Crystal and Magnetic Structures of the Ternary Ho2Ni0.8Si1.2 and Ho2Ni0.8Ge1.2 Compounds: An Example of Intermetallics Crystallizing with the Zr2Ni1–xP Prototype

We report two new rare-earth (R) ternary intermetallic compounds—Ho2Ni0.8T1.2 with T = Si and Ge—that correspond to the R5Ni2T3 phase earlier reported to form in Dy–Ni–T and Ho–Ni–T ternary systems. The compounds crystallize in a filled version of the orthorhombic Zr2Ni1–xP-type structure with x = 0.52; their stoichiometry, determined from both single-crystal and powder X-ray diffraction data, is centered on Ho2Ni0.8T1.2 with a narrow solid solubility range for the silicide, while the germanide appears to be a line phase. In addition to R = Dy and Ho, R2Ni0.8T1.2 compounds also form for R = Y and Tb, representing the first examples of rare-earth-based compounds adopting the Zr2Ni1–xP structural prototype. Bulk magnetization data reveal the main transitions of the ferrimagnetic or ferromagnetic type at TC = 38 K for Ho2Ni0.8Si1.2 and TC = 37 K for Ho2Ni0.8Ge1.2, which are followed by subsequent magnetic reordering at lower temperatures. Neutron diffraction shows complex magnetic structures below TC with both ferromagnetic and antiferromagnetic components and magnetic propagation vector κ1 = [0, 0, 0]. Below TN ≅ 24 K (22 K) for the silicide (germanide), an additional antiferromagnetic coupling following an incommensurate magnetic propagation vector κ2 = [κx, 0, 0] appears to coexist with the first magnetic structure.


INTRODUCTION
In addition to supporting continuous developments in industry, especially in high-technology areas, advanced materials help to save energy and reduce deleterious effects on the environment, thus improving standards of living. Among many classes of different materials, intermetallic compounds represent a vast and excellent resource, many of them with a strong potential to be deployed in various technological applications. Of note, R-based compounds, where R = rare earth, remain among the most interesting and investigated because of the emergence of unique, sometimes exotic, properties and functionalities brought about by the R atoms and their peculiar electronic structures, which also makes them crucial materials for many technologies. 1 During our earlier exploration of new ternary phases in the Dy−Ni−Si 2 and Ho−Ni−Ge 3 systems, we identified intermetallics forming with the approximate compositions of R 5 Ni 2 T 3 , where T = Si or Ge. At the time, the crystal structures, exact compositions, and properties of these two new compounds remained unknown. More recently, the same phase has been reported to form also in the Ho−Ni−Si ternary system, however, still without an investigation and determination of its crystal structure. 4 In this work, we establish the crystal structures of the "Ho 5 Ni 2 T 3 " compounds for T = Si and Ge and found them to crystallize in an orthorhombic unit cell whose prototype is Zr 2 Ni 1−x P [space group Pnma (No. 62); Pearson symbol oP32−y)]. 5 Therefore, the true stoichiometry is not R 5 Ni 2 T 3 but very close to it, namely, R 2 Ni 1−x T 1+x , with 0.094(1) ≤ x ≤ Kα radiation), utilizing the APEX2 and APEX3 software suites (for the former and latter diffractometers, respectively) for data collection between 2 and 60°of 2θ, integration, polarization, and empirical absorption correction. 13,14 The SHELXTL suite and XPREP algorithms were used to check for extinction conditions and E statistics in the intensity data sets necessary for assignment of the proper Pnma space group. Direct methods were used for structure solution (SHELXS-97). 15 APEX3 software was then used to carry out full structure refinement (determining atomic positions, mixed site occupancies, and anisotropic displacement parameters).
2.2. Thermal Analysis. Differential thermal analysis (DTA) was performed by using a Netzsch 404 thermal analyzer on bulk samples of 0.7−0.9 g, either as-cast or annealed, sealed in an outgassed Mo crucible under an Ar atmosphere. Data were recorded upon heating at 20 K/min and upon cooling at 10 K/min (temperature measurement accuracy ±5 K). The results obtained from DTA were, however, inconclusive for both Ho 2 Ni 0.8 Si 1.2 and Ho 2 Ni 0.8 Ge 1.2 , making it impossible to establish how both compounds form or melt/ decompose; it is likely that their formation/melting or decomposition temperatures are higher than the equipment limit of 1650°C.
2.3. Physical Property Measurements. The magnetization measurements were carried out using a Magnetic Property Measurement System (SQUID, Quantum Design). The measurements were performed on the samples prepared in the middle of the solid solubility range of the two Ho 2 Ni 1−x Si 1+x and Ho 2 Ni 1−x Ge 1+x phases; these turned out to be single phases with compositions close to Ho 2 Ni 0.8 Si 1.2 and Ho 2 Ni 0.8 Ge 1.2 (averaged data from the EDX microprobe and Rietveld refinement; Table 3). The dc magnetization as a function of the temperature was measured in both zero-fieldcooled (ZFC) and field-cooled (FC) modes between 2 and 300 K and under several applied magnetic fields. The isothermal magnetization was measured at various temperatures in applied fields up to 70 kOe for both compounds. Heat capacity data were collected between 2 and 100 K in both zero and applied magnetic fields using a home-built automated semiadiabatic calorimeter. 16 2.4. Neutron Diffraction Measurements. The neutron diffraction investigations were performed at the ILL, Grenoble, France, using the high-resolution powder diffractometer D2B (λ = 1.594 Å) and the high-intensity powder diffractometer D1B (λ = 2.52 Å). The temperature dependencies of the powder neutron diffraction patterns (thermodiffractograms) were measured on D1B between 1.5 and 40 K for the Si compound and between 1.5 and 46 K for the Ge compound by taking data at ΔT = 1.2 K intervals. High-resolution data were taken on D2B at 300 K for both compounds using the additional 10′ collimation of the primary beam. Data analysis was performed using the Rietveld refinement program FullProf; 12 magnetic symmetry analysis was performed using the program BASIREPS. 17 (5) compound are shown in Table S1, the refined atomic coordinates, site occupancies, and isotropic displacement parameters are listed in Table 1, and the anisotropic displacement parameters are found in Table S2.
As in the prototype, the unit cell accommodates eight 4c Wyckoff positions: four of them are fully occupied by the larger Ho atoms and four by the smaller Ni and Si atoms, including one site populated by a statistical mixture of Ni and Si in nearly equal ratio (52% Ni + 48% Si) and another that is mostly populated by Si atoms (98% Si + 2% Ni). Consequently, and for the sake of simplicity, in the following discussion, full Si occupancy is assumed for the Si1 (   Figure S1, respectively. The main phase in the three samples has compositions of Ho 50(1) Ni 18(1) Si 31(1) , Ho 50(1) Ni 20(1) Si 30(1) (matching the stoichiometry refined from the single-crystal XRD data well), and Ho 50(1) Ni 22(1) Si 28(1) , respectively. The results of microprobe analysis, therefore, indicate that the Ho 2 Ni 1−x Si 1+x compound is stable over a certain range of x.
The Rietveld refinements of the powder XRD patterns of all prepared samples with R = Ho are shown in Figures 1 and 2, fully corroborating the results obtained from SEM−EDX for the silicides.
Crystallographic data obtained from the Rietveld refinements, both for the main phase and for the detected impurity phase(s), are collected in Tables S3−S8. The nominal compositions, the resulting compositions of the main Ho 2 Ni 1−x T 1+x phase from EDX analyses, and the Rietveldrefined stoichiometries along with the lattice parameters, observed unit cell volumes (V obs ), and volume contractions (ΔV), are collected in Table 3. The volume contraction during the formation of a compound is defined as ΔV % = [(V obs − V calc )/V calc ] × 100, where V calc is the cell volume calculated from the individual atomic volumes 19 and V obs is the experimentally observed cell volume. Formation of the Ho 2 Ni 1−x T 1+x phases is accompanied by 10−12% volume contraction, indicating a high thermodynamic stability of these compounds, which explains the high melting/decomposition temperatures (likely higher than 1650°C, as noted above based on the DTA results).
Rietveld refinements confirm the bulk crystal structure determined using a small single crystal. Further, powder XRD data indicate that the two new orthorhombic phases exist over limited ranges of concentrations, that is, 0.094(1) ≤ x ≤ 0.250(1) (Δx ≈ 0.16) for Ho 2 Ni 1−x Si 1+x and 0.190(1) ≤ x ≤ 0.201(1) (Δx ≈ 0.01) for Ho 2 Ni 1−x Ge 1+x . The much narrower and practically negligible solubility range of the germanide phase compared to that of the silicide phase is likely due to the larger atomic size of Ge compared to that of Si [atomic volumes (of elements in n.c.) of 22.64 and 20.02 Å 3 for Ge and Si, respectively]. 19 The Ho 2 Ni 1−x T 1+x compounds belong to an extended family of rare-earth intermetallics, the crystal structures of which can be described by the packing of trigonal prisms formed by R atoms coordinating both M and T atoms (M and T are respectively a transition metal and a tetrel/p-block element). Here, these prisms are linked together by sharing square and triangular faces, forming a characteristic structural motif of interconnected columns, consisting of five trigonal prisms in a cross section, infinitely extending along the short b-axis direction ( Figure 3). The three prisms in the middle of the cross section are arranged so that the (pseudo)-3-fold prism axes are parallel to the ac plane, while the two prisms located at the ends are oriented with their axes along the b axis ( Figure  3).
The trigonal prisms may be distorted depending on the kind of atom hosted inside them; i.e., the prism edges are longer (shorter) when the prism coordinates the larger (smaller) Si (Ni) atoms. These distortions are similar to those observed in the binary HoNi [FeB-type, oP8; Pnma (No. 62)] and HoSi [CrB-type; oS8; Cmcm (No. 63) as the low-T form; FeB-type as the high-T form] compounds; 8,9 both structure types are based on the trigonal-prismatic coordination of the Ni and T atoms ( Figure 4). The ordering of the Ni and T atoms in Ho 2 Ni 1−x T 1+x is such that (i) the number of heteroatomic bonds (Ni−T) is maximized and (ii) the number of homoatomic T−T contacts is minimized (limited to those pertaining to the mixed site Ni2/T, where Ni and T are almost equally distributed). This result is quite interesting because it    (2) 14.9824 (1) 4.1468 (1) 11.0696 (1) 687.748 (7) −12.31 Inorganic Chemistry pubs.acs.org/IC Article polyhedra are very similar, corresponding to irregular pentagonal prisms capped on all of the faces. We also found that this new R 2 Ni 1−x T 1+x phase forms for R = Tb with Ge and for R = Y, Dy, and Ho with both Si and Ge; 20 these phases will be the subject of a forthcoming report. Notably, the R 2 Ni 1−x T 1+x compounds represent the first known examples of ternary R-based phases adopting the structure of the Zr 2 Ni 1−x P prototype. 6 (Figure 5a) and of 500 Oe, 1 kOe, and 5 kOe for Ho 2 Ni 0.8 Ge 1.2 (Figure 5b).
The magnetic behaviors of these two compounds are similar. The M(T) data reveal main transitions that are either ferrimagnetic (FIM) or ferromagnetic (FM) in nature, occurring at T C = 38 K for the silicide and T C = 37 K for the germanide. These transition temperatures are determined from the minima of the first derivatives of the magnetization with respect to the temperature (dM/dT; FC data at 500 Oe; see the insets of parts a and b of Figure 5, respectively). The derivatives plotted as a function of the temperature also reveal weak and broad additional minima at about 25 and 11 K for Ho 2 Ni 0.8 Si 1.2 and at 13 K for Ho 2 Ni 0.8 Ge 1.2 . Considering the phase purity of both materials (Tables S4 and S7), it is reasonable to assume that the additional low-temperature anomalies are intrinsic to these compounds. Thermomagnetic   Inorganic Chemistry pubs.acs.org/IC Article irreversibilities present between the ZFC and FC data below about 10−20 K are consistent with the nonzero hysteresis developing at the lowest temperature. The inverse magnetic susceptibility, 1/χ = H/M, is shown in parts a and b of Figure 6 for the two compounds, respectively.
The data follow the Curie−Weiss law χ(T) = C/(T − θ P ) (with C being the Curie constant) above 100 K for the silicide and above 75 K for the germanide. The least-squares fits to the data in the paramagnetic region give an effective magnetic moment, p eff , of 10.68 μ B for Ho 2 Ni 0.8 Si 1.2 and 10.75 μ B for Ho 2 Ni 0.8 Ge 1.2 . Both values are very close to the Hund's rule derived theoretical value of 10.61 μ B for the Ho 3+ ion, 23 indicating that the Ni magnetic moment is quenched, as is common for many other rare-earth compounds containing Ni. 24,25 The positive values of the Weiss temperatures, θ P , of 39 and 38 K respectively for the silicide and germanide are commensurate with either the FM or FIM ground states.
The isothermal magnetization, M(H), measured at T = 2 K (both compounds) and 15 and 30 K for the silicide in magnetic fields up to 70 kOe, is shown in Figures 7 and 8.
The measurements at T = 2 K show noticeable hysteresis, which is typical of FM/FIM materials formed by lanthanides with nonzero single-ion anisotropies. The M(H) data do not reach saturation even at the highest applied magnetic field of 70 kOe, approaching 8.33 μ B /Ho atom, a value lower than the expected 10 μ B /Ho if all Ho magnetic moments would align ferromagnetically, possibly indicating antiferromagnetic (AFM) contributions rather than a simple collinear FM ordering. A comparison between the isothermal magnetization of the two compounds, for data measured at 2 K, is shown in Figure S2; a very similar behavior is observed, with the coercive field slightly larger for the silicide (H C at 2 K is 2.6 and 2.0 kOe for Ho 2 Ni 0.8 Si 1.2 and Ho 2 Ni 0.8 Ge 1.2 , respectively).
3.2.2. Heat Capacity. The heat capacity has been measured for both compounds between 2 and 100 K in zero and applied magnetic fields of 10, 20, and 30 kOe (Figure 9a,b).
The data show the main λ-type peaks in agreement with the global magnetic ordering transition temperatures determined from the M(T) data, indicating that these phase changes are second-order. Plotting C P /T versus T of the zero-field data (insets of Figure 10) clearly reveals additional broad anomalies, approximately matching the weak anomalies seen in the M(T) data. Rapid upturns observed below ∼4 K in both compounds reflect the hyperfine field contributions commonly observed in other Ho-based intermetallics. 26 Under the applied magnetic field, the main peaks initially move to lower temperatures,   Inorganic Chemistry pubs.acs.org/IC Article suggesting at least some degree of antiparallel coupling between the Ho magnetic moments in both compounds. This supports the idea mentioned above that the low value of the magnetization at 70 kOe and its nonsaturation might be caused by AFM contributions. Broad anomalies are also observed at about 12 K for both compounds, likely indicating spin reordering under a magnetic field. 3.3. Magnetic Structure. High-resolution powder neutron diffraction data confirm the orthorhombic crystal structure of both the Ho 2 Ni 0.8 Si 1.2 and Ho 2 Ni 0.8 Ge 1.2 compounds as well as the mixed Ni/Si occupation of only one of the eight 4c Wyckoff sites (Figure 10a,b), with the final refined stoichiometries being about Ho 2 Ni 0.78(1) Si 1.22 (1) and Ho 2 Ni 0.76(2) Ge 1.24 (2) . No sign of the presence of any visible amounts of impurity phases is found.
The thermodiffractograms of the two compounds as measured using high-intensity powder neutron diffraction are shown in Figure 11a,b. A first magnetic transition manifests as the appearance of new Bragg peaks and the increase of the intensity of some nuclear Bragg peaks at T C = 38 and 37 K for the silicide and germanide, respectively.
All magnetic Bragg peaks can be indexed using the program K-search, which is part of the FullProf suite of programs 12 with a magnetic propagation vector κ 1 = [0, 0, 0]. Figure S3 shows the integrated intensity of the strongest among all of the magnetic peaks [i.e., the (1, 0, 0) magnetic peak] of this κ 1 phase (the first magnetic phase appearing upon cooling), as a function of the temperature, for Ho 2 Ni 0.8 Ge 1.2 ( Figure S3a) and Ho 2 Ni 0.8 Si 1.2 ( Figure S3b). A second magnetic transition seems to take place at about T N = 24 K in Ho 2 Ni 0.8 Si 1.2 and at    We will first discuss the magnetic structure present below T C before we deal with the situation below T N . Magnetic symmetry analysis using the program BASIREPS 17,18 determined the allowed irreducible representations (IRs) and their basis vectors (BVs) for κ 1 = [0, 0, 0] for the Wyckoff position 4c in the space group Pnma (Table S9). Among the eight allowed IRs, only one having a FM BV along the unit cell a direction and an AFM coupling (BV) in the c direction (IR7; Table S9) allows refinement of the diffraction data below T C . In order to have an increased sensitivity to the magnetic diffraction intensity, we refined difference data sets created by subtracting the purely nuclear intensity recorded in the paramagnetic region above T C . Figures 12a and 14 display the refinement of the difference patterns created by subtracting the 46 K data from the 26.6 K data for the germanide and the 40 K data from the 24.5 K data for the silicide.
Both compounds possess the same magnetic structure, which is displayed in an exemplary way for Ho 2 Ni 0.8 Ge 1.2 in Figure 13b. The magnetic unit cell is the same as the crystalline cell. The AFM component consists of FM stripes along the c direction of Ho1, Ho2, and Ho4 that are antiferromagnetically aligned along the a direction, separated by an AFM strip of Ho3 spins, which extends as well along the c-axis direction ( Figure 13a).
As the FM component along the a direction is added, the resulting magnetic structure is obtained, which represents a canted magnetic structure. Looking at the temperature dependence of the different magnetic reflections (Figure 11), they show a similar monotonic behavior indicating that the four Ho magnetic moments not only follow the same magnetic propagation vector but also order at the same temperature. This is equally true for both compounds. Even though all Ho sites occupy the same Wyckoff position (4c), this is not    As was already indicated above, the appearance of a very strong additional magnetic Bragg peak at very low 2θ values indicates a change in the magnetic structure and can be looked upon as a second magnetic transition defining a Neél temperature T N . The closeness of the magnetic transition temperature T N ∼ 24 K of Ho 5 Si 3 22 a possible impurity phaseto the here determined T N = 24 K for the silicide compound and a certain similitude of the main magnetic Bragg peak could question the origin of this second transition as coming from the Ho 2 Ni 0.8 Si 1.2 sample. The absence of any visible impurity phase in the high-resolution and high-intensity neutron diffraction data and the strong intensity of the additional low-angle magnetic peak exclude, however, this possibility. The same arguments speak against the origin of the low-angle magnetic peak in Ho 2 Ni 0.8 Ge 1.2 as coming from a hypothetical Ho 5 Ge 3 impurity; furthermore, in this case the transition temperatures are significantly different because T N = 27 K for Ho 5 Ge 3 22 and T N = 22 K for Ho 2 Ni 0.8 Ge 1.2 . The fact that only one broad new magnetic peak appears makes the determination of a magnetic propagation vector ambiguous, because an unlimited number of incommensurate values can be found that reproduce the position of the peak. Limiting oneself to magnetic propagation vectors having only one component and using the information on the absence of further new magnetic peaks, a simple solution can be found where κ 2 = [≈0.36, 0, 0] for Ho 2 Ni 0.8 Si 1.2 and κ 2 = [0.49, 0, 0] for Ho 2 Ni 0.8 Ge 1.2 . Magnetic symmetry analysis proposes four IRs, with two representing sine waves and two others representing cycloidal types of magnetic structures. Only one sine-wave model is able to reproduce the magnetic peak and the absence of any further magnetic peaks with reasonable magnetic moment values (Figure 12b). This sine-wave structure sees the magnetic component pointing along the unit cell b direction with a maximum amplitude of 5.0(1) μ B at 1.5 K for Ho 2 Ni 0.8 Ge 1.2 . Here, all Ho sites were constrained to have the same amplitude and the same phase. The superposition of this κ 2 = [κ x , 0, 0] modulation with the κ 1 = [0, 0, 0] order leads to a magnetic structure sketched in Figure 15. Table 5 lists the FM and AFM components of the κ 1 order and of the sine wave at 1.5 K, together with the resulting total magnetic moments of each site. The refinement assumed hereby that both magnetic couplings extend over the whole sample volume. A phase segregation scenario where one part of the sample volume follows κ 1 and the second part κ 2 cannot be taken into consideration as a solution because the total moment values would be higher than the free ion value of Ho 3+ , which is μ Ho 3+ = 10.61 μ B . The fact that the temperature dependence of the magnetic peaks created at T C do not show any change at T N (Figure 12a,b) speaks as well in favor of the additional magnetic coupling appearing at T N to act on top of the already existing magnetic order.
Because of the closeness of the first magnetic peak to the direct beam, it was not possible to attempt a refinement of the silicide data at 1.5 K including this second magnetic phase. However, it can be assumed that this second magnetic order is similar to that of the germanide because it shows a very similar temperature dependence and the same absence of additional   Table 5.
Comparing the results of neutron diffraction with those of the heat capacity and magnetic data, the question remains, why is the second transition at T N not clearly seen in the C P and magnetic data of the germanide and only very faintly seen in the data of the silicide. At least for Ho 2 Ni 0.8 Ge 1.2 , a hint is given by the temperature dependence of the peak width and peak position of the magnetic peak at very low angles, which has been used to define T N . Figure S4a−c shows that, as the temperature approaches the assumed value of T N ∼ 24 K, the peak position drifts to even lower angles, while the peak width strongly increases at the same time. This could indicate that the underlying AFM coupling is already present at higher temperatures but not developing sufficient long-range order to create a sharp peak visible in the diffraction data. This interpretation assumes therefore that at T C (where the κ 1 order sets in) short-range order of the κ 2 type appears as well already. No further clear peak in the C P data is therefore created at T N because only the correlation length of the coupling and the value κ x of the magnetic propagation vector κ 2 are changing. Figure S4 shows, furthermore, that a small anomaly is visible at around 13−14 K in the temperature dependence of the intensity of the strong low-angle peak of the κ 2 phase as well as in its full width at half-maximum and its position. It indicates a small change in the details of this incommensurate magnetic structure and can be related to the small anomaly seen in the magnetization data at 13 K.

SUMMARY
The crystal structure, magnetic properties, and magnetic structures of two new rare-earth-based intermetallic compounds, Ho 2 Ni 0.8 T 1.2 with T= Si and Ge, are reported. They correspond to the unidentified phase R 50 Ni 20 T 30 , namely, "Ho 5 Ni 2 T 3 ", earlier reported to form in the ternary systems Dy−Ni−T and Ho−Ni−T and crystallize with a filled version of the orthorhombic unit cell of the Zr 2 Ni 1−x P type [space group Pnma (No. 62); Pearson symbol oP32−y)]. While this prototype presents a vacancy of x = 0.52, which translates into a resulting stoichiometry of Zr 2 Ni 0.48 P, the stoichiometry of the two Ho compounds studied here is centered on Ho 2 Ni 0.8 T 1.2 with a very narrow solid solubility range for the silicide, while the germanide turns out to be a line phase. In addition to R = Dy and Ho, R 2 Ni 0.8 T 1.2 compounds are also formed for R = Y and Tb; attempts to prepare the homologous Gd-based Gd 2 Ni 0.8 T 1.2 failed. The R 2 Ni 0.8 T 1.2 compounds constitute the first example of an R-based compound crystallizing with the Zr 2 Ni 1−x P type, as well as the first case of an intermetallic phase adopting this ternary structural prototype.
FIM-or FM-type ordering, at 38 K for Ho 2 Ni 0.8 Si 1.2 and 37 K for Ho 2 Ni 0.8 Ge 1.2 , is revealed by the magnetization data; this main transition is then followed by subsequent magnetic orderings at lower temperatures. The susceptibility data in the paramagnetic region give effective moments, μ eff , of 10.68 and 10.75 μ B for the silicide and germanide, respectively; both values are very close to the theoretical value of 10.61 μ B . Neutron diffraction shows the existence of two magnetic propagation vectors in both compounds. First transitions at T C = 38 K for the silicide and at 37 K for the germanide lead to a commensurate κ 1 = [0, 0, 0] magnetic structure having FM and AFM components. At lower temperatures, an additional AFM coupling, appearing below T N2 ∼ 24 K for the silicide and ∼22 K for the germanide and following an incommensurate magnetic propagation vector κ 2 = [κ x , 0, 0], coexists with the first magnetic structure.
Single-crystal data, SEM photographs, Rietveld refinements data from powder XRD, isothermal magnetization plots of Ho 2 Ni 0.8 Si 1.2 and Ho 2 Ni 0.8 Ge 1.2 for data measured at 2 K, plots of the integrated neutron diffraction intensities of the (1, 0, 0) magnetic peak of both compounds, and temperature dependence of the strongest low-angle neutron diffraction peak of Ho 2 Ni 0.8 Ge 1.2 (PDF)