Structural and high-field magnetic properties of Laves phase RFe₂-H hydrides

Various classes of alloys of rare earth (R) and iron have been intensively studied and are widely employed in technology due to their unique physical properties.^1,2 Among them, the rare earth-rich Laves-phase compounds RFe₂ are crystallizing in a cubic crystal structure of the MgCu₂ type.^3,4 The good hard-magnetic properties, giant magnetostriction, high Curie temperatures, large magnetization, etc., make them interesting both fundamentally and application-wise.^5–7 Furthermore, RFe₂ often serves as a convenient object for testing existing theories.⁸ 

While RFe₂ with light rare earths (LREs) are ferromagnets, compounds with heavy rare earths (HREs) are ferrimagnets in which the mutual orientation of magnetic moments of the rare-earth and iron sublattices is antiparallel. By combining heavy and light rare earths, one can create multi-sublattice magnets with peculiar magnetic properties such as competing exchange interactions and compensated magnetization (mutually canceled magnetic moments of sublattices). Specifically, the system containing Tb (HRE) and Sm (LRE), (Tb,Sm)Fe₂ is particularly interesting from a practical point of view, because depending on the ratio of the rare earths, both the magnitude and sign of giant magnetostriction can be varied on demand in the alloy.^9–13 It should be noted that special conditions (often extreme, see, for example, Ref. 12 )should be used for the preparation of (Tb,Sm)Fe₂. Large variation of the synthesis parameters and heat treatment modes can influence remarkably the real properties of this practically important system.

The main magnetic characteristics of RFe₂ can be tuned in a variety of ways. Important information on the magnetic properties can be obtained using partial substitution of yttrium for magnetoactive rare-earth atoms, namely, (Y,R)Fe₂ compositions.^14,15 It was shown that a combination of substitutional and interstitial (hydrogen or deuterium) atoms enables an efficient control of the magnetic ordering temperature, magnetization, and magnetostriction of the (Y,Tb,Sm)Fe₂—H multicomponent system.¹⁵ Not only the magnetic but also the structural properties of (Y,Er)Fe₂ undergo significant changes upon hydrogenation.¹⁴ The strong response of RFe₂ to hydrogenation (or deuteration) is due to two main factors: a substantial increase in the unit cell volume, and as a consequence of the distances between the magnetoactive atoms, concomitant changes in the electronic structure.^16–18 Hydrogenation of RFe₂ increases the Fe sublattice magnetic moment due to a transition of part of the electrons from the 3d-band to the electronic states created by hydrogen.^19–22 Hydrogen absorption by the collinear ferrimagnet TmFe₂ leads to the formation of a noncollinear ferrimagnetic structure at low temperatures.²³ Furthermore, new compositions among the RFe₂-type hydrides and deuterides with a magnetic compensation can be found.

The complete magnetization process in RFe₂—H with a ferrimagnetic structure has been studied using high and ultrahigh magnetic fields.^14,23 Application of magnetic fields up to 60–100 T permits rotations of the individual sublattices' (Fe and R) moments and observation of the field-induced ferromagnetic state in some compounds.²³ The experimental data can be analyzed in order to determine the R-Fe exchange interaction and magnetocrystalline anisotropy.²⁴ 

The aim of this work is to investigate the high-field magnetization of (Tb,Y,Sm)Fe₂-H compounds with competing exchange interactions.

Details of the preparation of the parent samples (Tb_1−xY_x)_0.8Sm_0.2Fe₂ (without using extreme conditions), as well as their hydrides (Tb_1−xY_x)Sm_0.2Fe₂H_3.7, are given in Ref. 15. X-ray diffraction (XRD) patterns were obtained in a Bragg–Brentano geometry using a РANalytical Еmpyrean diffractometer with a two-coordinate detector Pixel3D, a system of variable slots, and a nickel filter. Data were collected using Cu-Kα radiation (operating mode I = 40 mA, U = 40 kV) in the range $2θ= 5 °− 140 °$ at a step of $0.026 °$⁠. In order to determine the structural properties, the whole diffraction patterns were analyzed using the Rietveld method and the Fullprof software. The error in the determination of the lattice parameters is $±0.002 A$⁠.

High-field magnetization was measured up to 58 T at 5 K using a compensated pair of coils at the Dresden High Magnetic Field Laboratory.^25,26 The rise time of 7 ms to 58 T results in a field sweep rate of about 0.1 ms/T. The high-field data were normalized to static-field measurements up to 10 T obtained using a PPMS installation (Quantum Design, USA).¹⁵ The measurements were carried out on free powder samples.

The x-ray diffraction patterns obtained at room temperature show that the compounds Tb_0.8Sm_0.2Fe₂ and Y_0.8Sm_0.2Fe₂ are single phase (Fig. 1). The crystal structure of both compounds is isotype to the cubic Laves-phase C15 (MgCu₂, space group Fd3m). The lattice parameter a (and unit cell volume V) is $7.358 A$ (⁠ $398.4 A 3$⁠) and $7.366 A$ (⁠ $399.7 A 3$⁠) for Tb_0.8Sm_0.2Fe₂ and Y_0.8Sm_0.2Fe₂, respectively. The relative volume change, $ΔV/V$⁠, upon full substitution of Tb for Y is −0.3%.

We find that hydrogenation does not alter the crystal lattice type. The Tb_0.8Sm_0.2Fe₂H_3.7 and Y_0.8Sm_0.2Fe₂H_3.7 hydrides are also single phase (Fig. 1). The lattice parameter a (and the unit cell volume V) is $7.985 A$ (⁠ $509.1 A 3$⁠) and $8.001 A$ (⁠ $512.2 A 3$⁠) for Tb_0.8Sm_0.2Fe₂H_3.7 and Y_0.8Sm_0.2Fe₂H_3.7, respectively. The relative volume change, ΔV/V, upon hydrogen absorption in Tb_0.8Sm_0.2Fe₂H_3.7 and Y_0.8Sm_0.2Fe₂H_3.7 is significant, ∼28%.

In (Tb_1−xY_x)_0.8Sm_0.2Fe₂ and their hydrides (Tb_1−xY_x)_0.8Sm_0.2Fe₂H_3.7 (x = 0.2, 0.4, 0.6, and 0.8) together with the main MgCu₂-type phase, we detect 5%–8% of a second phase with a crystal structure of the PuNi₃ type (space group R3m). Figure 2 shows XRD patterns of (Tb_1−xY_x)_0.8Sm_0.2Fe₂ with x = 0.4 and its hydride at room temperature. The impurity phase absorbs some hydrogen too. The exact amount of hydrogen we were not able to estimate since we do not know the chemical composition of this phase. However, the volume change estimated using XRD for the impurity phase is ∼18%–20%, whereas for the main phase it is higher, ∼28%. Taking into account the fact that hydrogenation practically does not change the ratio of the phases, we made the corresponding corrections when estimating the hydrogen content of the main phase.

Figure 3 shows the dependences of the lattice parameter a of the parent compounds (Tb_1−xY_x)_0.8Sm_0.2Fe₂ and their hydrides (Tb_1−xY_x)_0.8Sm_0.2Fe₂H_3.7 on the Y concentration. In general, the increase in the Y concentration results in an increase of a for both series of compounds due to the larger atomic radius of Y as compared to Tb. The drop in a in the vicinity of x = 0.8 is probably due to a small deviation in the composition as a result of a large amount of the second phase present in the sample (8%).

Magnetization measurements performed in static magnetic fields up to 10 T in Ref. 15 revealed an important feature of the parent compounds (Tb_1−xY_x)_0.8Sm_0.2Fe₂. As the Y content increases, the magnetization first decreases due to magnetic compensation of the Fe, Sm, and Tb sublattices and then increases. The sample with x = 0.6 was found to be the closest to the compensation. We also showed that the magnetic structure of the parent compounds (Tb_1−xY_x)_0.8Sm_0.2Fe₂ is collinear.

We constructed a phase diagram in Fig. 4 that shows the magnetization of (Tb_1−xY_x)_0.8Sm_0.2Fe₂ in both the ferrimagnetic and ferromagnetic states.

Figure 5 shows the field-dependent magnetization of (Tb_1−xY_x)_0.8Sm_0.2Fe₂ at 4.2 K up to 58 T. It can be seen that the M(H) curves for the ferrimagnets (Tb_1−xY_x)_0.8Sm_0.2Fe₂ with x = 0, 0.2 and 0.8 saturate. A slight increase in the magnetization is observed for the compositions (Tb_1−xY_x)_0.8Sm_0.2Fe₂ with x = 0.4 and 0.6 (i.e., close to the full compensation in composition with x ≈ 0.58).¹⁵ However, the magnetization in 58 T is very far from the calculated M_ferro (Table I), indicating that the exchange interactions between the sublattices have not been fully broken and the magnetic fields used are not sufficient to cause significant rotations of the magnetic moments of the individual sublattices.

Let us now consider the magnetization of the hydrides (Fig. 6). Taking into account the volume increase of 28% in the hydrides with a high hydrogen content (Tb_1−xY_x)_0.8Sm_0.2Fe₂H_3.7, one may expect a significant weakening of the exchange interactions due to the enlarged distances between the magnetoactive ions. Our preliminary studies of hydrides (Tb_1−xY_x)_0.8Sm_0.2Fe₂H_3.7 in static magnetic fields up to 10 T¹⁵ and current work showed that the compensation composition is different compared to the compounds without H. For the hydrogen concentration of 3.7 at. H/f.u., the compensated composition is expected to be x ≈ 0.

Assuming collinear magnetic structures for the hydrides, the use of Eq. (2) provides another x value for the compensated compound, x = 0.4 for $μ F e=2.1 μ B$ (see Fig. 4).^32–34 The difference between the estimation and experimental observation points to a possibility of the emergence of a noncollinear magnetic structure in the hydrides, which can contribute to the rotation of the magnetic sublattices in high magnetic fields. Indeed, a comparison of the experimental M(H) curves for (Tb_1−xY_x)_0.8Sm_0.2Fe₂ (Fig. 5) and (Tb_1−xY_x)_0.8Sm_0.2Fe₂H_3.7 (Fig. 6) shows that the hydrogenated samples (x = 0, 0.2, 0.4, 0.6, and 0.8) have a larger magnetization. The largest magnetization of the samples with x = 0.2 and 0.4 reached in a magnetic field of 58 T is still much lower than the potential magnetization of the field-induced ferromagnetic state (10.10 and $8.66 μ B$ for x = 0.2 and 0.4, respectively) when all three sublattices (Fe, Tb, and Sm) align parallel to the applied field.

Figures 7 and 8 show the high-field magnetization of free powder samples (Tb_1−xY_x)_0.8Sm_0.2Fe₂ with x = 0 and x = 0.6 and 0.8, respectively, at 4.2 K. Here, the horizontal lines M_ferro indicate the total magnetization in the ferromagnetic state calculated using Eq. (1) and listed in Table I. It can be seen that the M(H) curves for (Tb_1−xY_x)_0.8Sm_0.2Fe₂ with x = 0.6 and 0.8 are close to the full saturation. It allows us to estimate the critical fields, H_CR, of the transition to the ferromagnetic state as ∼ (80–100) and (65–70) T, respectively. For the composition (Tb_1−xY_x)_0.8Sm_0.2Fe₂ with x = 0, extrapolation of the M(H) curve to $H→∞$ is difficult because of the rather large expected H value.

We obtained $λ≈14±1$ and $20±3T/ μ B$ for the hydrides (Tb_1−xY_x)_0.8Sm_0.2Fe₂H_3.7 with x = 0.6 and 0.8, respectively. Our calculations basically provide a lower limit for the exchange parameter $λ$ in the case of a zero/small magnetic moment induced on Y sites in hydrides. Earlier studies of pseudobinary compounds (R,Y)Fe₂ (R = Gd, Tb, Ho, Er) showed that $λ$ changes considerably with composition.³⁸ For example, $λ$ is 32.7 and 62 $T/ μ B$ for Tb_0.6Y_0.4Fe₂ and Tb_0.3Y_0.7Fe₂, respectively. The present work shows a strong effect of interstitial and substitutional atoms on the inter-sublattice coupling of the Laves-phase type (Tb,Y,Sm)Fe₂H_z compounds. Earlier, we observed such a strong effect (up to 50%) in hydrides (Nd_0.5R_0.5)₂Fe₁₄BH_z with a high hydrogen content and non-diluted rare-earth sublattice.³⁵ 

We have observed many important phenomena that arise in hydrides of compounds with a Laves-phase structure. This is the phenomenon of magnetic compensation, the phenomenon of a ferromagnetic state induced by an external magnetic field, and the phenomenon of the violation of the collinear magnetic structure when hydrogen atoms are introduced into the crystal lattice. The simultaneous observation of these effects in the same compounds is unique. The results are undoubtedly important from the viewpoint of fundamental and applied science. The materials studied in this work can find applications as highly sensitive hydrogen sensors.

We demonstrate that hydrogenation is an efficient tool to tune the strength of R-Fe exchange coupling. The studies carried out in this work for the (R,Y,R′)Fe₂ compounds with R = Tb and R′ = Sm in high magnetic fields show a strong dependence of the critical field H on the Y content. From the simple mean-field model, the parameter of the inter-sublattice exchange interaction $λ$ was estimated for (Tb_1−xY_x)_0.8Sm_0.2Fe₂H_3.7 (x = 0.6 and 0.8). Similar studies performed for a wide class of substituted compositions (RR')Fe₂-H are desirable.

The structural studies are supported by the project “Nanomaterials Centre for Advanced Applications,” Project No. CZ.02.1.01/0.0/0.0/15_003/0000485, financed by ERDF. Magnetic studies in steady fields were performed under the support of the Czech Science Foundation (Project No. 19-00925S) and by MGML (https://mgml.eu) within the Program of Czech Research Infrastructures (Project No. LM2018096). For the high-field studies, we acknowledge the support of HLD at HZDR, a member of the European Magnetic Field Laboratory (EMFL). The authors are grateful to Dr. T. Yu. Kiseleva for help with the experiment.

The data that support the findings of this study are available within the article.