E. du Tremolet de Lacheisserie

Magnetostriction and internal stresses in thin films: the cantilever method revisited

Abstract The deformations of a bimorph, consisting of a non-magnetic substrate and a magnetic thin film, under the influence of (i) an isotropic stress, e.g. due to thermal expansion and (ii) a uniaxial magnetic field (Joule magnetostriction) have been derived: the formula proposed by Klokholm in 1976 and widely accepted until now predicts magnetostrictive strains about twice as large as the ones actually observed. The corrected formula takes into account the anisotropic character of the Joule magnetostriction. The conditions of validity of this formula are discussed.

Magnetic and quadrupolar properties of PrPb3

Abstract The cubic rare earth intermetallic compound PrPb 3 (AuCu 3 -type structure) undergoes a transition at 0.35 K: as it is a Van Vleck paramagnet, the low temperature phase was assumed to be quadrupolarly ordered. In order to specify this possibility, we first discuss the cubic level scheme using specific heat and first-order magnetic susceptibility results; afterwards we present an extensive study of the two (tetragonal and trigonal) symmetry lowering modes, investigated in the cubic paramagnetic phase by means of parastriction and third-order magnetic susceptibility. For the tetragonal symmetry, the quadrupolar pair interactions appear as negative, dominating the magnetoelastic coupling; as a result, the low temperature ordering may be antiferroquadrupolar, a new situation among rare earth intermetallics, the TmZn and TmCd ordering being ferroquadrupolar.

Magnetoelastic properties of amorphous alloys

Abstract A phenomenological description of the first and second order magnetoelastic effects is developed for amorphous ferromagnetic alloys: magnetostriction, Δ E effect and magnetoelastic contributions to the sound velocities are discussed in detail. A brief description is given of the main experimental methods used to study these effects. A general review of the available data is given for thermal expansion, spontaneous and forced magnetostriction, static elastic properties, acoustic resonance and sound waves propagation under a magnetic field.

From bulk to film magnetostrictive actuators

Abstract Bulk 3d–4f intermetallic compounds exhibiting a giant magnetostriction at room temperature have been developed since 1975 by A.E. Clark. Until recently, attempts to obtain thin films with high magnetoelastic coupling had failed, due to the sperimagnetic character of amorphous R-Fe 2 alloys. Two ways have been recently proposed for overcoming this problem, namely preparing (i) R-Fe 2 nanocrystalline alloys, and (ii) R-Co 2 amorphous alloys. Both methods have shown to be promising while still further improved performances have been reached using composite materials as for example multilayer systems (similar to the spring-magnets), which exhibit giant magnetostrictivity (exceeding 1000 MPaxa0T −1 under only 2 mT). We shall review these new materials of interest for microsystems.

Structural and magnetic properties in R2Fe14B compounds

Abstract The reduction of the Curie temperature in R 2 Fe 14 B compounds compared to Fe metal and the observation of a large anomalous thermal expansion are reminiscent of properties observed in R 2 Fe 17 compounds [1]. With the short interatomic distances between Fe atoms are associated weak magnetic interactions which are strongly distance dependent. In Nd 2 Fe 14 B, the anisotropy essentially results from a crystal field potential acting on the 4f ions. In agreement with the point-charge calculation, the dominant term, B 0 2 O 0 2 , is of opposite sign compared to other R-M compounds and favors the c -direction for the magnetization. Additional terms in the crystal field potential account for the intermediate direction for the spontaneous magnetization observed below 135 K. The reorientation of the magnetization towards the c -axis at higher temperatures is driven by exchange interactions which favor a collinear arrangement of Nd and Fe moments.

Magnetoelastic properties of nickel thin films

The deflection of bimorphs consisting of thin films of nickel on silicon substrates has been accurately measured as a function of applied in‐plane magnetic field, using an optical method. Striking differences in the magnetoelastic behavior are observed for these systems compared with bulk nickel, mainly due to the anisotropic behavior of silicon substrates and to large in plane tensile stresses in nickel films, which favor an easy magnetization axis perpendicular to the film plane: Deflections measured with the magnetic field parallel and perpendicular to the length of the bimorph exhibit the same sign, and the ‘‘parallel deflection’’ is enhanced by a factor 1.3. These are the first experiments demonstrating the validity of a formula recently derived for predicting the deflection of magnetostrictive bimorphs.

Magnetic properties and critical behaviour of GdAl2: Thermal expansion, magnetization, magnetostriction and magnetocaloric effect

Abstract The magnetic properties of GdAl 2 have been revisited with a special emphasis on their critical behaviour. Thermal expansion measurement has confirmed the spontaneous volume magnetostriction to be negative (Δ V / V = -11.6x10 -4 ). The paramagnetic susceptibility has been fitted up to 2 T c by a modified Curie-Weiss law: χ = χ 0 + ( C / T )(1- T c / T ) -γ with a paramagnetic moment equal to the theoretical one for J = 7/2 and a critical exponent γ = 1.13±0.01. At T = T c , σ ∼ H i 1/δ with δ = 3.60±0.05 and just below T c , M s ∼ (itT c - T ) β with β = 0.44±0.015 in excellent agreement with the scaling laws. Spontaneous and forced magnetostriction have been measured along [111] and [100] directions. λ ϵ,2 is found to exhibit a sign opposite to the one previously given in the literature. The magnetocaloric effect has been deduced from the difference between adiabatic and isothermal strains, and derived exactly in terms of γ above T c ; it is shown to decrease with temperature more slowly than the parastriction does.

Elastic properties of ferromagnetic single crystal with cubic symmetry

A group theoretical description is given of the first and second order magnetoelastic coupling for cubic ferromagnets. First, this coupling is expanded as a series of the Lagrangian tensor componentsηij, which definesN coefficients. An alternative expansion is given in terms of the symmetrical (εij) and antisymmetrical (ωij) components of the homogeneous strainsuij, which definesN(>N) coefficients. The conditions for rotational invariance of the energy are then written: they provide relations which reduce fromN toN the number of independent coefficients in the 2nd description. These relations were previously derived in the framework of the localised model and some features of this model are briefly discussed here: in particular, the exchange contributions to the elastic constants are corrected for volume effects and differ significantly from Fuchs and Satos formulae. In the next step, the magnetostriction is taken into account to derive the internal energy of a distorted crystal. It is then possible to analyse the ultrasonic waves propagation under high magnetic fields in terms of three main magnetic contributions, namely an isotropic exchange effect, an anisotropic morphic effect and a field dependent Simon effect.

Pair model of anisotropy and magnetostriction in soft amorphous magnets

Abstract A pair model for amorphous alloys has been developed, considering both the spherical symmetry (isotropic alloys) and the cylindrical one (alloys exhibiting pair ordering or microstructural anisotropy). The elastic energy has been first derived. Then starting from the Heisenberg exchange, the pseudodipolar (PSD), the cluster electric field (CEF) and the simple dipolar couplings, the magnetoelastic coupling and magnetic anisotropy energies have been written in the limiting case of a very small random anisotropy.

Magnetic and magnetoelastic properties of GdZn single crystals

Abstract 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 B γ,2 and the three isotropic second-order magnetoelastic coefficients exhibit a m 2 (1 − 0.5 m 2 ) 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.