The rare-earth oxide compound (tetragonal zircon structure) is investigated using the extended susceptibility formalism, which considers at any temperature all of the features of the crystalline electric field within the ground-state multiplet in the joint analysis of the magnetic, magnetoelastic and elastic properties. The magnetoelastic coefficients are determined from third-order magnetic susceptibility, parastriction and elastic constant measurements for the different symmetry modes. The dominant magnetoelastic coupling is associated with the orthorhombic -symmetry; however, tetragonal and symmetry-lowering modes are also observed to give rise to noticeable effects, in particular in the thermal expansion. The close coherency between the magnetoelastic coefficients in and is then emphasized: the tetragonal magnetoelastic coefficients are sizeable and all of the magnetoelastic couplings keep the same sign and order of magnitude in the two phosphates. This coherency appears to be valid throughout the large family of rare-earth zircons. Through these two examples, the occurrence of a quadrupolar ordering is then discussed as being governed by the crystalline electric field, and the role of undercritical quadrupolar interactions is emphasized in .

The rare-earth oxide compound ${\mathrm{HoVO}}_{4}$ (tetragonal zircon structure) is investigated in the extended susceptibility formalism, which includes all the features of the crystalline electric field in the analysis of the magnetic, magnetoelastic, and elastic properties as a function of temperature. The characteristic behavior of the first-order magnetic susceptibility allows us to refine the values of the crystalline electric-field parameters and to determine the strength of the magnetic interactions. The magnetoelastic coefficients are then found from third-order magnetic susceptibility, parastriction, and elastic-constants measurements for the different symmetry modes. Their coherency with values determined for ${\mathrm{TbPO}}_{4}$ is then emphasized: They have the same sign and order of magnitude; in particular the magnetoelastic coefficients for the tetragonal symmetry are sizable in these rare-earth oxides in contrast to the case of rare-earth intermetallics. The unusual temperature dependence of the third-order magnetic susceptibility along the tetragonal axis is a precursor of the level crossing in high magnetic fields associated with a magnetization jump of about 8${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ at 11.4 T, which we study as a function of temperature down to 0.1 K. The existence of a two-step jump of the magnetization at low temperatures, if not driven by mechanical stresses, remains an intriguing result.

Magnetostriction experiments have been performed on a TbMn2 polycrystalline sample. A large volume shrinkage is shown when applying a magnetic field in the ordered low temperature magnetic phase. It confirms the occurrence of a field induced first order transition from a Mn antiferromagnetism to a magnetic structure where magnetic and non-magnetic Mn are coexisting.

The magnetic and magnetoelastic properties (third-order magnetic susceptibility and parastriction) of ${\mathrm{TbPO}}_{4}$, which has the zircon-type tetragonal structure, are analyzed in the paramagnetic phase. The susceptibility formalism is then used to describe all the symmetry-lowering modes in a rare-earth insulator. The dominant magnetoelastic coupling is associated with the \ensuremath{\delta} symmetry and is, at least partly, responsible for the transition occuring at 2.15 K in the antiferromagnetic phase and clearly dominates the \ensuremath{\gamma}-symmetry mode. However, none of the different symmetry-lowering modes can be completely neglected and we determine parameters for the \ensuremath{\alpha}1 and \ensuremath{\alpha}2 tetragonal modes and the \ensuremath{\varepsilon} monoclinic mode. Owing to the close vicinity of the first excited singlet to the ground-state doublet, the \ensuremath{\alpha} quadrupolar interactions play an important role in determining the temperature dependence of the level spacing at low temperature, in particular in the ordered phases. The determination of all the magnetoelastic modes of ${\mathrm{TbPO}}_{4}$ is an essential step towards the understanding of the complex magnetic properties in the ordered phases, where numerous interactions coexist.

The cubic AuCu3 type system NdIn3 exhibits complex magnetic structures at low temperature. Immediately below the Néel temperature, TN = 6 K, the spins assume a sine wave modulated arrangement; for 5.5 K >T > 4.7 K, the modulation tends towards a square wave. Finally, below 4.7 K, a simple commensurate structure is stabilized. We first confirm here the complex magnetic phase diagram by means of resistivity measurements. In order to quantitatively understand the low temperature properties, the crystalline electric field is determined by inelastic neutron spectroscopy. An extensive study of the magnetic, magnetoelastic and quadrupolar properties in the paramagnetic phase by magnetization, ultrasonic velocity and parastriction measurements is then presented. The values of one-ion magnetoelastic coefficients agree with previous determinations in isomorphous systems. Quadrupolar pair interactions are found to be positive for the tetragonal symmetry lowering mode, in agreement with the symmetry of collinear magnetic structures. However the only quadrupolar model fails to coherently describe the whole set of paramagnetic properties, in particular the third order magnetic susceptibility. The existence of two-ion magnetoelasticity is then discussed in relation to the ultrasonic velocity and parastriction results. The description of the magnetic phase diagrams will be reported elsewhere.

The occurrence of a nonmagnetic transition at 5 K in ${\mathrm{TmAg}}_{2}$ (${\mathrm{MoSi}}_{2}$-type tetragonal symmetry) is analyzed as a ferroquadrupolar ordering within the orthorhombic \ensuremath{\gamma}-symmetry-lowering mode. The crystalline-electric-field parameters are obtained by inelastic-neutron-scattering and magnetic-susceptibility measurements. Both the magnetoelastic couplings and the quadrupolar pair interactions are then determined by third-order magnetic-susceptibility, parastriction, and ultrasonic-velocity experiments. The great coherency between these determinations allows us to understand completely the magnetic properties in both the orthorhombic and tetragonal phases. ${\mathrm{TmAg}}_{2}$ is then an archetype for compounds ruled by quadrupolar interactions.

A survey of the properties of 4f quadrupolar moments in rare earth intermetallic compounds is proposed. The double nature, one-ion magnetoelasticity and pair interactions, of the quadrupolar couplings as well as the different types of ferro-and antiferroquadrupolar orderings are first reviewed. The quadrupolar consequences on the magnetic properties, such as the order of the magnetic transition and the nature of the magnetic structure are then discussed. This interplay between quadrupoles and spins is illustrated by the competitions between collinear and multiaxial structures or between commensurate and modulated ones, sometimes in a same compound.

The study of the magnetoelasticity of the cubic (CsCl-type) rare earth intermetallic DyAg allows us to determine the strength of both the magnetoelastic coupling and the quadrupolar pair interactions. These latter ones are observed to be negative (antiferroquadrupolar type) for the tetragonal symmetry as well as for the trigonal one. They drive the magnetic structure to be triple-q at low temperature: the cubic magnetic cell consists of four pairs of ferromagnetic moments pointing along each of the treefold axes. At high temperature, it is replaced by a double-q structure, then, immediately below TN, by a modulated arrangement. The magnetization processes have been thoroughly studied along the three main axes in fields up to 40 T and compared with previous results in isomorphous DyCu and in the AuCu3-type compound TmGa3. The sequences under field of the different magnetic structures are identical and mainly determined by the crytalline electric field and the antiferroquadrupolar interactions. These 3 compounds do not set a peculiar case, but seem to belong to a larger family of cubic compounds with multiaxial structures governed by antiferroquadrupolar terms.

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A susceptibility formalism is developed for analyzing the magnetic and quadrupolar interactions in hexagonal and tetragonal rare-earth compounds. Symmetrized expressions are given for the one-ion magnetoelastic coupling and for the two-ion quadrupolar interactions. This formalism, derived from perturbation theory, leads to specific magnetic, strain, and quadrupolar susceptibilities considering both the crystalline-electric-field effects and quadrupolar interactions. It allows an analytical description of physical properties, such as the first- and third-order paramagnetic susceptibilities, the parastriction, and the elastic constants.

One- and two-ion quadrupolar interactions have been determined in CeMg, CeZn by ultrasonic velocity measurements. As in CeAg, they are large and in agreement with previous determinations in normal isomorphous intermetallics. They drive a quadrupolar ordering in CeAg and deeply influence the magnetic properties of CeMg and CeZn.

Determination de la force des interactions quadripolaires a l'aide de mesures de vitesses d'ultrasons. Pour la symetrie quadratique, les termes ferroquadripolaires sont suffisamment forts pour expliquer la transition du premier ordre au point de Neel

Magnetoelastic and magnetic studies in the paramagnetic phase of TmGa3 have allowed us to determine both the magnetoelastic coefficients and the strength of the ferroquadrupolar pair interactions. For the tetragonal and trigonal symmetries, these interactions are too weak to explain the first-order transition observed at 4.29 K as a ferroquadrupolar ordering. On the contrary, antiferroquadrupolar interactions appear to be dominant and to stabilize a multiaxial spin structure. In comparison with previous studies on CsCl-type rare earth intermetallics, the magnetoelasticity and the quadrupolar pair coupling appear to be smaller in the AuCu3-type compounds.

The magnetoelastic properties of CePb3 are analysed from ultrasonic velocity and magnetostriction measurements in the paramagnetic state. Magnetoelastic effects are rather weak in agreement with the non-quadrupolar nature of the Γ7 ground state. The magnetoelastic coefficients are normal for the tetragonal, trigonal and cubic strain modes. Kondo contributions are observed only on the bulk modulus and the parastriction of the tetragonal symmetry. This anisotropic behaviour of the parastriction seems to be observed for the first time and may be related to the [001] easy magnetization direction in the ordered phase.

The Crystalline Electric Field, the bilinear and quadropolar pair interactions as well as the magnetoelasticity have been studied in the CsCl-type structure compound TmMg by means of neutron spectroscopy, magnetization, parastriction and elastic constants experiments. Each of these couplings is then analysed in comparison with previous determinations for other isomorphous thulium compounds.

The study of the magnetoelastic properties of DyCu allows us to show unambiguously that the magnetic structure is of the triple-q type. It consists of 4 pairs of ferromagnetic spins pointing along each of the threefold axes. The lack of any spontaneous magnetostriction in spite of a large magnetoelastic coupling agrees with the cubic symmetry of triple-q structure, which is shown to be stabilized by negative quadrupolar interactions of trigonal symmetry. A coherent analysis of the complex magnetization processes for magnetic fields applied along the three main crystallographic directions is then proposed. A comparison with other related compounds within the CsCl-type structure, DyAg, DyZn and DyCd reveals the important role of the quadrupolar interactions, in connection with the crystalline electric field level schemes. The crystal field favours the threefold axes as the easy magnetization direction for all the four compounds. In DyAg and DyCu, the addition of negative quadrupolar interactions of trigonal symmetry leads to observed non-collinear structures; in DyZn and DyCd, the positive tetragonal quadrupolar interactions are strong enough to establish a collinear arrangement along a fourfold axis.

Magnetoelastic effects are very large in cubic rare-earth intermetallic compounds, especially for the tetragonal and trigonal strain modes. This magnetoelasticity of dominant one-ion origin appears to be the best experimental probe for studying the large quadrupolar pair interactions observed in these compounds. The used Hamiltonian includes the crystalline electric field, the bilinear interactions and the Zeeman coupling with an applied magnetic field, the quadrupolar pair interactions and the magnetoelastic coupling. The free energy is derived using in the non-ordered phase an analytical susceptibility formalism: the anisotropic magnetization and parastriction and the various elastic modes are then deduced. The full coherency of the determinations for both the magnetoelastic coefficients and the quadrupolar pair interactions parameters is demonstrated in TmZn, TmCd and PrPb3, where a quadrupolar ordering occurs in the paramagnetic phase and is explained in detail.

Parastriction and ultrasonic velocity experiments have been performed in order to have a better knowledge of the magnetic and quadrupolar interactions in PrAg, an intermetallic compound (CsCl-type structure) which exhibits puzzling magnetic properties, extensively studied in the recent past. As a first result, the existence of a ferromagnetic transition at Tc = 7.3 K below the Néel temperature (TN = 10.5 K) is confirmed on monocrystalline samples. In all the ordered range, the magnetic structure is proved to be multiaxial: first the knowledge of the magnetoelastic coefficients allows us to rule out the collinear structure, explaining the lack of any spontaneous strain. On the other hand, the quadrupolar interactions, found weakly negative, favour an antiferroquadrupolar arrangement in agreement with a multiaxial spin ordering. The stability of the CsCl-type lattice at low temperature is then discussed in connection with the instability features observed in neighbouring compounds LaAg and CeAg. It appears that in these three compounds many origins may be simultaneously proposed for the instability tendency: an electronic deformation potential coupling, a ∈3 strain coupling with zone boundary phonon and the magnetoelastic coupling. PrAg appears to be clearly more stable than the other two compounds.

The thermal variations of the first-order magnetoelastic coupling coefficients. Bγ,2 and Bϵ2, have been measured accurately in the whole ferromagnetic range. Bϵ,2 is found to vary as m2 + m8 where m is the reduced magnetization: the magnetization of nickel as given by various authors is discussed and found to be somewhat inaccurate above room temperature. Bγ,2m2 remains constant up to 340 K and decreases drastically above: this unexpected behaviour has been carefully checked and raises new questions about the band structure of nickel; we compare these data with the results observed in a Ni 3.3 at% Ru single crystal. The second-order magnetoelastic coefficients have been also investigated: the pulse echo method under a magnetic field up to 60 kOe rotatable in any direction allowed us to observe for the first time the morphic effect in nickel. Anharmonic contributions to this effect have been shown to be far from negligible.

The magnetic and magnetoelastic properties of GdZn have been investigated by various ways: magnetization, magnetic susceptibility, magnetocaloric effect, pressure dependence of the Curie temperature, spontaneous magnetostriction, parastriction and sound velocity measurements. The γ-mode strain is large for an S-state ion, and two orders of magnitude larger than the ϵ-one. Both the first-order Bγ,2 and the three isotropic second-order magnetoelastic coefficients exhibit a m2(1 − 0.5m2) thermal variation (where m(T, H) is the reduced magnetization), which differs from the classical behaviour. All the results suggest a noticeable contribution of the conduction band to the magnetism of GdZn.