The crystal structure and magnetic properties of the multicomponent compounds (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{z} (*x* = 0, 0.2, 0.4, 0.6, 0.8, 1; *z* = 0 and 3.7) are investigated. The compounds crystallize in the MgCu_{2} type of structure. While the parent compounds Tb_{0.8}Sm_{0.2}Fe_{2} and Y_{0.8}Sm_{0.2}Fe_{2} are single phase, we detect 5%–8% of a second phase with a crystal structure of the PuNi_{3} type (space group R3m) in the alloys with 0.2 ≤ *x* < 0.8. Hydrogen absorption does not change the space group of the (Tb,Y,Sm)Fe_{2} compounds but boosts significantly the lattice parameter *a*. A large volume change of *ΔV/V* ∼ 28% upon hydrogen absorption is observed. By applying high magnetic fields up to 58 T, we observed rotations of the magnetic sublattices and hence we were able to determine the critical transition fields, H, from the ferrimagnetic to the ferromagnetic state and the inter-sublattice exchange parameter $\lambda $. The magnetic compensation occurs at *x* ≈ 0.6 and 0.2 in (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{z} at *z* = 0 and 3.7, respectively. While maintaining the collinear magnetic structure, the phenomenon of compensation in hydrides should be observed at *x* ≈ 0.4.

## I. INTRODUCTION

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 RFe_{2} are crystallizing in a cubic crystal structure of the MgCu_{2} 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, RFe_{2} often serves as a convenient object for testing existing theories.^{8}

While RFe_{2} 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)Fe_{2} 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)Fe_{2}. 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 RFe_{2} 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)Fe_{2} 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)Fe_{2}—H multicomponent system.^{15} Not only the magnetic but also the structural properties of (Y,Er)Fe_{2} undergo significant changes upon hydrogenation.^{14} The strong response of RFe_{2} 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 RFe_{2} 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 TmFe_{2} leads to the formation of a noncollinear ferrimagnetic structure at low temperatures.^{23} Furthermore, new compositions among the RFe_{2}-type hydrides and deuterides with a magnetic compensation can be found.

The complete magnetization process in RFe_{2}—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)Fe_{2}-H compounds with competing exchange interactions.

## II. EXPERIMENTAL DETAILS

Details of the preparation of the parent samples (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} (without using extreme conditions), as well as their hydrides (Tb_{1−x}Y_{x})Sm_{0.2}Fe_{2}H_{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 $2\theta =5\xb0\u2212140\xb0$ at a step of $0.026\xb0$. 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 $\xb10.002A$.

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.

## III. RESULTS AND DISCUSSION

### A. Crystal structure

The x-ray diffraction patterns obtained at room temperature show that the compounds Tb_{0.8}Sm_{0.2}Fe_{2} and Y_{0.8}Sm_{0.2}Fe_{2} are single phase (Fig. 1). The crystal structure of both compounds is isotype to the cubic Laves-phase C15 (MgCu_{2}, space group Fd3m). The lattice parameter *a* (and unit cell volume *V*) is $7.358A$ ($398.4A3$) and $7.366A$ ($399.7A3$) for Tb_{0.8}Sm_{0.2}Fe_{2} and Y_{0.8}Sm_{0.2}Fe_{2}, respectively. The relative volume change, $\Delta V/V$, upon full substitution of Tb for Y is −0.3%.

We find that hydrogenation does not alter the crystal lattice type. The Tb_{0.8}Sm_{0.2}Fe_{2}H_{3.7} and Y_{0.8}Sm_{0.2}Fe_{2}H_{3.7} hydrides are also single phase (Fig. 1). The lattice parameter *a* (and the unit cell volume *V*) is $7.985A$ ($509.1A3$) and $8.001A$ ($512.2A3$) for Tb_{0.8}Sm_{0.2}Fe_{2}H_{3.7} and Y_{0.8}Sm_{0.2}Fe_{2}H_{3.7}, respectively. The relative volume change, *ΔV/V*, upon hydrogen absorption in Tb_{0.8}Sm_{0.2}Fe_{2}H_{3.7} and Y_{0.8}Sm_{0.2}Fe_{2}H_{3.7} is significant, ∼28%.

In (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} and their hydrides (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{3.7} (*x* = 0.2, 0.4, 0.6, and 0.8) together with the main MgCu_{2}-type phase, we detect 5%–8% of a second phase with a crystal structure of the PuNi_{3} type (space group R3m). Figure 2 shows XRD patterns of (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} 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−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} and their hydrides (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{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%).

### B. High-field magnetic properties

Magnetization measurements performed in static magnetic fields up to 10 T in Ref. 15 revealed an important feature of the parent compounds (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}. 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−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} is collinear.

It is known^{27,28} that when sufficiently strong magnetic fields are applied to ferrimagnetic samples, field-induced ferromagnetism can be observed. In this case, the magnetic moments of the Fe, Sm, and Tb sublattices will be parallel to each other. The total magnetization in the forced ferromagnetic state for (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} can be estimated (without taking into account calculated/measured moment of Y)^{29,30} as

where $MFe=2\xd7\mu Fe$, $MSm=0.2\xd7\mu Sm$, and $MTb=\mu Tb\xd7(1\u2212x)\xd70.8$ (*x* = 0, 0.2, 0.4, 0.6, and 0.8) taking into account the magnetic moments of Fe, Sm, and Tb ($\mu Fe=1.45\mu B$,^{31} $\mu Sm=0.7\mu B$, $\mu Tb=9\mu B$). All calculated M_{ferro} values are listed in Table I.

. | x = 0
. | x = 0.2
. | x = 0.4
. | x = 0.6
. | x = 0.8
. |
---|---|---|---|---|---|

z = 0 | 10.24 | 8.80 | 7.36 | 5.92 | 4.48 |

z = 3.7 | 11.54 | 10.10 | 8.66 | 7.22 | 5.78 |

. | x = 0
. | x = 0.2
. | x = 0.4
. | x = 0.6
. | x = 0.8
. |
---|---|---|---|---|---|

z = 0 | 10.24 | 8.80 | 7.36 | 5.92 | 4.48 |

z = 3.7 | 11.54 | 10.10 | 8.66 | 7.22 | 5.78 |

Recall^{15} that within the model of a three-sublattice ferrimagnet (with the magnetic moments oriented collinearly with respect to each other), a different expression should be used to determine the magnetization of the ferrimagnetic state,

We constructed a phase diagram in Fig. 4 that shows the magnetization of (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} in both the ferrimagnetic and ferromagnetic states.

Figure 5 shows the field-dependent magnetization of (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} at 4.2 K up to 58 T. It can be seen that the M(H) curves for the ferrimagnets (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} with *x* = 0, 0.2 and 0.8 saturate. A slight increase in the magnetization is observed for the compositions (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} 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−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{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−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{3.7} in static magnetic fields up to 10 T^{15} 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 $\mu Fe=2.1\mu B$ (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−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} (Fig. 5) and (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{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 $8.66\mu B$ 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−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} 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−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2} 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−x}Y

_{x})

_{0.8}Sm

_{0.2}Fe

_{2}with

*x*= 0, extrapolation of the M(

*H*) curve to $H\u2192\u221e$ is difficult because of the rather large expected

*H*value.

The magnetization increase of the hydrides is due to the higher Tb magnetic moments, which align antiparallel to the Fe and Sm magnetic moments; however, the antiparallel coupling is broken by an external magnetic field of sufficient strength. By analyzing *H*, the coupling strength (*λ*) between the sublattices can be estimated within a mean-field model.^{35–37} The following expression can be used for (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{3.7}:

where $MFe=2\xd7\mu Fe$, $MTb=\mu Tb\xd7(1\u2212x)\xd70.8$, H = 2K_{1}/M_{Fe}, and $\xi =0.2/(1+\lambda Sm\xd7\chi Sm)$. 2.1 and 9 $\mu B$ are the atomic magnetic moments of Fe and Tb, respectively. $\lambda Sm$ and $\chi Sm$ are the exchange parameter and susceptibility of the Sm sublattice, respectively, and K_{1} is a magnetic anisotropy constant. The product $\lambda Sm\xd7\chi Sm$ does not exceed 0.02.^{27} The second term describing the anisotropy can be taken into account for a more accurate estimate of the critical fields. It was shown earlier^{35} that in strong magnetic fields, the anisotropy term does not significantly change *H*. Equation (3) is universal and can be used for various types of compounds containing rare-earth elements.

We obtained $\lambda \u224814\xb11$ and $20\xb13T/\mu B$ for the hydrides (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{3.7} with *x* = 0.6 and 0.8, respectively. Our calculations basically provide a lower limit for the exchange parameter $\lambda $ in the case of a zero/small magnetic moment induced on Y sites in hydrides. Earlier studies of pseudobinary compounds (R,Y)Fe_{2} (R = Gd, Tb, Ho, Er) showed that $\lambda $ changes considerably with composition.^{38} For example, $\lambda $ is 32.7 and 62 $T/\mu B$ for Tb_{0.6}Y_{0.4}Fe_{2} and Tb_{0.3}Y_{0.7}Fe_{2}, 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)Fe_{2}H_{z} compounds. Earlier, we observed such a strong effect (up to 50%) in hydrides (Nd_{0.5}R_{0.5})_{2}Fe_{14}BH_{z} with a high hydrogen content and non-diluted rare-earth sublattice.^{35}

## IV. CONCLUSIONS

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′)Fe_{2} 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 $\lambda $ was estimated for (Tb_{1−x}Y_{x})_{0.8}Sm_{0.2}Fe_{2}H_{3.7} (x = 0.6 and 0.8). Similar studies performed for a wide class of substituted compositions (RR')Fe_{2}-H are desirable.

## ACKNOWLEDGMENTS

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.

## DATA AVAILABILITY

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

## REFERENCES

_{2}intermetallic compounds