3.1 Crystal chemistry and chemical bonding

More than 30 intermetallic cerium compounds CeTX crystallize with the hexagonal ZrNiAl type structure [54, 80, 81], space group P6̅2m, Pearson symbol hP9, and Wyckoff sequence gfda. The basic crystallographic data of these phases are listed in Table 1. The ZrNiAl structure itself can be considered as a ternary ordered version of the Fe₂P type [82]. The basic crystal chemistry of the ZrNiAl phases (the Pearson data base [1] lists more than 1700 entries for this structure type) is well documented [2, 83, 84]. Herein we focus only on the peculiarities of the cerium containing materials.

The CeTX phases show broad coloring on the T and X sites, i.e., T= Ni, Cu, Rh, Pd, Ag, Ir, Pt, and Au and X= Mg, Zn, Cd, Hg, Al, Ga, In, Tl, Sn, and Pb, leading to a large structural flexibility. These colorings offer valence electron counts between 14 (CeRhMg) and 17 (CeAuIn). Three further phases show the same atomic sites, but a coloring exclusively with p elements. In the structures of CeMgX (X= Ga, In, Tl) [39–42], the p element takes the position of the transition metals, leading to a different bonding pattern.

As an example we present the CeRhSn structure in Fig. 1. Ce atoms fill Wyckoff site 3f (x 0 0) with x= 0.41444, the two crystallographically independent rhodium sites are 2d (1/3 2/3 1/2) (Rh1) and 1a (0 0 0) (Rh2), and the Sn atoms are on 3g (x 0 1/2) with x= 0.75012. The striking structural motif is the trigonal prismatic coordination of the Rh atoms. Rh1 has six cerium neighbors at 304 pm Rh1–Ce and the Rh2 has six tin neighbors at 277 pm Rh2–Sn. The Rh1@Ce₆ prisms are condensed via common edges in ab direction forming six-membered rings which further condense in c direction via common triangular faces. This substructure leaves large channels which are filled by rows of Rh2@Sn₆ prisms. Both prismatic substructures are shifted with respect to each other by half the lattice parameter c. This leads to coordination number 9 for both Rh atoms in the form of tri-capped trigonal prisms (Fig. 2), a typical coordination in intermetallic compounds [15]. The high structural flexibility of this structural arrangement relies on the easy adjustment of the size of the two trigonal prisms (c/a ratio) through changes of the lattice parameters and the two x parameters.

Fig. 1:

The crystal structure of CeRhSn [75]. Cerium and tin atoms are drawn as blue and magenta circles, respectively. The trigonal prisms around the two crystallographically independent rhodium atoms are emphasized.

Fig. 2:

Coordination of the two rhodium atoms in CeRhSn. The site symmetries are indicated.

The shortest interatomic distances in the CeRhSn structure occur for Rh–Sn (277 and 285 pm), only slightly longer than the sum of the covalent radii of 265 for Rh + Sn [13]. One can thus assume significant Rh–Sn bonding and the formation of a three-dimensional polyanionic [RhSn]^δ– network (Fig. 3), in agreement with electronic structure calculations [9, 75]. The triangular faces of the Rh2@Sn₆ prisms show Sn–Sn distances of 323 pm, close to the Sn–Sn distances in metallic β-Sn (4 × 302 and 2 × 318 pm) [85]. Besides covalent Rh–Sn bonding, the [RhSn]^δ– network is additionally stabilized through Sn–Sn bonding interactions.

Fig. 3:

The structure of CeRhSn. Cerium, rhodium, and tin atoms are drawn as blue, black, and magenta circles, respectively. The three-dimensional [RhSn]^δ– polyanionic network is emphasized.

Ce atoms have five Rh atoms as closest neighbors with Ce–Rh distances of 304 and 309 pm, slightly longer than the sum of the covalent radii for Ce + Rh of 290 pm [13]. These bonding interactions are a direct consequence of the course of the electronegativities, rhodium being more electronegative than tin. Electronic structure calculations showed remarkable covalent Ce–Rh bonding. These bonds play an important role for the physical properties of CeRhSn (vide infra). The near-neighbor coordination of the Ce atoms in CeRhSn is presented in Fig. 4. Each Ce atom has a sandwich-like coordination by two slightly distorted but planar Rh₂Sn₃ pentagons which are connected through a common Rh atom. Within the ab plane there are four cerium neighbors at 389 pm and two further cerium neighbors at 409 pm above and below (the c lattice parameter).

Fig. 4:

Coordination of the cerium atoms in CeRhSn. Cerium, rhodium, and tin atoms are drawn as blue, black, and magenta circles, respectively. Relevant interatomic distances (in units of pm) are given.

The Ce–Ce and Ce–T distances are important parameters for the magnetic ground state of the CeTX compounds. For those compounds where structure refinements based on powder or single crystal X-ray diffraction data are available we list the corresponding Ce–Ce and Ce–T distances in Table 2. For the whole series of CeTX intermetallics the Ce–Ce distances range from 359 to 433 pm. For comparison, the Ce–Ce distance in fcc cerium [85] is 365 pm. Furthermore, all Ce–Ce distances in the CeTX phases are longer than the Hill limit of 340 pm for 4f electron localization [86]. This will be discussed further along with the magnetic data (vide infra). Also the Ce–T distances play an important role for the magnetic behavior. For the series of CeTX compounds the Ce–T distances range from 288 to 325 pm (Table 2). The course of these distances is primarily a consequence of the size of the transition metal atom. In all cases (for electrostatic reasons), the more electronegative transition metal is the nearest neighbor for the Ce atom. This is also the case for the three triel compounds CeMgX (X= Ga, In, Tl), which can be considered as a gallide, indide, and thallide. These phases can be taken as p element analogs of CeMgT (T= Rh, Pd, Ag, Pt, Au) which carry a partial negative charge on the T atoms [87, 88].

Experimental data on the electronic structures of CeTX intermetallics were obtained from XPS measurements. These experiments gave direct evidence for the location of the Ce(4f) and T(nd) levels with respect to the Fermi level. Detailed studies were performed for the indides CeTIn (T= Ni, Cu, Pd, Pt, Au) [59, 62, 67, 71]. The XPS spectra clearly confirm the intermediate cerium valence in CeCuIn [62]. For CeRhIn and CeRhSn high-resolution photoemission studies have revealed a strong Ce(4f¹) contribution near the Fermi level. Together with a weak Ce(4f⁰) peak this indicates strong valence fluctuations in both compounds, but with a weaker hybridization strength in CeRhSn [89].

Not all ZrNiAl type CeTX compounds are stable over the whole temperature range. The gallide CeNiGa [90, 91] and the zinc compound CePdZn [50] transform to TiNiSi type high-temperature modifications. In the case of CePdZn, electronic structure calculations along with magnetic data point to larger Ce(4f)–Pd(4d) hybridization for the ZrNiAl type phase.

3.2 Magnetic properties

The intermetallic CeTX compounds belong to the class of strongly correlated electron systems. The main parameter that governs the broadly varying physical properties is the coupling constant J_cf between the Ce(4f) and the conduction electrons. One can then observe competition between the well-known indirect RKKY interactions [92–94] and the Kondo effect [95, 96]. The interplay of these parameters has qualitatively been described in the Doniach diagram [97] and its updated versions [2, 98, 99]. Based on this scheme on can roughly regroup the cerium compounds into three classes, i.e., (i) a normal localized Ce(4f) state along with a magnetic moment (called a magnetic RKKY metal) occurs if the Ce(4f) level lies below the Fermi level, (ii) a magnetic Kondo system, when the Ce(4f) level approaches the Fermi level, leading to a reduction of the magnetic ordering temperature and the magnetic moment, and (iii) a non-magnetic Kondo system in the case of a further increase of J_cf, leading to valence fluctuations. Some correlation of the magnetic properties of the CeTX intermetallics with the interatomic distances and the cell volume has been observed. Besides these general parameters influencing the Ce(4f) states, the triangular arrangement of the Ce atoms (slightly distorted Kagomé network) in the ZrNiAl type can cause topological frustration of the Ce(4f) moments. This will be discussed in more detail along with the magnetic structures determined from neutron diffraction data (vide infra). In the following discussion we start with the materials of the first group which show magnetic ordering. As is evident from Table 1, the Néel temperatures are low in all cases.

All CeTX compounds with trivalent cerium show experimental effective magnetic moments close to the free ion value of 2.54 μ_B for Ce³⁺. As a first example we present the ternary gallide CeMgGa which orders antiferromagnetically at T_N= 3.1 K [39] and shows a metamagnetic transition at a critical field strength of 1 T. In the magnetically ordered state, the magnetic moment at 5 T and 1.72 K of 0.8 μ_B per cerium atom is significantly reduced when compared with the theoretical value of 2.14 μ_B according to g × J, frequently observed in many cerium based intermetallics.

The high-pressure modifications HP-CePdSn [32] and HP-CePtSn [33] also show stable trivalent cerium over the whole temperature range. Low-field magnetic susceptibility and specific heat data point to antiferromagnetic ordering at T_N= 5 K for the palladium compound, while HP-CePtSn remains paramagnetic down to 2 K. In comparison with the TiNiSi type normal-pressure modification of CePdSn one observes a decrease of the magnetic ordering temperature from 7.5 to 5 K.

The magnesium compounds CePdMg, CePtMg, and CeAuMg [12, 45] show Curie-Weiss behavior and negative paramagnetic Curie temperatures of –36, –35, and –57 K, respectively, hinting to antiferromagnetic interactions in the paramagnetic range. Low-field susceptibility measurements have shown antiferromagnetic ordering at T_N= 2.1, 3.6, and 2.0 K for CePdMg, CePtMg, and CeAuMg, respectively, and this was confirmed through specific heat measurements. The isotypic silver compound CeAgMg is also trivalent with 2.52 μ_B per Ce atom; however, no magnetic ordering occurs down to 2 K [47]. When substituting magnesium by cadmium one obtains the isoelectronic compound CeAuCd which orders antiferromagnetically at T_N= 3.7 K [53]. This increase is most likely not due to geometrical parameters, since the unit cells of both gold compounds are very similar (Table 1).

The aluminide CeCuAl (T_N= 5.2 K) has one of the highest Néel temperatures in the series of CeTX compounds [102, 103, 105]. A curvature in the temperature dependence of the magnetic susceptibility at low temperatures is indicative of the presence of crystal field effects. The trivalent ground state of cerium in CeCuAl has been confirmed by core-level spectroscopy [105]. An important issue regarding the investigated CeCuAl samples concerns ferromagnetic impurity phases which can affect the susceptibility measurements. The isotypic indide CeCuIn does not order magnetically down to 1.9 K [62, 63]. Nevertheless, cerium is in a stable trivalent ground state with an experimental effective magnetic moment of 2.50 μ_B per cerium atom. This is underlined by XPS spectra which also show some hybridization of the Ce(4f) states with the conduction band states.

The so far highest Néel temperature in this structural family has been measured for CeAuIn (T_N= 6 K) [106–108]. The magnetic structure determination of CeAuIn was based on neutron powder diffraction data. CeAuIn is a simple antiferromagnet with a propagation vector k= (0, 0, 1/2) and an absolute value of the cerium magnetic moment (lying within the ab plane) of 1.2 μ_B.

The magnetic behavior of CePdAl has been studied in detail on powder samples as well as on single crystals grown by the Czochralski method [109, 110]. A partially ordered antiferromagnetic ground state has been observed below T_N= 2.7 K. The main interest of these investigations concerned frustration of the cerium magnetic moments, a consequence of the Kagomé-related arrangement of the Ce atoms. Besides the susceptibility and heat capacity studies also theoretical investigations were performed. The thermodynamic properties of CePdAl were evaluated along with orbital degeneracy and crystal field effects. Approval of the model was obtained through fits of the specific heat data [111]. The heavy fermion character of CePdAl was evidenced from C_P data which revealed an electronic specific heat coefficient of γ ≈ 610 mJ mol^–1 K^–2 [112]. Electronic structure calculations along with XPS core level and valence band spectra show strong hybridization of the Ce(4f) and Pd(4d) states, strongly influencing the magnetic ground state properties of CePdAl [113]. The crystal electric field (CEF) levels of ≈ 240 K and > 400 K were determined from inelastic neutron scattering experiments. The energies of the CEF excitations are E₁= 21.09 and E₂= 44.7 meV [114].

The geometrical magnetic frustration in CePdAl was thoroughly studied by neutron diffraction [115–117]. The alignment of the cerium magnetic moments is not as simple as in CeAuIn discussed above. The diffraction data showed an incommensurate antiferromagnetic propagation vector k= (1/2, 0, 0.35), leading to a longitudinal sine-wave modulated arrangement of the spins. Within this spin structure, magnetically ordered moments coexist with frustrated, disordered moments. In total, only 2/3 of the cerium magnetic moments are in an ordered state with moments of 1.6–1.8 μ_B. Additional neutron diffraction experiments on a CePdAl single crystal under an applied magnetic field of 5.5 T along the easy axis of magnetization (c axis) show a hysteretic process. Those moments that are geometrically frustrated under zero-field conditions can be lifted under the influence of the applied field [117].

²⁷Al solid state NMR spectroscopic data on polycrystalline CePdAl samples are indicative of a slow spin fluctuation rate below the Néel temperature [109, 118, 119]. Spin-echo spectra are compatible with the partially ordered magnetic state derived from the neutron diffraction experiments.

The stability of the partial antiferromagnetic ground state of CePdAl was tested under high magnetic field and high-pressure conditions [120–123]. Magnetization experiments were carried out up to an external field strength of 43 T. CePdAl shows three filed-induced transitions at critical field values of 3.2, 3.4 and 4.0 T and a saturation magnetic moment of 1.05 μ_B at 1.75 K and 43 T, significantly reduced when compared with the theoretical value of 2.14 μ_B, indicating substantial crystal field splitting of the J= 5/2 ground state. Resistivity measurements under high-pressure show disappearance of the magnetic ordering at pressures above 1 GPa.

Now we turn to the compounds with reduced magnetic ordering temperature. Strong Ce(4f)-Pd(4d) hybridization has been substantiated from electronic structure calculations for α-CePdZn [50]. This low-temperature modification contains stable trivalent cerium (μ_eff= 2.42 μ_B), but no magnetic ordering was evident down to 2 K. The plumbides CePdPb and CePtPb show similar behavior. Susceptibility and specific heat studies gave no hint for magnetic ordering of CePdPb down to 3 K [78]. CePtPb [20] orders antiferromagnetically at T_N= 0.9 K and a magnetization isotherm at 2.3 K shows a saturation value of 0.92 μ_B per Ce atom (perpendicular to the c axis) at 18 T. Pressure-dependent ac susceptibility measurements show an almost linear increase of the Néel temperature with increasing pressure with a value of 1.2 K at 17 kbar. The physical property measurements on a single crystal point to strongly anisotropic behavior which has its origen in the low symmetry CEF at the cerium site within the distorted Kagomé-like networks in the ZrNiAl-type structure.

Broad studies on polycrystalline material as well as for single crystals were reported for the dense Kondo compound CePdIn [23, 68, 124–129]. CePdIn orders antiferromagnetically at T_N= 1.65 K and the heavy fermion ground state was derived from specific heat data. The specific resistivity exhibits a pronounced Kondo minimum around 20 K. Well resolved specific heat studies down to the mK regime reveal a two peak structure for the lambda transition with maxima at 1.7 and 0.9 K [126]. The transition at 1.7 K was attributed to the onset of antiferromagnetic ordering, and the second one to a reorganization of the localized Ce(4f) moments. Another possibility is a competition between the antiferromagnetic ordering and formation of a heavy fermion state [128]. The anisotropy of the magnetic behavior was evident from single crystal data, similar to CePtPb [20]. The paramagnetic Curie temperatures along the a and c axis of –65 and –43 K show distinct differences and the kink at the Néel point is only visible for the data along c [127].

The Debye temperature of CePdIn is 190.7 K and the Ce^{3+ 2}F_5/2 ground state multiplet splits into three Kramers doublets at 0, 75, and 288 K [67]. Inelastic neutron scattering experiments gave no hint for a noticeable contribution from the CEF at energies up to 18.4 meV [130]. The electronic structure of CePdIn (along with CeNiIn, CeCuIn and CeAuIn) was investigated by X-ray photoelectron spectroscopy [59] and the spectra were analyzed on the basis of the Gunnarsson-Schönhammer model [131–133]. A large hybridization parameter Δ of 177 meV was derived.

The last trivalent compound in the CeTIn family is the indide CePtIn. Its physical properties were studied on polycrystalline material and oriented single crystals [26, 125, 128]. Similar to the CePdIn analogue, CePtIn was also classified as a heavy fermion material (C/T ≥ 0.5 J K^–2 below 1 K) [134]; however, no magnetic ordering occurs down to 60 mK. The electronic structure of CePtIn was established experimentally on the basis of X-ray photoelectron spectroscopy [71]. The Ce(3d) spectrum was analyzed by the Gunnarsson-Schönhammer model, yielding an energy value of 170 meV for the hybridization between the Ce(4f) and the conduction electron band.

Finally we turn to the non-magnetic Kondo compounds, where a further increase of J_cf leads to valence fluctuations. This peculiar magnetic behavior preferentially occurs for the CeTX phases with small T and X atoms and thus smaller cell volumes. CeNiZn shows an almost temperature independent magnetic susceptibility down to 50 K with an absolute value of ca. 1.2 × 10^–3 emu mol^–1, indicating a nearly tetravalent state of cerium [48], i.e., the Ce(4f) shell is practically depleted. In view of the low absolute susceptibility, one can classify CeNiZn as a Pauli paramagnet. The whole susceptibility contribution can be attributed to the conduction electrons.

Susceptibility measurements on CeRhPb also showed Pauli paramagnetism with a comparatively low susceptibility of 2 × 10^–3 emu mol^–1 [77]. In agreement with the non-magnetic 4f⁰ ground state, electronic structure calculation revealed a very small 4f contribution in the DOS at the Fermi level.

CeNiAl has the smallest cell volume in the CeNiX (X= Al, Ga, In) series, and the low susceptibility values indicate mixed valence behavior. No hints for magnetic ordering are evident neither from susceptibility nor from specific heat data [135–137]. α-CeNiGa exhibits comparable behavior of the magnetic susceptibility and the electrical resistivity [90, 91].

The valence fluctuating compound CeNiIn [22, 125, 128] was studied in many combined investigations along with the higher congeners CePdIn and CePtIn. Single crystals of CeNiIn can be grown by the Czochralski technique. Susceptibility, resistivity and specific heat data measured on such single crystals point to significant anisotropic Kondo anomalies. Again, this is a consequence of the anisotropic mixing of Ce(4f) and conduction electron states along the a, respectively c axis.

In the series of RERhIn indides, the cell volume of CeRhIn deviates substantially from the expected lanthanide contraction [64], indicating intermediate valence for the cerium atoms. This is underlined by temperature dependent magnetic susceptibility values which (i) show small absolute values and can (ii) be understood on the basis of the interconfiguration fluctuation model (ICF) proposed by Sales and Wohlleben [138], dividing the whole susceptibility term into Ce³⁺ and Ce⁴⁺ contributions. The strong reduction of the cerium magnetic moment has also been observed in local susceptibility measurements of ¹⁴⁰Ce in RERhIn (RE= Y, La, Ce, Gd), using the method of perturbed angular correlation at different temperatures [139]. The elastic properties of CeRhIn were measured on a Czochralski-grown single crystal [24, 140]. The elastic modulus decreases with decreasing temperature (softening) and shows a pronounced minimum around 120 K which is close to the maximum in the magnetic contribution to the specific heat. This maximum is also reproduced in the temperature dependence of the thermopower [141].

Experimental data for the location of the Ce(4f) states were obtained from high-resolution Rh(3d)–Ce(4f) resonance photoemission spectroscopy [89] in comparison with isotypic CeRhSn. The samples were grown as single crystals via the Czochralski technique. Both compounds show a strong Ce(4f¹) contribution near the Fermi energy and a weak Ce(4f⁰) peak, in agreement with strong valence fluctuation behavior. In comparison, the Ce(4f) conduction electron hybridization strength in CeRhSn is weaker than that in CeRhIn. These experimental features have been complemented by electronic structure calculations [142].

First hints for intermediate cerium valence in CeRhSn were evident from the course of the cell volume in the series of RERhSn stannides and from susceptibility data [74, 75, 104, 143–149]. CeRhSn and isotypic CeIrSn were then also studied with respect to their thermoelectric behavior. The maxima were observed around 150 K (60 μV K^–1) and 300 K (40 μV K^–1) for CeRhSn and CeIrSn, respectively [143]. Especially the low temperature properties of CeRhSn were studied in detail and repeatedly reviewed [144–146, 148]. Specific heat measurements showed an enhanced electronic specific heat coefficient of 160 mJ mol^–1 K^–2 and resistivity data point to non-Fermi liquid behavior. The spin fluctuations that were evident from the susceptibility data were confirmed by ¹¹⁹Sn solid state NMR data in the low temperature regime [147].

3.3 Electrical properties

Resistivity data for diverse CeTX intermetallic compounds were measured on polycrystalline as well as single crystalline specimens. The polycrystalline samples often show severe microcracks [e.g., 102 or 106] which irreversibly falsify the absolute values. For this reason often reduced resistivity data are plotted in order to reduce these inconsistencies. For many CeTX compounds only the magnetic contribution (magnetic scattering) is of interest. Therefore the isotypic lanthanum compounds were measured for comparison and the data substracted from the cerium data (see e.g., Ref. [148]).

Usually the RKKY metals show resistivity behavior that can easily be described by a combined Bloch-Grüneisen term in the temperature regime above the magnetic ordering. This model accounts for the residual and spin disorder resistivity, the scattering of conduction electrons on phonons as well as interband scattering processes. Typical examples are CeMgGa [39] or CeCuIn [62]. Another typical feature of the transport properties is the pronounced Kondo minimum observed before the onset of magnetic ordering in the dense Kondo materials. A representative example is CePdIn [127].

The intermediate valence compounds like CeRhIn and CeRhSn show the typical quadratic temperature dependence of the resistivity at low temperatures followed by an almost linear increase. The magnetic scattering of the intermediate valence compounds is expressed through a broad maximum in the high-temperature region [64].

3.4 ¹¹⁹Sn Mössbauer spectroscopy

So far, ¹¹⁹Sn Mössbauer spectroscopy has only been applied to samples of the stannides CeRhSn and CeIrSn and their hydrides [74]. In agreement with the crystal structures, the ¹¹⁹Sn spectra show only one crystallographic tin site for the stannide and the corresponding hydride. The non-cubic site symmetry m2m leads to quadrupole splitting. At 78 K the isomer shifts (δ) of CeRhSn (1.84 mm s^–1) and CeIrSn (1.76 mm s^–1) are very similar and fall in the typical range for intermetallic tin compounds [150, 151]. The hydrides CeRhSnH_0.8 (δ= 1.87 mm s^–1) and CeIrSnH_0.7 (δ= 1.85 mm s^–1) show isomer shifts almost similar to that of the parent ternary stannide, indicating very similar s electron density at the tin nuclei [74]. This means that the hydrogenation primarily influences the Ce–T bonding and thus the cerium valence, similar to the pair of compounds CeRhSb and CeRhSbH_0.2 [152].

The crystal field parameters of CeRhSn were derived from the quadrupole splitting parameters ΔE_Q of the ¹⁵⁵Gd nuclear ground state in isotypic GdRhSn [149]: B₀²= –17.8 K and B₂²= –6.4 K.

3.5 High-pressure studies

The first aspect of high-pressure high-temperature studies concerns the synthesis condition. The stannides HP-CeTSn (T= Ni, Pd, Pt) adopt the orthorhombic TiNiSi type structure under ambient conditions and transform to the hexagonal ZrNiAl type upon pressure and temperature treatment [31–33]. Exemplarily, the HP-CePtSn sample was studied by high-temperature, in-situ X-ray powder diffraction showing re-transformation to the TiNiSi type normal-pressure modification at around 1170 K [33]. Electronic structure calculations showed a decrease of the covalent binding energy in the high-pressure phase, indicating increasing metallization (delocalization) of all bonds along with a volume contraction. Assuming a rigid band model, bonding in HP-CeNiSn and HP-CePdSn is very similar.

Besides the synthetic studies, only few physical property studies of CeTX intermetallics under high-pressure conditions have been reported. Most of these investigations concerned the resistivity behavior under hydrostatic pressures (see e.g., Ref. [129]).

3.6 Hydrogenation behavior

The coupling constant J_cf between the Ce(4f) and the conduction electrons has been discussed on the basis of the Doniach diagram in Chapter 3.2 as the important parameter which governs the magnetic ground state of a given CeTX phase. Hydrogenation of these intermetallics leads to an increase of the unit cell volume along with a decrease in the strength of the J_cf parameter. Thus, especially the CeTX phases with intermediate valent cerium are interesting candidates for hydrogen induced changes of the magnetic behavior.

The basic crystallographic data of the CeTXH_x hydrides are listed in Table 3. In addition to these samples, several other CeTX phases have been treated under hydrogen atmosphere. Not all of these samples keep the ZrNiAl structure for the metal substructure of the hydride. CeNiAl [37, 55, 153] and CeNiGa [90, 91] transform to an AlB₂ related metal substructure upon hydrogenation. In the present review we focus only on the hydrides with ZrNiAl-type metal substructure.

Besides control of the volumetric hydrogen uptake and the hydrogenation kinetics, the quantity of absorbed hydrogen and the structural consequences are the decisive issues. The latter concern the changes of the unit cell parameters as well as the crystallographic sites occupied by the H atoms. First we discuss the consequence on the lattice parameters. Hydrogenation causes an anisotropic expansion of the unit cell with much larger expansion of the c vs. the a axes (see data in Table 3). The cell volumes show an increase of up to 11 %, leading to crumbling of the samples.

Since hydrogen has an extremely weak scattering power for X-rays (especially in the neighborhood to the heavy metals of the metal substructure), their position can hardly be detected from X-ray diffraction experiments. First attempts to identify the interstitial sites for the H atoms were of purely geometric nature, analyzing the CeTX substructures with respect to their tetrahedral voids. The possible interstices have been analyzed geometrically for isotypic NdNiIn [154]. In all cases, only part of these voids are filled. The maximum hydrogen content observed corresponds to a composition CeTXH_1.8.

Several hydrides CeTXH_x have been tested for their thermal stability. Complete release of hydrogen requires temperatures in the range of 700–800 K. Usually the initial CeTX host structure is formed again. The hydrogen desorption can proceed in different steps., which were monitored by differential thermal analyses for selected CeTXH_x samples [154].

The nickel-containing deuterides CeNiInD_0.48 and CeNiInD_1.24 were studied by powder neutron diffraction [61]. Both samples show deuterium only on the 4h site with occupancy parameters of 0.362 and 0.927 for CeNiInD_0.48 and CeNiInD_1.24, respectively. Cutouts of the structures of the host CeNiIn and the deuteride CeNiInD_1.24 are presented in Fig. 5. D or H atoms fill edge- and face-sharing Ce₃Ni tetrahedra along the c axis. The drawing readily reveals the increasing c/a ratio in the deuteride (16.6 % increase of the c axis!). Each D atom has three cerium neighbors at 237 pm and one nickel neighbor at 151 pm. Within such a tetrahedral chain a NiD₂ deuteridonickelate subunit is formed. The face-sharing connectivity of the tetrahedra leads to short D–D distances of 161 pm. The hydrogen substructure has been confirmed by ¹H solid state NMR spectroscopy for CeNiInH and CeNiInH_1.6 samples in the temperature range 140 to 300 K [155].

Fig. 5:

Comparison of the empty and filled Ce₃Ni tetrahedra in the structures of CeNiIn and CeNiInD_1.24. Cerium and nickel atoms are drawn as blue and black circles, respectively. Both substructures are drawn with the same enlargement factor.

Besides the CeNiInD_x phases, also CePdInD_1.1 has been studied in detail by powder neutron diffraction [156] along with other rare earth representatives of that series. This study used a systematic symmetry analyses (including group-subgroup relations) for an exploration of all possible models with different hydrogen positions. The best fit of the diffraction data was obtained for an occupancy of three different Wyckoff sites with deuterium: 50 % on 4h, 35 % on 3g, and 8 % on 3f. Neutron powder diffraction patterns for the CePdInD_1.1 sample were also collected at 0.8 K. No superstructure reflections indicating long-range magnetic ordering have been detected.

The structural investigations have been accompanied by detailed electronic structure calculations for a concise study of chemical bonding and an evaluation of the magnetic ground states, in comparison of the CeTX and CeTXH_x phases [157–159]. Intermediate-valence CeNiIn was studied along with its hydride. Magnetic calculations of the hydride indicate a finite magnetic moment on the Ce atoms (Ce(4f) localization), thus underlining the results of the experimental magnetic property investigations (vide infra). Optimization of the hydride structures (cell volumes and c/a ratios) led to a good agreement with the experimental data. Crystal orbital Hamilton populations underline the Ni–H bonding in the NiH₂ hydridometallate subunits. Another main concern of the calculations were the short H–H distances determined from the neutron diffraction data. All these hydrides violate the so-called Switendick rule [160] (200 pm H–H separation). The first-principles calculations showed a paired and localized electron distribution at the hydrogen sites which is polarized towards the Ce and In atoms, thus reducing the repulsive H–H interactions. Extension of the study to the palladium and platinum containing members showed similar results.

Now we turn to the magnetic and electrical property studies of the hydrides. The most detailed studies were performed on the CeNiInH_x hydrides [36, 38, 161, 162]. Samples with x values of 0.5, 0.6, 0.7, 0.67, 0.75, 1.0, 1.6, and 1.8 have been prepared and studied with respect to the magnetic ground state. Increasing hydrogen content leads to an increase of the cerium magnetic moment, and the hydride with the highest hydrogen content, CeNiInH_1.8 [161] shows purely trivalent cerium along with a transition to a ferromagnetically ordered state at T_C= 6.8 K. Thus, hydrogenation leads to a drastic decrease of the Kondo interactions and switches the magnetic ground state from intermediate valence to ferromagnetism. This is also expressed in the temperature dependent resistivity data [36]. Specific heat data for a CeNiInH_1.6 sample show a sharp λ-type transition at T_C, while a moderately hydrogenated sample of composition CeNiInH_0.6 shows no sign of magnetic ordering [38]. Specific heat measurements on CeNiInH_1.8 show a significant magnetocaloric effect [163].

CePdIn absorbs one equivalent of hydrogen per formula unit [69]. Cerium remains trivalent in CePdInH. The paramagnetic Curie temperature increases from –42 to –28 K in the sequence CePdIn → CePdInH, indicating decreasing Kondo-type interactions. The Néel temperature increases from 1.65 to 3.0 K. The temperature dependence of the thermoelectric power of CePdInH shows a maximum of 9 μV K^–1 around 90 K. Polycrystalline CePdInD_1.1 showed paramagnetic behavior (μ_exp= 2.59 μ_B) down to 2 K [156], in contrast to antiferromagnetic CePdInH [69]. This might be a consequence of the slightly different H/D content, leading to domains of different degree of hydrogenation (3 sites were evident from neutron diffraction data) in the polycrystalline samples. The samples without long-range magnetic ordering most likely show strongly delocalized Ce(4f) states.

Hydrides CeRhInH_x have been studied for x= 0.55 and 1.58, respectively [65, 164]. The hydride with the larger hydrogen content shows an orthorhombic phase besides the hexagonal one and is transformed to CeRhInH_0.55 within a short time. Such an instability has rarely been observed for the CeTXH_x phases. CeRhInH_0.55 shows a slight expansion of the unit cell with respect to CeRhIn. Hydrogenation decreases the occupancy of the rhodium d bands (partial charge transfer to hydrogen), thus decreasing the hybridization between the Ce(4f) with the Rh(4d) states, inducing a shift of the cerium valence towards a nearly trivalent state. The experimental effective magnetic moment of 2.25 μ_B, however, is still reduced when compared with the free ion value of 2.54 μ_B for Ce³⁺. This behavior is similar to that of the stannides CeRhSn and CeIrSn which form the hydrides CeRhSnH_0.8 and CeIrSnH_0.7 [74].

CePtIn renders the hydride CePtInH_0.7 [70]. Under ambient conditions one observes decomposition of the hydride within a few weeks, leaving the parent compound CePtIn. CePtInH_0.7 is trivalent without any signs of magnetic ordering down to 2 K. Hydrogenation experiments along with solid state NMR studies were also carried out with CeCuAl [165, 166]. Although hydrogen contents CeCuAlH_0.64 and CeCuAlH_1.51 were reported, structural data on the hydride phases are not available.

Finally some words of caution seem appropriate. The different hydrogenation experiments of the CeTX phases lead to CeTXH_x phases with hydrogen contents up to x= 1.9 [167]. Temperature, pressure and grain size of the initial CeTX phases are important parameters that influence the hydride formation. The volumetric measurement of the hydrogen quantity always leaves a small uncertainty for the composition of the final hydride. The neutron diffraction experiments showed different and partial site occupancies for the H atoms. Thus, polycrystalline CeTXH_x samples might have a distribution of domains with different hydrogen content and/or differently occupied interstitial sites. This can easily lead to differences in the magnetic behavior. Especially the different results obtained from the neutron diffraction studies of the nickel indide and palladium indide series are a clear indication that possibly each CeTXH_x phase has its individual hydrogen substructure.

3.7 Solid solutions

As discussed above, distinctly different magnetic ground states occur for the CeTX compounds. Several studies have been devoted to solid solutions in order to investigate transitions between dissimilar ground states or to check whether or not Vegard-type behavior occurs for a given physical property. Examples have been reported for solid solution on all three sites.

Our summary starts with dilution of the cerium magnetic moments through substitution of the rare earth site with non-magnetic lanthanum or yttrium atoms. The evolution of the lattice parameters as a function of cerium-yttrium substitution has been studied in detail for the complete solid solution Ce_1–xY_xPdAl [57]. A distinct anomaly occurs in the range of 0.4 ≤ x ≤ 0.6. These samples show two sets of hexagonal lattice parameters. This indicates coexistence of an yttrium- and a cerium-richer phase, probably due to a miscibility gap. A relation with the high c/a ratio was discussed, however, based on the c/a ratios listed in Table 1 for the whole series of CeTX compounds, these arguments are hardly convincing.

Lanthanum has been substituted for cerium in Ce_1–xLa_xPdAl in the range of 0 ≤ x ≤ 0.2 [168]. Temperature dependent susceptibility measurements showed a weak decrease of the Néel temperature with increasing lanthanum concentration. Normalization of the susceptibility data to the cerium concentration revealed tri-valent cerium in all samples. An even stronger reduction of the Néel temperature is observed for the solid solution Ce_1–xY_xPdAl in the range 0 ≤ x ≤ 0.4 [169], most likely a consequence of the smaller size of the Y atoms. Again, the cerium remains trivalent in this concentration range. These results have been confirmed through specific heat studies [170].

Dilution of the cerium magnetic moments has also been investigated for Ce_1–xLa_xRhSn [171, 172]. Both the a and c lattice parameters increase with increasing lanthanum content. Detailed studies of the thermal and magnetic properties around the critical concentration of x ≈ 0.5 show spin fluctuation behavior for samples with higher lanthanum content but formation of magnetic clusters (mictomagnetism) towards higher cerium concentration. The origen of a ferromagnetic state at much higher temperatures (around 220 K) is a strange feature. Often iron-contaminated cerium is a reason for such anomalies.

The course of the lattice parameters in the solid solution Ce_1–xLa_xPtIn [173] shows almost Vegard-type behavior. The cerium magnetic behavior strongly depends on the lanthanum content. Samples in the range 0 ≤ x ≤ 0.2 show dense Kondo behavior which switches to a single-ion Kondo region for 0.3 ≤ x ≤ 0.8. These features are also manifested in resistivity and magnetoresistivity data.

The second group of solid solutions concerns substitution on the transition metal sites. Complete solid solutions are formed in CeNi_xPd_1–xIn [174] and CePd_xRh_1–xIn [175]. Starting from CePdIn, the cell volume decreases with increasing nickel, respectively rhodium content (a consequence of the smaller radii of nickel and rhodium). A small degree of palladium-nickel substitution still allows magnetic ordering. The Néel temperature of 1.7 K of CePdIn drops to 1.3 K for a sample of composition CeNi_0.2Pd_0.8In, followed by a break-down of the antiferromagnetic ground state for nickel concentrations larger than 40 %. In the solid solution CePd_xRh_1–xIn the magnetic ground state changes from antiferromagnetic to intermediate cerium valence. This is similar for CePd_1–xNi_xAl [176–178]. Several samples of this solid solution have been prepared in single crystalline form for specific heat and thermoelectric power measurements.

Solid solutions are also formed in the case of structurally different end members. CeRhSn shows substitution of rhodium by cobalt, nickel, and ruthenium [179]. These studies were performed up to 25 at.-%. The complete solid solution CeRh_1–xRu_xSn was studied recently [180]. The ZrNiAl-type structure is stable up to CeRh_0.8Ru_0.2Sn and then switches to the monoclinic CeRuSn type [181, 182]. Cerium is in an intermediate valence state over the entire concentration range. This is evident from magnetic susceptibility studies evaluated with the interconfiguration fluctuation (ICF) model introduced by Sales and Wohlleben, as well as from XANES data. The situation is similar for CeRh_1–xPd_xSn [183] and CeRu_1–xNi_xAl [184] which show the ZrNiAl-type structure for 0 ≤ x ≤ 0.8 and 0.9 ≤ x ≤ 1, respectively. Special cases are CeRu_1–xPd_xSn [183] and CeRu_1–xNi_xSn [185]. CeRuSn allows only for tiny substitutions of ruthenium on the one side, and the end members CePdSn and CeNiSn crystallize with the orthorhombic TiNiSi type on the other. Thus one observes formation of the ZrNiAl-type phases only for 0.1 ≤ x ≤ 0.7 and 0.1 ≤ x ≤ 0.4, respectively. In all these regimes, the ZrNiAl-type phases show intermediate cerium valence.

Substitution on the transition metal positions is also possible with another p element. Two recent examples concern the solid solutions CeRh_1–xGe_xIn (0.1 ≤ x ≤ 0.3) [186] and CePd_1–xGe_xIn (0.1 ≤ x ≤ 0.4) [187]. Single crystal diffraction data revealed Rh/Ge respectively Pd/Ge mixing only on the 2d sites, i.e., within the trigonal prisms formed by the Ce atoms. For the CeRh_1–xGe_xIn series, with increasing germanium content the intermediate cerium valence changes to a localized Ce(4f) state. A change of the magnetic ground state is also observed for the palladium based series. With increasing germanium content the coherent Kondo state of CePdIn vanishes gradually.

The last two solid solutions concern substitutions on the X sites. Sn atoms of CeRhSn have gradually been replaced by indium [188]. The course of the magnetic susceptibility data and the electric transport properties showed a transition from a non-Fermi liquid state to intermediate valence behavior. In the solid solution CeAuIn_1–xMg_x [189] one observes a direct break-down of magnetic ordering when indium is substituted by magnesium. Over the whole range of solid solutions one observes only very small changes in the lattice parameters.