1.5 K. At 1.5 K additional Bragg peaks appear. Two magnetic satellites are observed near the (101) nuclear Bragg reflection. As it can be clearly seen in Fig. 5b, the magnetic contribution to the neutron diffractograms is most reflected by the appearance of a new set of satellites. These (101)⁻ and (101)⁺ magnetic satellites can be fully indexed using an incommensurate propagation
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. a) Rietveld refinement of the neutron diffraction pattern for YCo₁₂B₆ recorded at 1.5 K. b) Only the diffraction angle range from 20° to 35° is shown to better illustrate the development of magnetic peaks. The (101)⁻ and (101)⁺ magnetic satellites are identified on the 1.5 K diffractogram.</figcaption></figure>

wave vector $k = (0, 0, \pm0.0432)$, denoting a long incommensurate period along the threefold symmetry axis c. It is noteworthy that a macroscopic ferromagnetic behavior has been reported earlier for YCo₁₂B₆ [5,6,12,23–25]. The (101)⁻ and (101)⁺ satellites observed on the neutron diffraction contradicts such hypothesis of pure ferromagnetic alignment and R$\overline{3}$m (#166) magnetic space group. Not knowing a priori the orientation of the ordered moments in the magnetic ground state, all possible magnetic arrangements derived from the nuclear R$\overline{3}$m crystal symmetry and the (0,0,kz) propagation vector have been considered. Rietveld analyses of the 1.5 K diffractogram have been conducted considering alignments of the magnetic moments along the c axis and in the (a,b)-plane of the rhombohedral cell. R$\overline{3}$' and R$\overline{3}$m' magnetic space groups do not allow the existence of ferromagnetic component since the time reversal of $\overline{3}$' symmetry will lead to cancellation of the overall magnetization value. However, YCo₁₂B₆ is known to present macroscopic magnetization ruling out these two magnetic space groups. By contrast, R$\overline{3}$m' space group allows a ferromagnetic component along the c axis and an antiferromagnetic one in the (a,b)-plane for the Co sublattice. In such R$\overline{3}$m' magnetic space group the Co-18h and Co-18g are located on m' and 2' symmetry. In order to determine all possible symmetry-allowed magnetic structures for the Co atoms at the

18g and 18h inequivalent crystal sites, we carried out representational analysis using the BasIreps program (part of the FullProf suite [38]) and all notations used in our paper follow that employed in BasIreps. The decomposition of the magnetic representation, for $k = (0, 0, 0.0432)$, is composed of three representations:

$$ \Gamma_{\text{Mag}}^{18g} = 3\Gamma_1 + 3\Gamma_2 + 6\Gamma_3 \qquad (1) $$

$$ \Gamma_{\text{Mag}}^{18h} = 4\Gamma_1 + 2\Gamma_2 + 6\Gamma_3 \qquad (2) $$

Among the irreducible representations, two of them are one-dimensional ($\Gamma_1$ and $\Gamma_2$) and one is two-dimensional ($\Gamma_3$). We do not give the basis vectors of the 36 atoms of the magnetic representation $\Gamma_{\text{Mag}}$, because they can be deduced from the information given in the output file of BasIreps. The irreducible representations for the Co atom at the 18g site are no more real, but complex. The best refinements were achieved considering a conical spin configuration with a canting angle of 57(6)° away from the high-symmetry direction c. The Co magnetic moments were refined independently for the two inequivalent Wyckoff positions and the corresponding magnetic structure is depicted in Fig. 6. Rietveld refinement of the 1.5 K diffraction pattern was also performed assuming the same magnitude of magnetic moments on both Co sites 18g and 18h. The magnetic agreement factor ($R_{\text{mag}}$) obtained for this configuration is 24.3 %. Considering the same value of Co magnetic moments leads to much worse fit compared to that in which the Co magnetic moments are refined independently giving much smaller reliability factor 17.8 %.

Furthermore, only very weak intensity adds at the top of some nuclear Bragg lines such as (101) and (110) below the ordering temperature; indicating the presence of a magnetic contribution which is characterized by a magnetic propagation vector $k = (0, 0, 0)$. The thermal evolution of the integrated intensity of the (101) peak is displayed in Fig. 7. The intensity of the (101) reflection decreases upon heating.

The Rietveld-refined structural parameters and the Co magnetic moments are summarized in Table 1. At 1.5 K, the deduced magnetic moment of Co at the 18h crystal site amounts to 0.84(9) µB against 0.52 (7) µB on the 18g position. These ordered magnetic moments are of similar magnitude than the values obtained for the isotype LaCo₁₂B₆ compound [23]. An important feature stands out: the Co magnetic moment in the 18h Wyckoff position is 1.6 times larger than that in the 18g crystal site, a result consistent with NMR work [14]. This observed

<figure><img src="image_9.png" /><figcaption>Fig. 6. Schematic representation of the magnetic structure of YCo₁₂B₆ at 1.5 K. For the sake of clarity, the Y and B atoms are not shown.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 7. Thermal evolution of the integrated intensity of (101) peak.</figcaption></figure>

difference in the Co magnetic moments is driven by the different local chemical environments (distinct nearest-neighbor configurations). The 18h crystallographic position possesses three B and nine Co neighbors whereas the 18g position has four B and seven Co neighbors, giving rise to a larger magnetic moment at the 18h crystal site [19,22,23]. It is also well established that the proximity to the B neighbors – short Co-B interatomic distances – favors the diminution of the Co ordered moments in various R-Co-B alloys [40–42].

Similar difference of magnitude of Co moment on the inequivalent Wyckoff atomic positions seems to be a general feature of the RCo₁₂B₆ compounds since it has been reported for R = La, Gd, Ho [19,22,23]. This confirms the influence of the local atomic environment on the magnitude of the Co moment. It is worth to point out that the, here obtained magnetic structure for YCo₁₂B₆, is close to that reported earlier for LaCo₁₂B₆ [23]. The latter compound exhibits a conical magnetic arrangement but a slightly different magnetic propagation vector **k** = (0;0;±0.0643). Both compounds having non-magnetic rare-earth, the similarity of their magnetic structure reveals the intrinsic magnetic features of the Co sublattice in the RCo₁₂B₆ compounds. In particular, the ferromagnetic component is along the **c** axis whereas antiferromagnetic coupling occurs in the basal plane leading to the observed cone. The difference in the *k*<sub>*z*</sub> component of the propagation vector for YCo₁₂B₆ and LaCo₁₂B₆ most probably reflects the alteration of the magnetic exchange interaction resulting from the large difference of unit

cell between the two compounds. Indeed, the unit cell is much larger for the La-based compound than for the Y isotype one.

Furthermore, as can be seen from Fig. 8a, the propagation vector of YCo₁₂B₆ is also evolving versus temperature. *k*<sub>*z*</sub> increases significantly upon heating and reaches 0.057 ± 0.001 at 100 K, a value approaching the value reported for LaCo₁₂B₆. On the other hand, according to the refinement, the magnitude of the Co magnetic moment does not change much upon increasing temperature. The magnitude of the Co-18g (Co-18h) ordered moment varies from 0.41μ<sub>B</sub> to 0.47μ<sub>B</sub> (from 0.72 μ<sub>B</sub> to 0.73 μ<sub>B</sub>) when the temperature changes from 50 K to 100 K – Fig. 8b. The temperature-induced increase of *k*<sub>*z*</sub> may be connected to the lattice expansion observed upon heating. The Rietveld analysis indicates that the tilt angle of the cone remains the same ≈ 57 ± 6° in the 1.5–100 K temperature interval.

The thermal evolution of the lattice parameters has been derived from the Rietveld analysis of the thermodiffraction data. The cell dimensions *a* and *c*, and unit-cell volume *V* of the rhombohedral structure are plotted against temperature in Fig. 9. It is remarkable that the expected reduction of the unit-cell volume occurs regularly upon cooling. The temperature dependence of the lattice constants is more complex. The unit-cell dimension *a* shrinks as the temperature is lowered. On the contrary, the *c* lattice parameter first decreases below 300 K and change behavior around the magnetic ordering temperature with a slight increase below and a saturation at the lowest temperatures. Such anisotropic behavior of the lattice parameters reminds the thermal expansion anomalies of ferromagnetic rare-earth transition metal binary intermetallic compounds [43]. The anomalous behavior of the spontaneous magnetostriction that occurs reflects the importance of the magnetoelastic coupling in such compound, an interesting property that deserves to be investigated in more details in future.

It is interesting to analyze the above discussed thermal expansion anomalies for YCo₁₂B₆ in the light of the magnetic structure. Anomalous behavior has been observed along the *c* axis, a result consistent with the existence of ferromagnetic component of the magnetization along the high-symmetry axis *c*. However, the more conventional behavior observed along *a*-axis direction (in the basal plane) can be related to the absence of magnetization in the basal plane resulting from the cone structure. In other words, the thermal evolution of the lattice parameters reflects the obtained magnetic structure.

4. Conclusions

Neutron powder diffraction study on YCo₁₂B₆ has established that the Co sublattice orders in an incommensurate conical magnetic

<figure><img src="image_11.png" /><figcaption>Fig. 8. a) Thermal evolution of the *k*<sub>*z*</sub> component of the propagation vector refined for the magnetic structure of YCo<sub>12</sub>B<sub>6</sub>. b) Evolution of the cobalt magnetic moment amplitude versus temperature on the two different atomic positions as derived from Rietveld refinement of the neutron diffraction patterns for YCo<sub>12</sub>B<sub>6</sub>.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Thermal evolution of the lattice parameters, *a* and *c*, and unit-cell volume *V* of the rhombohedral cell for YCo₁₂B₆ as deduced from Rietveld refinement of the neutron diffraction patterns.</figcaption></figure>

structure described by a propagation vector **k** = (0, 0, ±0.0432). The magnetic moments are tilted 57° away from the high-symmetry axis *c*. The Co-18*ħ* magnetic moment is found to be significantly larger than the Co-18g moment by a factor of at least 1.6. This observed difference sheds light on the influence of the local chemical environment on the magnitude of the Co moment. The lattice expansion in YCo₁₂B₆ intermetallic compound proves peculiarly anisotropic: upon cooling the cell shrinks

progressively in the basal plane while it slightly expands along the threefold symmetry axis *c* below the Curie point.

### CRediT authorship contribution statement

**B. Vallet-Simond:** Writing – review & editing, Visualization, Resources, Methodology, Investigation, Formal analysis, Data curation. **O. Isnard:** Writing – review & editing, Supervision, Resources, Project administration, Methodology, Investigation, Data curation, Conceptualization. **L.V.B. Diop:** Writing – review & editing, Writing – original draft, Visualization, Supervision, Resources, Project administration, Methodology, Investigation, Formal analysis, 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.

### Acknowledgements

We are indebted to the Institut Laue Langevin, Grenoble, France for the allocated beam time.

### References

[1] K. Niihara, S. Yajima, Chem. Lett. 1 (1972) 875.

[2] B. Yu, G.V. Kuz'ma, Chernyak, N.F. Chaban, Dopov. Akad. Nauk. Ukr. RSR 12 (1981) 81.

[3] W. Jung, D. Quentmeier, Z. Krist. 151 (1980) 121.

[4] G. Cordier, R. Klemens, B. Albert, Z. Anorg. Allg. Chem. 633 (2007) 1603.

[5] M. Mittag, M. Rosenberg, K. Buschow, J. Magn. Magn. Mater. 82 (1989) 109.

[6] M. Rosenberg, M. Mittag, K.H.J. Buschow, J. Appl. Phys. 63 (1988) 3586.

[7] M. Jurczyk M, A.T. Pedziwiatr, W.E. Wallace, J. Magn. Magn. Mater. 67 (1987) L1.

[8] G.F. Zhou, X. Li, F.R. de Boer, K.H.J. Buschow, Physica B 177 (1992) 286.

[9] M. Rosenberg, T. Sinnemann, M. Mittag, K.H.J. Buschow, J. Alloy. Compd. 182 (1992) 145.

[10] G.F. Zhou, X. Li, F.R. de Boer, K.H.J. Buschow, J. Magn. Magn. Mater. 109 (1992) 265.

[11] J.M. Cadogan, S.J. Campbell, X.L. Zhao, E. Wu, Aust. J. Phys. 46 (1993) 679.

[12] Z. Arnold, O. Isnard, H. Mayot, M. Misek, J. Kamarad, J. Magn. Magn. Mater. 322 (2010) 1117.

[13] G.I. Miletic, Z. Blazina, J. Magn. Magn. Mater. 323 (2011) 2340.

[14] K. Erdmann, M. Rosenberg, K.H.J. Buschow, J. Appl. Phys. 63 (1988) 4113.

[15] Z. Arnold, O. Isnard, H. Mayot, Y. Skorokhod, J. Kamarad, M. Misek, Solid State Commun. 152 (2012) 1164.

[16] M. Nagahama, S.I. Satohira, T. Akazawa, F. Nakamura, T. Fujita, M. Kawakami, J. Phys. Soc. Jpn. 60 (1991) 3855.

[17] M. Kawakami, S. Satohira, J. Magn. Magn. Mater. 104–107 (1992) 1313.

[18] E. Wu, J.M. Cadogan, S.J. Campbell, X.L. Zhao, Hyperfine Interact. 94 (1994) 1903.

[19] L.V.B. Diop, O. Isnard, N.R. Lee-Hone, D.H. Ryan, J.M. Cadogan, J. Phys. Condens. Matter 25 (2013) 316001.

[20] O. Isnard, Y. Skourski, L.V.B. Diop, Z. Arnold, A. Andreev, J. Wosnitza, A. Iwasa, A. Kondo, A. Matsuo, K. Kindo, J. Appl. Phys. 111 (2012) 093916.

[21] Z. Ma, P. Xu, J. Ying, Y. Zhang, L. Li, Acta Mater. 247 (2023) 118757.

[22] L.V.B. Diop, O. Isnard, J. Phys. Condens. Matter 27 (2015) 026004.

[23] L.V.B. Diop, Z. Arnold, O. Isnard, J. Kamarad, J. Alloy. Compd. 593 (2014) 163.

[24] B. Vallet-Simond, S. Giron, L.V.B. Diop, O. Isnard, J. Alloy. Compd. 926 (2022) 166700.

[25] B. Vallet-Simond, L.V.B. Diop, O. Isnard, J. Magn. Magn. Mater. 587 (2023) 171307.

[26] S.P. Lee, C.K. Kim, K. Nahm, M. Mittag, Y.H. Jeong, C.-M. Ryu, J. Appl. Phys. 81 (1997) 2454.

[27] M. Misek, Z. Arnold, O. Isnard, H. Mayot, Y. Skorokhod, J. Kamarad, Acta Phys. Pol. A 113 (2008) 263.

[28] F. Mesquita, L.V.B. Diop, G. Fraga, O. Isnard, P. Pureur, IEEE Mag. Lett. 6 (2015) 1.

[29] F. Mesquita, S. Magalhaes, P. Pureur, L.V.B. Diop, O. Isnard, Phys. Rev. B 101 (2020) 224414.

[30] K. Nahm K, C.K. Kim, M. Mittag, Y.H. Jeong, J. Appl. Phys. 78 (1995) 3980.

[31] F. Mesquita, L.V.B. Diop, O. Isnard, J. Alloy. Compd. 763 (2018) 355.

[32] L.V.B. Diop, O. Isnard, J. Alloy. Compd. 804 (2019) 392.

[33] J.M. Cadogan, S.J. Campbell, X.L. Zhao, H.S. Li, P.W. Thompson, Hyperfine interactions, in: M.F. Thomas, J.M. Williams, T.C. Gibb (Eds.), Proc, 5, Springer, Netherlands, Dordrecht, 2002, pp. 119–122.

[34] L.V.B. Diop, Z. Arnold, J. Kamarád, O. Isnard, J. Magn. Magn. Mater. 476 (2019) 106.
[35] X.L. Zhao, S.J. Campbell, J.M. Cadogan, H.-S. Li, P.W. Thompson, SIF Conf. Proc. (ICAME1995), vol. 50, Rimini, Italy, 1996, pp 211–4.

[36] X. Zhao, J.M. Cadogan, S.J. Campbell, J. Magn. Magn. Mater. 140–144 (1995) 959.

[37] N.R. Lee-Hone, D.H. Ryan, O. Isnard, L.V.B. Diop, J.M. Cadogan, J. Appl. Phys. 113 (2013) 17E119.

[38] J. Rodriguez-Carvajal, Physica B 192 (1993) 55.

[39] L.V.B. Diop, Structure et propriétés physiques de composes magnétiques de type RT₁₂B₆ et (Hf,Ta)Fe₂ et leur dépendance en fonction de la pression (physique ou chimique) (Ph.D. thesis), Université Grenoble Alpes, Grenoble/France, 2014.

[40] C. Chacon, O. Isnard, J. Phys. Condens. Matter 13 (2001) 5841.

[41] C. Zlotea, C. Chacon, O. Isnard, J. Appl. Phys. 92 (2002) 7382.

[42] O. Isnard, C. Chacon, J. Alloy. Compd. 442 (2007) 22.

[43] A.V. Andreev, Thermal expansion anomalies and spontaneous magnetostriction in rare-earth intermetallics with cobalt and iron, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, 8, Elsevier, Amsterdam, 1995, pp. 59–187, chapter 2.