Cerium intermetallics CeTX – review III

3.1.1 CeTX phases with AlB₂ related structures

Most of the remaining phases discussed in the present review crystallize with ternary ordering variants of the AlB₂ type. Although more than 40 superstructures of the AlB₂ type are known today [1, 5, 47, 48], the phases discussed herein all keep hexagonal symmetry. A compact and concise way to systemize such structures relies on group-subgroup relations and is best monitored through a Bärnighausen tree [49–52]. A cutout of the complete Bärnighausen tree [47] is presented in Fig. 2 with an emphasis on the CeTX phases.

Fig. 2:

Group-subgroup scheme in the Bärnighausen formalism [49–52] for CeTX phases that derive from the aristotype AlB₂. The indices for the translationengleiche (t), klassengleiche (k), and isomorphic (i) symmetry reductions, and the unit cell transformations are given.

Keeping the Bärnighausen tree in mind it is readily evident, that T/X ordering is only possible for the YPtAs [53], ZrBeSi [54], NdPtSb [53]/LiGaGe [55], and SrPtSb [56] type structures. Nevertheless, many of the CeTX phases listed in Table 1 have been ascribed to the AlB₂ subcell structure or to the CaIn₂ type with a statistical distribution of the T and X atoms on the hexagons. In view of the largely differing chemical potentials of the T and X atoms, such random distributions are not the energetically stable ground state. There might be several reasons: (i) small homogeneity ranges CeT_1±xX_1±x hamper long-range ordering and (ii) weak superstructure reflections have been overlooked. Especially in the case of similar scattering powers of the T and X atoms the superstructure reflections (which are the response of T/X ordering) are weak. Most likely all phases reported with one of the subcell structures are indeed ordered.

Before we discuss the structure types, we briefly comment on the symmetry reductions that lead to the different superstructures. In going from the AlB₂ subcell structure to the SrPtSb type (reported for CeNiAs [57]), the space group symmetry is reduced by a translationengleiche symmetry reduction of index 2 (t2) from P6/mmm to P6̅m2 (Fig. 2). In this case, the Ni/As ordering is only evident through changes in the subcell intensities. These intensity changes are weak, since nickel and arsenic differ only by five electrons.

The CaIn₂ structure [58] reported for many of the CeTX phases allows a puckering of the hexagons, however, only with random T/X distribution. The unit cell is doubled along the c axis through a klassengleiche symmetry reduction of index 2 (k2) along with a symmetry reduction from P6/mmm to P6₃/mmc (Fig. 2). This superstructure formation is expressed through the occurrence of additional reflections, so-called superstructure reflections. Ordering of T and X is then only possible through removal of the inversion center. This corresponds to a translationengleiche symmetry reduction of index 2 (t2) from P6₃/mmc to P6₃mc, leading to the NdPtSb type. Often these structures show twinning by inversion. All NdPtSb type CeTX phases show puckering of the T₃X₃ hexagons, and adjacent hexagons are rotated by 60°.

A similar ordering pattern, but with planar T₃X₃ hexagons occurs in the ZrBeSi type [54]. This structure derives from the AlB₂ subcell via a klassengleiche symmetry reduction of index 2 (k2) along with a doubling of the c lattice parameter (Fig. 2). The two symmetry reductions to the CaIn₂ and NdPtSb types lead to the same space group type, but different subcell mirror planes are lost. Puckering of the T₃X₃ hexagons occurs when the inversion center of the ZrBeSi type (translationengleiche symmetry reduction of index 2) is removed.

The largest unit cell of the hexagonal phases occurs for the YPtAs type compounds. This superstructure contains four AlB₂ subcells and requires two steps in symmetry reduction, an isomorphic step of index 2 to P6/mmm and a klassengleiche transition of index 2 to P6₃/mmc. Both steps double the unit cell along the c axis.

Examples for the ordered phases are presented in Fig. 3 for CeZnSn [59], CePdP [60], CeAuSn [61], and CeNiAs [57]. The main crystal chemical motifs are ordered T₃X₃ hexagons perpendicular to the c axis with T–X distances close to the sums of the covalent radii, indicating substantial covalent T–X bonding within the networks. This was underlined by several electronic structure calculations.

Fig. 3:

The crystal structures of CeNiAs, CeAuSn, CeZnSn, and CePdP. The two- and three-dimensional polyanionic [TX]^δ– networks are emphasized.

The four different superstructures vary in the stacking sequence and the orientation of the T₃X₃ hexagons. The simplest structure occurs for CeNiAs. The ordered Ni₃As₃ hexagons are planar and stacked in AA sequence. In CePdP every other planar Pd₃P₃ hexagon is rotated by 60°, leading to AB stacking. CeAuSn can be considered as the puckered version of CePdP. Four ordered Zn₃Sn₃ hexagons are stacked in AA’BB’ sequence in the structure of CeZnSn. Between the AA′ and BB′ layers one observes weak Zn–Zn and Sn–Sn inter-layer bonding. Stronger inter-layer bonding only occurs in CeAuSn and the other NdPtSb phases with puckered hexagons.

The cerium atoms in all these hexagonal CeTX phases are sandwiched by two T₃X₃ hexagons. The Ce–T and Ce–X distances are equal in the case of planar, but different in the case of puckered hexagons. Depending on the structure (YPtAs or NdPtSb type), the cerium atom are closer to T or X atoms (Fig. 3). In the NdPtSb type phases the closest contacts always occur for Ce–T. The degree of puckering depends on the size of the T and X atoms and some series of RETX phases show continuous transitions from two- to three-dimensional [TX] networks [62].

Finally we need to comment on the planar T₃X₃ hexagons. Many structure refinements have resulted in enhanced U₃₃ parameters of the transition metal atoms, giving strong hint for the beginning of puckering. This phenomenon has been studied in detail for CeCuSn [63]. The low-temperature form crystallizes with the NdPtSb type with a puckering of the Cu₃Sn₃ hexagons, similar to CeAuSn. A quenched sample shows the ZrBeSi structure with large U₃₃ parameters for the copper atoms. As emphasized in Fig. 4 one can rationalize this fact as a superposition of two differently tilted Cu₃Sn₃ hexagons since the diffraction data did only allow for a determination of the average structure.

Fig. 4:

Arrangement of the Cu₃Sn₃ hexagons in α- and β-CeCuSn. The copper and tin atoms are drawn as blue octands and magenta circles, respectively. β-CeCuSn shows disorder with a superposition of the ordered arrangements of α-CeCuSn. For details see text.

The puckerings and distortions of the T₃X₃ hexagons can be influenced by external parameters. High-pressure studies of hexagonal CeAuGe (NdPtSb type) in diamond anvil cells revealed a transition to the orthorhombic TiNiSi type above 8.7 GPa [64]. This phase transition leads to a three-dimensional [AuGe] polyanionic network, while the puckered Au₃Ge₃ layers in the normal-pressure phase show two-dimensional character.

3.1.2 CeTX phases with LaNiAl and related structures

The LaNiAl structure type [65] is an intergrowth variant of TiNiSi [66] and ZrNiAl [67–69] type slabs. In the family of CeTX intermetallics this structure type occurs for CeRhZn [70], CeRuAl, and CeRhAl [71]. As an example we present a projection of the CeRhZn structure in Fig. 5. The striking structural motifs are the rhodium centered trigonal prisms, similar to the TiNiSi and ZrNiAl phases [14, 15]. The CeRhZn structure contains two prism types, Rh@Ce₆ and Rh@Ce₂Zn₄. These prisms are condensed via common edges within the ac plane and via common triangular faces along the b axis. Adjacent prismatic motifs are shifted by half the translation period of b. The rectangular faces of each prism are capped by a further atom, leading to coordination number 9, frequently observed in related intermetallic structures [1, 7]. The difference of this new arrangement of prisms as compared to the TiNiSi and ZrNiAl types is due to two crystallographically independent cerium sites in CeRhZn as compared to one site in the TiNiSi and ZrNiAl type CeTX phases.

Fig. 5:

Projection of the CeRhZn and LT-CePdAl structures along the short unit cell axis. Cerium, rhodium (palladium) and zinc (aluminum) atoms are drawn as light gray, blue, and magenta circles, respectively. The rhodium (palladium) centred trigonal prisms are emphasized. All atoms lie on mirror planes that are shifted by half a translation period, indicated by thin and thick lines.

An even more complicated condensation pattern of such prismatic units was found for the low-temperature modification LT-CePdAl [72]. As is evident from the projection presented in Fig. 5, now three prism types occur, Ce₆, Ce₂Al₄, and Al₆. The condensation pattern of the trigonal prisms is similar to that of CeRhZn, but the LT-CePdAl structure has larger ZrNiAl-related slabs. A detailed comparison of these structural variants was presented in the original work on CeRhZn [70] and LT-CePdAl [72] and in a recent summary of the solid solutions CeRu_1–xPd_xAl [73]. The lower space group symmetry in LT-CePdAl (as compared to CeRhZn) is expressed in four crystallographically independent cerium sites. Due to the different condensations of the trigonal prisms both CeRhZn and LT-CePdAl do not show the typical geometrical frustration which has intensively been discussed for the hexagonal CeTX phases [14].

Important parameters for the physical properties concern the Ce–Ce and Ce–T distances. In the hexagonal AlB₂ derived phases described in the previous subchapter and in CeRhZn and LT-CePdAl, the Ce–Ce distances are longer than the Hill limit of 340 pm for 4f electron localization [74]. This will be discussed further along with the magnetic data (vide infra).

3.1.3 CeTX phases with LaPtSi and LaIrSi type structures

The silicides CeNiSi [75] and CePtSi [76] as well as the phosphides CeRhP [77] and CeIrP [78] crystallize with the tetragonal LaPtSi type structure [79], a ternary ordered version of the α-ThSi₂ type [80]. The T/X ordering leads to a reduction of the space group symmetry from I4₁/amd to I4₁md through a translationengleiche reduction of index 2. The CePtSi structure is presented as an example in Fig. 6. The platinum and silicon atoms build up a three-dimensional [PtSi] network with platinum and silicon in almost trigonal planar coordination. The Pt–Si distances of 242 pm are indicative of strong covalent Pt–Si bonding. The cerium atoms are placed within cavities of this polyanionic network. They have coordination number 12 by six platinum and six silicon atoms. The polyhedron consists of two parallel Pt₂Si₃ pentagons which are bridged by two further platinum atoms. This arrangement resembles the ZrNiAl type CeTX phases [14]. The two silicides and phosphides all have a valence electron count of 17 and can thus be considered as isoelectronic.

Fig. 6:

The crystal structures of CePtSi and CeIrSi. The three-dimensional [PtSi] and [IrSi] networks are emphasized.

CeRhSi [81] and CeIrSi [82] adopt the cubic LaIrSi type [83] which is a ternary ordered version of SrSi₂ [84]. Similar to the tetragonal structure discussed above, the T/X ordering in CeRhSi and CeIrSi leads to a symmetry reduction from P4₁32 to P2₁3 (t2 step). The CeIrSi structure is presented as an example in Fig. 6. Each iridium atom has three silicon neighbors and vice versa in a slightly distorted trigonal planar coordination. This is similar to the [PtSi] polyanion discussed above. However, we observe a different connectivity pattern of these IrSi_3/3 monomeric units. The Ir–Si distances of 229 pm again underline the strong covalent Ir–Si bonding. The cerium atoms have a slightly lower coordination number of 11 with 4 Ir and 7 Si neighbors. The valence electron count of CeRhSi and CeIrSi is 16.

3.1.4 CePdSi with PrPdSi type structure

The occurrence of a certain structure type for a CeTX phase is not simply a function of the valence electron count or the size of the atoms. This is readily evident for the silicides CeTSi (T = Ni, Pd, Pt). While the nickel and platinum compound crystallize with the tetragonal LaPtSi type (vide supra), CePdSi adopts the monoclinic PrPdSi structure [85]. The unit cell of CePdSi (space group P2₁/c) is quite complex at first sight (Fig. 7), however we find well known coordination motifs. Both crystallographically independent palladium atoms in the three-dimensional [PdSi] polyanion have distorted trigonal-planar silicon coordination with Pd–Si distances ranging from 243 to 256 pm. This is indicative of substantial Pd–Si bonding. The coordination is similar to that in CeIrSi and CePtSi as discussed above, however, the condensation pattern of the TSi_3/3 monomeric units is different in the three compounds.

Fig. 7:

The crystal structure of CePdSi, space group P2₁/c. The three-dimensional [PdSi] network is emphasized.

A peculiar feature of the CePdSi structure is the occurrence of Si–Si bonding (234 pm; single bond character) in the [PdSi] polyanion. This is different from all other CeTX phases which exclusively show heteroatomic bonding. Both cerium sites have coordination number 12 with a different ratio of palladium to silicon: Ce1@Pd₇Si₅ and Ce2@Pd₅Si₇. A very detailed crystal chemical discussion of this unique structure type was published for the prototype PrPdSi [85].

3.1.5 CePdBi and CePtBi with MgAgAs type structure

The bismuthides CePdBi [86] and CePtBi [87] crystallize with the cubic MgAgAs structure [88], the so-called half-Heusler type [89]. As an example we present the unit cell of CePdBi in Fig. 8. Since all atoms reside on special positions, the interatomic distances of these phases can easily be calculated from the lattice parameters. The cerium and bismuth atoms in CePdBi build up a rocksalt-type substructure in which half of the tetrahedral voids are filled in an ordered manner by the palladium atoms. This leads to a hetero-cube-like coordination around each palladium atom, i.e. Pd@Bi₄Ce₄ with Pd–Bi and Pd–Ce distances of 295 pm, each.

Fig. 8:

The crystal structure of CePdBi (MgAgAs type structure). The tetrahedral bismuth coordination of the palladium atoms is emphasized.

3.1.6 CeTX phases with CeFeSi and CeScGe type structures

The next groups of CeTX intermetallics have tetragonal crystal structures. As an example we present CeMnSi [90] with CeFeSi type structure [91] and CeScGe with an ordered version of the La₂Sb type [92] in Fig. 9. The manganese atoms in CeMnSi have tetrahedral silicon coordination with Mn–Si distances of 254 pm. These tetrahedra share common edges, leading to a dense layer perpendicular to the c axis. The MnSi_4/4 layers are separated by double layers of cerium atoms. The two cerium layers are shifted with respect to each other by 1/2 1/2 0 (a consequence of the n glide plane in space group P4/nmm). This way one obtains voids between tetrahedra of cerium atoms; a feature which is discussed later with respect to hydrogenation reactions.

Fig. 9:

The crystal structures of CeMnSi and CeScGe. The tetrahedral manganese-silicon coordination is emphasized in ball-and-stick model and in polyhedral presentation. The planar ScGe_4/4 coordination is highlighted for CeScGe.

The CeFeSi type occurs only for silicides and germanides in the family of CeTX intermetallics. The compound with the lowest valence electron count (VEC) is α-CeTiGe [93] (11 valence electrons) while CeCoSi [94] has a VEC of 16. Although this is quite a large range, α-CeTiGe can be considered as an exception, since most of the CeFeSi type phases have VECs between 14 and 16.

α-CeTiGe shows a temperature induced transformation to α-CeTiGe with the CeScGe type (space group I4/mmm). The structure of the prototype is presented in Fig. 9. The scandium atoms form square grids at z = 0 and z = 1/2 with comparatively short Sc–Sc distances of 307 pm. They are coordinated by four germanium atoms in a rectangular planar fashion with Sc–Ge distances of 289 pm. The ScGe_4/4 rectangles are condensed via common egdes and one obtains dense blocks perpendicular to the c axis, similar to CeMnSi discussed above. Again, every other layer is shifted by 1/2 1/2 0, since space group I4/mmm also contains an n glide plane. The stacking principle is then comparable to the P4/nmm phases. The [Sc₂Ge₂] layers are separated by double layers of cerium atoms which are also shifted with respect to each other and they also leave tetrahedral voids. The range of VECs is much smaller for the CeScGe phases; 10 for the pure rare earth phases and 11 for β-CeTiGe.

3.1.7 CeTX phases with CeCoAl related structures

The most complex structural behavior among the CeTX phases occurs for CeCoAl [95], CeCoGa [96], and the stannide CeRuSn [97, 98]. Our discussion starts with the subcell structure of the aluminide. A projection of the CeCoAl subcell structure along the monoclinic axis is presented in Fig. 10. The cobalt and aluminum atoms build up a complex three-dimensional network which leaves cavities for the cerium atoms. Around the inversion centers, symmetric Co₂Al₂ rhombs are the basic building motifs of the [CoAl] polyanionic network. These rhombs are connected via Al–Al contacts.

Fig. 10:

Projection of the CeCoAl and CeRuSn structures along the monoclinic axis. The three-dimensional [CoAl] and [RuSn] networks are emphasized.

At ambient temperature CeRuSn [97] shows a doubling of the subcell c axis. This superstructure formation corresponds to an isomorphic transition of index 2 (i2) from C2/m to C2/m with a thinning of the symmetry elements. Half of the inversion centers are lost as a consequence of the symmetry reduction and the ruthenium atoms show a pronounced shift off the subcell positions. The consequences for the cerium coordination are shown in Fig. 11. The upper part of the drawing shows the average CeRuSn structure, refined without the superstructure reflections. The ruthenium atoms show distinct anisotropic ellipsoids that are well resolved in the superstructure. The two crystallographically independent cerium sites in the superstructure are shown at the bottom of Fig. 11. The shifts of the ruthenium atoms lead to short Ce–Ru distances of 233 and 245 pm for Ce1 and an elongation to 288 and 289 pm for Ce2. This is a direct consequence of different cerium valencies: almost tetravalent Ce1 and trivalent Ce2, a kind of charge ordering in CeRuSn. This crystal chemical behavior with extremely short Ce–Ru distances seems unusual at first sight; however, meanwhile a whole series of ternary cerium ruthenium intermetallics has been published [99, 100] which all show the drastic shortening of the Ce–Ru contacts along with intermediate cerium valence.

Fig. 11:

Cerium coordination in the subcell and the 2c superstructure of CeRuSn. Cerium, ruthenium, and tin atoms are drawn as medium grey, blue, and magenta circles, respectively. Relevant Ce–Ru distances (in units of pm) and atom designations for the two crystallographically independent cerium sites of the superstructure are given.

Powders and single crystals (grown by the Czochralski technique) of CeRuSn have meanwhile been studied by a variety of techniques that all underline the intermediate cerium valence [101–109]. In going to lower temperature, CeRuSn shows a modulated structure which can be described within the superspace formalism in (3+1) dimensions. After a strong initial temperature dependence, the modulation vector approaches a value close to q = (0 0 0.35). The structural anomalies are in close relation with anomalies in the physical properties as discussed later.

Concerning the structurally related phases CeCoAl and CeCoGa, detailed studies of the phases of the Ce-Co-Al system [110–112], the enthalpies of formation [113], and the glass forming abilities [114] have been conducted. Recent reinvestigations of both structures revealed additional reflections, indicating superstructure formation. Heat capacity measurements of a CeCoAl sample [194] showed a phase transition at 271 K and magnetic susceptibility measurements clearly substantiated the intermediate cerium valence. Satellite reflections occurred below 271 K giving rise to the superspace group C2/m(α0γ)00; α = 2/3, γ = 2/5, with the q vector depending on the temperature. The driving force for the modulated superstructure is the formation of short Ce–Co distances. Similar results were obtained for CeCoGa [195]: superspace group C2/m(α0γ)00; α = 2/3, γ = 1/3. Thermal analysis revealed a phase transition at 475 K. The two different superstructures were discussed on the basis of group-subgroup relations for reasonable approximants [195].

3.2.1 CeMnSi, CeFeSi and CeMnGa

The CeTX silicide with the highest magnetic ordering temperature is CeMnSi [90, 128]. The manganese substructure shows antiferromagnetic ordering below T_N = 240 K. Neutron diffraction experiments revealed the arrangement of the magnetic moments. The magnetic structure shows an alternate stacking of antiferromagnetically coupling manganese layers, while the cerium layers are ferromagnetically coupled with opposite sign in every other layer. Variation of the refined magnetic moments indicates a Néel temperature of 175 K for the cerium magnetic substructure. The ordered moments on the manganese and cerium atoms were 2.71 and 0.78 μ_B, respectively. Conductivity measurements of CeMnSi have confirmed semiconducting behavior [128]. The sign of the Seebeck coefficient changes from positive to negative around 220 K, indicating hole carriers below 220 K. The chemical bonding characteristics were derived from K and L band spectra using X-ray spectroscopy [196]. Substitution of manganese by iron completely changes the magnetic ground state. CeFeSi is a simple Pauli paramagnet [149].

CeMnGa [124, 197, 198] remains paramagnetic down to 4.2 K. The manganese and gallium atoms show random occupancy on the tetrahedral network of the MgCu₂ type structure, hampering long-range magnetic ordering. The magnetic moment in the paramagnetic range is 3.1 μ_B per formula unit along with a comparatively low paramagnetic Curie temperature of –144 K [198]. The specific resistivity of CeMnGa is > 100 μΩcm over the whole temperature range. The large residual resistivity is another hint for atomic disorder within the CeMnGa sample.

3.2.2 CeTX phases with an electron-poor transition metal

The magnetic properties of CeScSi and CeScGe were determined on polycrystalline samples [30, 199] and Czochralski-grown single crystals [35, 200]. Both tetrelides order antiferromagnetically at 26 (CeScSi) and 46 K (CeScGe). These Néel temperatures (determined from susceptibility and specific heat measurements) are among the highest ones observed in the whole family of CeTX intermetallics [14, 15]. The stable antiferromagnetic ground states are supported by distinct metamagnetic steps at critical fields of 3.6 and 4.4 T for CeScSi and CeScGe, respectively. Single crystal data [35] showed directional differences for the metamagnetic steps which are more pronounced for the c axis. The antiferromagnetic ordering in both compounds is also evident as a weak kink in the resistivity measurements [199]. A discreapancy concerns parallel investigations which claim a ferromagnetic ground state for CeScGe based on LMTO electronic structure calculations [200]. The magnetic ordering temperature of CeScGe is susceptible to external pressure [201]. T_N decreases to ca. 15 K under a hydrostatic pressure of 60 kbar. This data was obtained from resistivity measurements.

The isotypic antimonide CeScSb [21] has a higher valence electron count. CeScSb orders ferromagnetically at T_C ≈ 9 K, however, showing a broad peak in the specific heat data, most likely indicating some degree of disorder within the sample. Low-temperature neutron diffraction experiments have indicated additional magnetic intensity of the nuclear reflections. The cerium magnetic moments were determined to lie within the ab plane and the refined moment was 0.96 μ_B per cerium atom, substantially reduced when compared with the maximal value of 2.14 μ_B.

CeTiGe [131, 143, 144, 202, 203] is isoelectronic with CeScSb but exhibits two modifications, i.e. a CeScSi type high-temperature (space group I4/mmm) and a CeFeSi type low-temperature (space group P4/nmm) modification. This structural phase transition has a significant impact on the magnetic properties of the two modifications. The low-temperature modification shows stable trivalent cerium, but no magnetic ordering is evident down to 4.2 K [131]. Based on detailed resistivity and specific heat measurements, LT-CeTiGe has been classified as a non-magnetically ordered heavy-fermion system [144]. Seebeck coefficient measurements have revealed a maximum value around 60 μV K^–1 at 17 K, and low-temperature magnetization studies showed a pronounced metamagnetic transition at a critical field of 12 T. Data was recorded up to an external field of 60 T [203]. Interestingly ordered moments close to 2 μ_B Ce atom^–1 were obtained at the highest field values, classifying CeTiGe as one of the remarkable CeTX materials. The high-temperature modification [143] shows no magnetic ordering down to 2 K and can be classified as a non-magnetic, strongly correlated electron system. Comparison of both CeTiGe modifications indicates a decrease of the crystal field hybridization parameter J_cf between the Ce 4f and the conduction electrons from LT- to HT-CeTiGe.

3.2.3 Intermediate cerium valence in CeRuSn, CeCoAl, and CeCoGa

CeRuSn is one of the outstanding materials in the family of CeTX phases. In the original study [97] a lock-in phase (2c CeCoAl superstructure) has been reported which contained two crystallographically independent cerium sites. Only one of these sites carries a magnetic moment and a remarkable hysteresis was observed below the phase transition temperature of 283 K. The hysteretic behavior has then been studied in more detail and it is also evident in the temperature dependence of the specific heat, the resistivity, and the Seebeck coefficient [102, 104]. The transitions also cause a strong shrinking along the c axis, as it was clearly proven from thermal expansion experiments on Czochralski-grown single crystals [36]. The trivalent cerium atoms in CeRuSn order antiferromagnetically below T_N = 2.8 K [103, 105]. The nuclear and the low-temperature magnetic structure of CeRuSn was studied on the basis of powder and single-crystal neutron diffraction [103, 106]. The structure can be described by the superspace formalism in (3+1) dimensions. The nuclear propagation vector for this modulated structure is q_nucl = (0 0 0.35). In the antiferromagnetically ordered regime a magnetic propagation vector of q_mag = (0 0 0.175) has been determined. The magnetic structure refinement showed that the cerium magnetic moments are nearly collinear with the ac plane and modulated between values of 0.11 and 0.95 μ_B in c direction [106].

Parallel to the neutron diffraction studies, the subtle changes in the CeRuSn structure were investigated by the atomic pair distribution function as a local probe using high-energy synchrotron X-ray diffraction [107]. Additionally, the ratio of the two different cerium valences (Ce³⁺ vs. Ce^(4–δ+)) was studied by XANES as a function of temperature [37, 108]. These two inequivalent cerium sites are also evident from polarized neutron diffraction studies. Below the transition temperature, a redistribution of the cerium spin densities became evident from the neutron diffraction data [109].

Many solid solutions based on the parent CeRuSn structure have thoroughly been studied with respect to cerium, ruthenium, and tin substitution. These results are summarized in a separate chapter at the end of this review.

Besides the very detailed studies of the physical properties of CeRuSn, only few data is known on the structurally closely related phases CeCoAl and CeCoGa. This is due to a more difficult sample preparation. Often tiny amounts of cobalt remain at the grain boundaries, hampering the property studies. Early studies of CeCoAl and CeCoGa [204–206] by thermal expansion, Seebeck coefficient, resistivity, and magnetic susceptibility measurements have already substantiated the deviation from a stable trivalent ground state for the cerium atoms. Especially magnetic susceptibility measurements showed a valence change with temperature, with almost tetravalent cerium at high temperature and a tendency towards intermediate cerium valence with decreasing temperature. Recent susceptibility data of CeCoGa have indicated antiferromagnetic ordering below T_N = 4.3 K. The presented band structure calculations, however, have suffered from the wrong structural model. The modulated structure with an adequate approximant was not known at that time.

3.2.4 CeTAl (T = Rh, Pd) and CeRhZn

CeRhZn, CeRhAl (both LaNiAl type) and LT-CePdAl (own type) are intergrowth structures with TiNiSi and ZrNiAl related slabs. These complex structures have two, respectively four crystallographically independent cerium sites. It is remarkable that CeRhZn [70] is a rare example of cerium intermetallics with multiple cerium sites where both kinds of cerium atoms are in an almost tetravalent state. Magnetic measurements have shown very weak susceptibility values and a very low moment of only 0.33 μ_B per cerium atom. This is in close agreement with electronic structure calculations, which showed almost empty 4f states above the Fermi level.

All cerium atoms in the low-temperature modification of CePdAl are trivalent. Susceptibility and specific heat data of LT-CePdAl show antiferromagnetic ordering at T_N = 2.5 K [72]. Due to the structural intergrowth, the strictly triangular building units are lost, leading to magnetic frustration in many of the hexagonal ZrNiAl type phases [14]. Resistivity measurements have confirmed classical Kondo lattice behavior.

Contradicting property studies were reported for CeRhAl. The early reports by Kumar and Malik claimed mixed valent behavior and no magnetic ordering for the cerium atoms [116, 207, 208]. Their samples showed substantial deviations from Curie–Weiss behavior over the whole temperature range. Both cerium valences were also evident from XANES spectra [208]. Reinvestigation of CeRhAl confirmed antiferromagnetic ordering of the cerium atoms at T_N 3.8 K [115]. The magnetic phase transition has also been substantiated through a well-defined lambda-type anomaly in specific heat measurements. Probable reasons for the discreapancy might be some degree of atomic disorder (Rh/Al mixing or formation of domains of a rhodium- and/or aluminum-rich solid solution) or the different annealing sequences used during sample preparation.

3.2.5 CePtSi and CeRuSi

CePtSi (space group I4₁md) has thoroughly been studied on polycrystalline and single crystalline samples [34, 148, 209–219]. Susceptibility measurements showed stable trivalent cerium but no magnetic ordering down to the lowest available measurement temperatures. The remarkable feature derived from specific heat measurements is the extremely large gamma value of 700–800 mJ mol^–1 K^–2 [148, 209], classifying CePtSi as a heavy-fermion material. Independent measurements by different groups showed sample dependent properties. It was assumed that the sample composition and disorder effects might be the reason. Indeed, platinum-silicon mixing has been observed during a reinvestigation of the CePtSi structure [76]. Recent studies of the low-temperature properties down to the mK scale have confirmed that non-centrosymmetric CePtSi exhibits no quantum critical point [219]. Electrical resistivity measurements are in line with only very small crystal electric field splitting [34]. Temperature dependent Hall data point to the existence of a phase transition around 2.3 K [210], evident from an enhancement of the Hall effect. Resistivity measurements under pressures up to 15 kbar [213] have indicated a delicate interplay between Kondo lattice behavior and cerium mixed valence as a consequence of different interatomic distances. The crystal field parameters have been determined from inelastic neutron diffraction studies: 6.3 meV from the ground to the first excited state and 17.8 meV from the first to the second excited state [215].

Temperature dependent susceptibility studies of CeRuSi have shown trivalent cerium (2.56 μ_B Ce atom^–1), while isotypic CeOsSi exhibits a substantially reduced experimental moment of only 2.03 μ_B Ce atom^–1 [23]. In addition, the smaller cell volume of the osmium phase is a strong hint towards intermediate cerium valence. This is in line with X-ray absorption spectra of the Ce L_2,3 edge [220], pointing towards partial delocalization of the cerium 4f electrons. The CeFeSi type structure of CeRuSi shows some anisotropy [183]. This has been studied in detail by ²⁹Si solid state NMR spectroscopy [221], where different shift components were observed for the ab and c directions.

3.2.6 The germanides CeTGe (T = Co, Cu, Ag, Au)

CeCoGe was first studied by Welter et al. [139]. Temperature dependent susceptibility data revealed Curie–Weiss paramagnetism and the experimental moment of 2.6 μ_B Ce atom^–1 indicated a stable trivalent ground state. No magnetic ordering was reported in that study. Reinvestigation of CeCoGe by resistivity and magnetic susceptibility measurements pointed to antiferromagnetic ordering below T_N = 5.0 K [141]. The magnetic structure was solved from neutron powder diffraction data and consists of ferromagnetic (001) planes that are antiferromagnetically stacked along c (+–+– sequence). A moment of 0.38 μ_B per cerium atom has been refined from the 1.5 K diffraction data.

Ferromagnetic ordering at 10 K was determined for CeCuGe [222]. Saturation of the magnetization is already reached around an external field strength of 2 kOe (1 kOe = 7.96 × 10⁴ A m^–1). The Curie point is also visible in the temperature dependence of the specific resistivity, however, the kink is weak. A decrease of the magnetic moment below 70 K in the paramagnetic range is attributed to crystalline electric field (CEF) effects. The corresponding parameters and the CEF scheme were deduced from inelastic neutron scattering data [140, 223]. CeCuGe shows a moderate Seebeck coefficient with a maximum value of ~10 μV K^–1 around 30 K. Isoelectronic CeAgGe orders antiferromagnetically at the much lower Néel temperature of T_N = 4.8 K [142]. The magnetic structure of CeAgGe shows a propagation vector k = [1/3 0 0]. The cerium magnetic moments lie in the ab plane and a moment of 1.6 μ_B per cerium atom has been determined [224].

CeAuGe orders ferromagnetically at T_C = 10 K [136, 225]. Similar to CeCuGe, also for the gold compound only a weak kink is observed in the temperature dependence of the specific resistivity. The ferromagnetic ordering was confirmed by neutron powder diffraction data at 1.7 K with a refined magnetic moment of 1.1 μ_B per cerium atom, lying approximately along the a axis [224]. The CEF excitation (derived from the 4f contribution of the specific heat) amounts to Δ_CEF/k_B = 240 K [135].

3.2.7 The coinage metal stannides CeTSn (T = Cu, Ag, Au)

The magnetic properties of CeCuSn have repeatedly been studied for different poly- and single-crystalline (Czochralski method) samples [33, 63, 226–230]. Differences in the Néel temperature are due to structural disorder, e.g. a different degree of puckering of the Cu₃Sn₃ networks. Samples prepared at high temperatures or via quenching directly after arc-melting exhibit distinctly higher disorder than samples annealed for longer periods at lower temperature. This has been studied in detail by single crystal diffraction data [63]. The CeCuSn low-temperature modification shows a sharp increase of the magnetic susceptibility below 8.6 K, in agreement with antiferromagnetic ordering of the cerium magnetic moments [63]. Results of single-crystal neutron diffraction studies are in line with these observations and showed a magnetic wave vector of k = (0.115 0 0) [33]. Susceptibility, resistivity, and specific heat studies on comparable Czochralski grown single crystals support this behavior [226]. The complex magnetic phase diagram was constructed from a large series of magnetization measurements [227]. Quenched CeCuSn samples show magnetic inhomogeneities [228, 229], a consequence of missing long-range order within the Cu₃Sn₃ networks. A detailed study of CeCuSn (along with CeAgSn and CeAuSn) by inelastic neutron scattering has led to precise values for the crystal field parameters [230].

CeAgSn orders antiferromagnetically at T_N = 3.6 K [231]. Neutron powder diffraction studies have revealed complete Ag-Sn ordering within the Ag₃Sn₃ hexagons. The propagation vector is k = (1/2 0 0) and a moment of 0.8 μ_B per cerium atoms was derived from the diffraction data. Chemical bonding in CeAgSn was studied experimentally from X-ray photoemission spectroscopy [232]. The spectra were analyzed on the basis of the well-known Gunnarsson–Schönhammer model, giving rise to absolute values for the energy levels. In addition, Fus et al. studied the total energies of CeAgSn for a disordered CaIn₂ type vs. an ordered LiGaGe type model, clearly underlining the fully ordered LiGaGe type.

The magnetic ground state of CeAuSn is finally antiferromagnetic at T_N = 4.1 K [123]. Experimental studies of the electronic structure of CeAuSn were performed by X-ray photoelectron spectroscopy [233]. The experimental and calculated valence band spectra showed good agreement.

3.2.8 Equiatomic plumbides CeTPb (T = Cu, Zn, Ag, Au)

So far, only few data is available for the CeTPb plumbides since they are all sensitive to moisture, hampering many property studies. The isotypic phases CeTPb with T = Cu, Ag, Au (all crystallize with the NdPtSb type) order antiferromagnetically below Néel temperatures of 8.2, 7.4, and 3.7 K, respectively [25, 26]. The magnetic phase transitions are clearly manifested by lambda-type anomalies in the temperature dependence of the specific heat. Resistivity data has only been reported for the copper phase. CeCuPb is a moderate metallic conductor. The plumbide CeZnPb [155] shows Curie–Weiss paramagnetism and the experimental magnetic moment is in good agreement with trivalent cerium. Antiferromagnetic ordering occurs below T_N = 3.8 K. The stable antiferromagnetic ground state is supported by two pronounced, successive metamagnetic transitions at critical fields of approximately 1.1 and 7.0 kOe. Specific heat data give a hint for a spin reorientation at 2.6 K. Electronic structure calculations have confirmed the antiferromagnetic ordering and indicate that geometric frustration of the cerium magnetic moments is most likely the origin for the metamagnetic steps.

3.2.9 The antimonide CeNiSb

CeNiSb has repeatedly been studied with respect to its crystal structure and physical properties [166–168, 173, 176, 177, 234, 235]. Originally this antimonide was ascribed an AlB₂ structure, with a random occupancy of the boron network by nickel and antimony atoms. Subsequent studies indicated the ZrBeSi type structure with a complete ordering on Ni₃Sb₃ hexagons and rotation of every other layer by 60°. In this arrangement (space group P6₃/mmc) all Ni₃Sb₃ hexagons are planar. Since all X-ray diffraction studies on the diverse CeNiSb sample were carried out only on the basis of powder X-ray diffraction, it cannot be excluded that also a weak puckering of the Ni₃Sb₃ hexagons might occur. Keeping these structural constraints in mind, it is not surprising that slightly different properties have been reported. The local structure around the cerium atoms certainly depends on the thermal treatment of the samples. The structural disorder (planar vs puckered layers) is directly expressed in the strongly varying c lattice parameters of the different CeNiSb samples (Table 1).

Skolozdra and coworkers reported ferromagnetic ordering at T_C = 7 K [167] and classified CeNiSb as a Kondo system. The magnetic characterization was supported by resistivity and magnetoresistance measurements. The absence of magnetic ordering reported in a subsequent study is most likely due to a slightly different sample composition and/or structural disorder, preventing long-range magnetic ordering [166]. Kondo lattice behavior was confirmed by Menon and Malik, however, they reported a much lower Curie temperature of 4 K and also the possibility of off-stoichiometry for a sample CeNiSb_0.9 [173]. All available studies do not show a clear correlation of the Curie temperature with the lattice parameter c, clearly indicating that not only puckering but also differences in composition influence the coupling of the cerium magnetic moments.

The magnetic structure of CeNiSb was investigated on a larger, inductively melted sample using powder neutron diffraction [176]. A severe problem of larger powdered quantities of CeNiSb concerns surface oxidation. The powder diffraction patterns revealed small amounts of the sesquioxide Ce₂O₃. Evaluation of the neutron data indicated a modulated magnetic structure with a propagation vector q = (0 0 0.25). Additional work using inelastic neutron scattering revealed the complete set of CEF parameters for CeNiSb [234].

The ferromagnetic ordering in CeNiSb is sensitive to substitution and external pressure [235]. A small degree of nickel-rhodium substitution leads to an increase of T_C from 4.6 K (CeNiSb sample) to 5.2 K for a starting composition CeNi_0.9Rh_0.1Sb. The resistivity behavior of CeNiSb was studied under external pressures up to about 20 kbar. Both the Curie and Kondo temperature significantly increase with pressure, a clear sign for an increase of the J_cf coupling, in agreement with the Doniach diagram [236–238].

3.2.10 Equiatomic pnictides CeTPn (T = Rh, Pd, Pt; Pn = P, As, Sb, Bi)

The physical properties of the remaining phases are discussed as a function of the pnictide component. CeRhP [77] crystallizes with the LaPtSi type with one crystallographic cerium site. Although it has a similar valence electron count as CePtSi (see chapter 3.2.5), the magnetic ground state is drastically different. CeRhP is a valence fluctuating compound with metallic character. The Kondo temperature was estimated to be 400–500 K.

CePdP contains stable trivalent cerium and orders ferromagnetically at 5.2 K [158]. Specific heat data revealed a moderate γ value of 69.2 mJ mol^–1 K^–2. Anisotropy in the CePdP structure was confirmed by the CEF parameters. CePtP has a lower Curie temperature of 3.1 K followed by a spin reorientation at T_N = 1 K [193]. A highly interesting point concerns the saturation magnetization. In the ferromagnetically ordered regime (2 K data) the magnetization is 2 μ_B per formula unit at 5 T and almost reaches the theoretical value of 2.14 μ_B. Full saturation is observed for the 0.45 K isotherm. The low-temperature antiferromagnetic state is supported by three successive metamagnetic transitions. Both phase transitions are clearly manifested in the temperature dependence of the specific heat. Magnetoresistance data and results of de Haas-van Alphen effect measurements point to cylindrical Fermi surfaces for CePtP and the isotypic arsenide CePtAs [192, 240]. These experimental results are in line with FLAPW band structure calculations. The binding energies determined through high-resolution resonance photoemission spectroscopy show remarkable differences for the bulk and the surface layers [42, 239].

Most studies on CePdAs were performed on single crystals which are accessible through the Bridgman technique [40, 241–245]. CePdAs is a 6.2 K ferromagnet [158, 241]. Resistivity measurements on CePdAs and the isotypic antimonide have shown a strong anisotropy, and both pnictides tend towards two-dimensional conductors [40]. Precise experimental studies on the electronic structures of CePdAs and CePdSb were performed through high-resolution resonance photoemission spectroscopy [242–245]. Small differences in the hybridization strength between CePdAs and CePdSb can be resolved in the spectra, and the experimental results are well reproduced by calculations using the single-impurity Anderson model [243]. In going to CePtAs [39, 246, 247] one observes a drastic reduction of the magnetic ordering temperature. CePtAs is a 1.0 K antiferromagnet and shows a pronounced metamagnetic step in the 0.54 K magnetization isotherm. Resistivity measurements showed the same anisotropy as for CePdAs and have substantiated the Kondo-type character.

The most remarkable and deeply studied pnictide is CePdSb [41, 169, 171, 175, 248–260] due to its high Curie temperature of 17 K. Magnetization measurements revealed the typical reduced magnetic moment in the ordered state, a consequence of anisotropy and CEF splitting. The onset of ferromagnetic ordering is also evident as a strong drop in the temperature dependence of the specific resistivity [248], due to a reduction of spin-disorder scattering. This is similar to the temperature dependence of the Seebeck coefficient where a steeper slope was observed below T_C [258]. The maximum Seebeck value of ca. 70 mV K^–1 occurs at room temperature [250, 258]. Under hydrostatic pressure one observes a significant increase of the Curie temperature with a maximum value of 31 K at 10 GPa [251, 257].

The thermal expansion of CePdSb single crystals (Bridgman crystal growth) shows a strong anisotropy [253, 256]. The expansion coefficient is one order of magnitude larger in the magnetically hard c direction as compared to a and b. This anisotropy is independently evident from a detailed evaluation of the specific heat data [249] which are not compatible with a simple isotropic exchange model but point to differences in inter- and intra-chain exchange parameters J. A parallel study of CePdSb via ¹²¹Sb(¹²³Sb) NMR as a function of pressure has underlined the pressure-dependent susceptibility data [254]. A summary of the CePdSb properties and a comparison with related CeTX phases under consideration of the valence electron count has been published by Ślebarski [259].

CePtSb has a lower Curie temperature of T_C = 4.7 K [41, 175, 260–262]. The experimental data were also measured on single crystals and the anisotropy was comparable to that of CePdSb. In this case, especially optical conductivity spectra pointed to an anisotropic carrier concentration.

The last pnictide in this series is cubic CePdBi [152]. A magnetic phase transition is evident around T_C = 2 K. About 8 % of the sample undergoes a superconducting phase transition close to 1.3 K. It was assumed that this transition was caused by disordered parts of the sample.