Magnetic exchange driven magnetoelastic properties in GdCu2

The magnetoelastic properties of GdCu₂ have been investigated by thermal expansion and magnetostriction measurements. GdCu₂ orders antiferromagnetically with a noncollinear magnetic structure. The anisotropic magnetostriction is of similar magnitude as in other RCu₂ compounds and can be explained by a contribution of the bilinear exchange interaction to the magnetoelastic energy. For several compounds this contribution is as important as the single ion magnetoelastic exchange. The pressure dependence of the Néel temperature of GdCu₂ is found to be in agreement with the data of thermal expansion.     

The magnetoelastic contribution to thermal expansion of rare-earth metal scheelites RLiF<Subscript>4</Subscript> (R = Tb-Yb)

The paper presents systematic experimental and theoretical studies of thermal expansion for rare-earth metal scheelites RLiF₄ (R = Tb-Ho, Tm, and Lu). Pronounced thermal expansion anomalies were observed. The magnetoelastic contributions were determined taking into account corrections for changes in the phonon contribution in the RLiF₄ series according to the Debye thermal expansion model. The calculated multipole moments of various orders for various rare-earth metal ions were compared to analyze the applicability of the quadrupole approximation to totally symmetric modes in the scheelite structure. For some ions (Ho and Tm), the magnetoelastic contributions to thermal expansion could not be described by the temperature dependences of their quadrupole moments, that is, multipole moments made considerable contributions. The totally symmetric magnetoelastic coefficients for the scheelite structure were determined from the experimental data on magnetoelastic contributions. These coefficients were compared with those for the zircon structure.     

Magnetoelastic contribution to the thermal expansion of the rare-earth phosphates TbPO4 and TmPO4

The thermal expansion of the rare-earth phosphates TbPO₄ and TmPO₄ having zircon structure has been investigated experimentally and theoretically. Significant magnetoelastic anomalies of the thermal expansion have been identified and the magnetoelastic contributions have been isolated allowing for corrections to the variation of the phonon contribution along the rare-earth ion series. It is shown that the magnetoelastic contribution to the thermal expansion of terbium and thulium phosphate is well described by the temperature dependence of the quadrupole moments of the rare-earth ions. The fully symmetric magnetoelastic coefficients for Tb³⁺ and Tm³⁺ are determined and a comparison is made of the magnetoelastic anomalies of the thermal expansion and the magnetoelastic coefficients of rare-earth phosphates and vanadates allowing for the differences in the crystal fields of the two isomorphic groups of zircons. Fiz. Tverd. Tela (St. Petersburg) 39, 106–111 (January 1997)     

Anomalies in thermal expansion of DyVO4 induced by quadrupolar ordering

The thermal expansion of the DyVO₄ crystal has been experimentally and theoretically investigated in the range of the Jahn-Teller structural phase transition. The manifestation of totally symmetric magnetoelastic interactions upon this transition has been studied for the first time. It is found that the temperature dependences of the unit-cell and thermal expansion parameters along the nonactive Jahn-Teller direction in the basal plane for the DyVO₄ crystal exhibit characteristic magnetoelastic anomalies at T<T _c due to the ordering of quadrupole moments of Dy³⁺ ions. The magnetoelastic contributions of the totally symmetric ε^α1 and ε^α2 and symmetry-lowering ε^γ modes to the thermal expansion are calculated within the general crystal-field formalism. The total quadrupolar coefficient G ^γ and magnetoelastic coefficient B ^γ are determined from the spectroscopic and spontaneous deformation data. It is demonstrated that the thermal expansion of the DyVO₄ crystal in the tetragonal and orthorhombic phases is well described in the framework of the unified model using a common set of interaction parameters for both phases.     

Magnetoelastic effects in rare-earth vanadates YbVO4 and HoVO4

Magnetoelastic anomalies in the thermal expansion and Young modulus, as well as the ΔE-effect in rare-earth vanadates RVO₄ (R = Ho, Yb), are investigated experimentally and theoretically. A considerable softening of the Young modulus is observed for HoVO₄ and YbVO₄ at T < 70 K and T < 150 K, respectively; this effect is adequately described in the framework of the generalized susceptibility formalism. It is shown that the field dependences of the ΔE-effect and their temperature variation in YbVO₄ can also be described using this approach. To compare with experiment, the magnetoelastic contributions to the Young modulus of an isotropic polycrystal from various elastic modes have been averaged. For the Yb vanadate, considerable magnetoelastic anomalies in the thermal expansion along the tetragonal a and c axes have been discovered. The magnetoelastic contributions are used for determining completely symmetric magnetoelastic coefficients; the role of the completely symmetric quadrupole constant for magnetoelastic effects is analyzed.     

Magnetoelastic properties of Nd6Fe13Cu intermetallic compound

Magnetoelastic properties of Nd₆Fe₁₃Cu intermetallic compound are reported. To study the magnetoelastic behaviour of this compound, the thermal expansion as well as the longitudinal (λ_l) and transverse (λ_t) magnetostriction were measured by using the strain gauge method in the selected temperature range of 80-500 K under applied magnetic fields up to 1.5 T. An anomaly and invar-type effects are observed in the linear thermal expansion and α(T) curves at the Néel temperature. The linear spontaneous magnetostriction decreases sharply by approaching the Néel temperature and also shows the short-range magnetic ordering effects when antiferromagnetic-paramagnetic transition occurs. In the low field region, the absolute values of the anisotropic magnetostriction are small and then start to increase with applied magnetic field. Each isofield curve of the anisotropic magnetostriction passes through a minimum and then approaches to zero with increasing temperature. This magnetostriction compensation arises from the difference in the magnetoelastic coupling constants of the sublattices in this compound.     

Magnetic and quadrupolar properties of PrPb3

The cubic rare earth intermetallic compound PrPb₃ (AuCu₃-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.     

A finite element analysis of the bending of crystalline plates due to anisotropic surface and film stress applied to magnetoelasticity

The bending of crystalline plates in response to a non-isotropic stress on one of the two surfaces is investigated with special attention to magnetoelastic effects. The crystalline plates are assumed to have cubic symmetry, expose either (1 0 0) or (1 1 1) surfaces, and be clamped along one edge. It is shown that the effect of clamping can be described by a dimensionless parameter, the “dimensionality” D, which in general depends on the length-to-width ratio of the sample, the Poisson ratio ν, and the elastic anisotropy A. Using a finite element analysis we find that the dimensionality parameters for anisotropic and isotropic surface stresses are identical. The theory is applied to the bending caused by magnetoelastic stresses in deposited thin films. Expressions are derived to calculate the magnetoelastic coupling constants of films with cubic, tetragonal, or hexagonal symmetry from a measurement of the change of radius of curvature of the film–substrate composite upon an in-plane reorientation of the film magnetization.     

Thermodynamic properties of BaRuO3

We have investigated the specific heat, thermal expansion and thermodynamic properties of BaRuO₃ in rhombohedral, hexagonal and cubic phase using the modified rigid ion model (MRIM) by incorporating the effect of lattice distortions. The calculated Debye temperature, specific heat and other thermal properties reproduce well with the available experimental data, implying that MRIM represents properly the nature of the perovskite-type BaRuO₃. Besides, we have reported the thermal expansion (α), bulk modulus (B), cohesive energy (?), molecular force constant (f), Reststrahlen frequency (υ), Debye temperature (θ _D), and Gruneisen parameter (γ).     

Synthesis hexagonal ZrW2O8 and its thermal properties

ZrW₂O₈ as the typical negative thermal expansion (NTE) material has attracted much attention for the potential applications in various fields such as tailored coefficient of thermal expansion (CTE) composites. The hexagonal ZrW₂O₈ (h-ZrW₂O₈), with the combination of ZrO₂ and WO₃ in a composite, was synthesized at a pressure of 2 GPa and the temperature between 600°C and 700°C. We found h-ZrW₂O₈ decomposes to ZrO₂+WO₃ oxides that start from 500°C and end at 800°C, and determined the CTE of h-ZrW₂O₈ is?16.3×10^?6°C^?1 in the temperature range from 150°C to 450°C. The results show that ZrW₂O₈ with a hexagonal structure is metastable and exhibits high NTE property like its cubic structure.     

Thermal stability of the cubic phase in Ba0.5Sr0.5Co0.8Fe0.2O3 - δ (BSCF)1

Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3 - δ (BSCF) is a material with excellent oxygen ionic and electronic transport properties reported by many research groups. In its cubic phase, this mixed ionic-electronic conducting (MIEC) perovskite is a promising candidate for oxygen permeation membranes. For this application, its long-term stability under operating conditions (especially temperature and oxygen partial pressure) is of crucial importance.The present work is focused on the thermal stability of the BSCF cubic phase in the targeted temperature range for applications (700…900 °C) in light of previous studies in literature reporting a reversible transition to a hexagonal phase somewhere below 900 °C.To this end, single phase cubic BSCF powders were annealed at different temperatures over varying periods of time. Phase composition was subsequently analysed by X-ray diffractometry (XRD) in order to determine both the temperature limit and the time-scale for the formation of the hexagonal phase. Additionally, the long-term behaviour of the electrical conductivity was examined on bulk samples at 700 °C, 800 °C and 900 °C over several hundreds of hours, showing a prolonged decrease at 800 °C. The decrease in electrical conductivity at this temperature was also examined on bulk samples with different grain sizes, showing a more pronounced decrease the smaller the average grain size.Coexistence of both phases (cubic and hexagonal) could also be shown for 700 °C, however with a different phase equilibrium than at 800 °C.     

Rotation of magnetization in unison and langevin equations for a large spin

A single-domain ferromagnetic particle is represented as a large spin (model of rotation in unison) whose stochastic dynamics is derived from a spin-boson Hamiltonian. It is shown in the Markovian limit that thermal equilibrium exists provided that the fluctuation-dissipation theorem is supplemented by a symmetry constraint which for bilinear anisotropic and nonlinear (magnetoelastic) spin-bath coupling can only be satisfied in the underdamped limit. Only for bilinear isotropic coupling (Gilbert's theory) is it satisfied identically for arbitrary damping strength. Uniaxial and cubic symmetries are considered. For a model uniaxial crystal the thermal decay rate of M and the thermal enhancement of the macroscopic quantum tunneling rate are calculated for Gilbert and magnetoelastic dissipative couplings and compared. The effects of memory are discussed.     

Magnetoelasticity,rotational invariance and magnetoacoustic birefringence in CeAl2

A thorough experimental investigation of elastic and magnetoelastic properties for CeAl₂ is given. The temperature dependence of the various elastic modes is accounted for with a magnetoelastic coupling of the strain components to crystal field split magnetic ions. Large magnetic field effects for thec ₄₄-mode in various geometries are observed. The rotational invariant magnetoelastic interaction is deduced from the experiment and quantitatively accounted for. Magnetoacoustic analoga of the Faraday and Cotton-Mouton-Voigt effect are observed for the first time in the paramagnetic phase.     

Moment-volume instabilities in alloys with compositions around the C14 laves phase

We measured the thermal expansion and the specific heat of Ti_xFe_100-x alloys with x = 30.5, 32.5 and 35, all with hexagonal C14 laves phase structure (MgZn₂) like TiFe₂, and determine the temperature dependence of the magnetic contributions to the thermal expansion and the specific heat c_mag. For fixed composition and c mag ( T ) show the same type of behavior, demonstrating that both anomalies are of the same microscopic nature. They originate from moment-volume fluctuations (antiferromagnetic Invar-effect) as a comparison with total energy calculations as a function of atomic volume and moment for TiFe₂ reveals. Received: 26 January 1998 / Accepted: 17 April 1998     

X-ray studies of the (La,Sr)MnO<Subscript>3</Subscript> perovskite manganite structure

X-ray studies of perovskite manganites (La_0.9Sr_0.1)_0.9MnO₃ and La_1?xSr_xMnO₃ (x = 0.1, 0.15, 0.2, 0.25) are reported. The atom positions and interatomic distances and angles are calculated as a function of Sr doping at room temperature using the FullProf software. The temperature dependences of the crystal lattice parameters and unit cell volume are investigated. The effects of structural and magnetic phase transitions on the crystal lattice parameters are studied in detail. The bulk magnetoelastic contribution to thermal expansion is studied experimentally and calculated.     

Effets magnétostrictifs spontanés de quelques composés des terres rares

X-ray measurements as a function of the temperature of the crystal lattice parameters of EuO and EuS reveal a volume reduction of 0.3% and 0.12%, respectively, when these crystals are cooled through the Curie temperature. This contraction can be assigned to the exchange-striction and the relative volume variation is proportional to the spin correlation function. Within the molecular field approximation, this magnetoelastic interaction is described by the relationT _C=T ₀[1+β(V?V ₀)/V ₀]. For EuO and EuS the values of the magnetoelastic interaction parameterβ are ?3.5 and ?6.4, respectively, in agreement with the values derived from measurements of the pressure dependence of the Curie temperature. No anomaly of the expansion coefficient has been detected in the EuSe and EuTe compounds.     

Magnetoelastic properties of ErMn6Sn6 intermetallic compound

The thermal expansion and magnetostriction of polycrystalline sample of the ErMn₆Sn₆ intermetallic compound with hexagonal HfFe₆Ge₆-type structure are investigated in the temperature range of 77 K to above 400 K. The thermal expansion measurement of the sample shows anomalous behavior around its T_N=340 K. The isofield curves of volume magnetostriction also reveal anomalies at paramagnetic-antiferromagnetic and antiferromagnetic-ferrimagnetic phase transitions. In the antiferromagnetic state, the transition to ferrimagnetism can be induced by an applied magnetic field. The threshold field for the metamagnetic transition H_th increases from 0.18 T at 84 K to about 1 T around 220 K, and then decreases monotonously to T_N. This behavior is well consistent with that observed earlier on magnetization curves attributed to exchange-related metamagnetic transition rather than the anisotropy-related one. Furthermore, the low H_th values suggest that the Mn-Mn coupling in ErMn₆Sn₆ is not so strong. The experimental results obtained are discussed in the framework of two-magnetic sublattice by bearing in mind the lattice parameter dependence of the interlayer Mn-Mn exchange interaction in this layered compound. From the temperature dependence of magnetostriction values and considering the magnetostriction relation of a hexagonal structure, we attempt to determine the signs of some of the magnetostriction constants for this compound.     

On the magnetoelastic contribution to the magnetic anisotropy of thin epitaxial Permalloy films: an ab initio study

Permalloy films are often used in the magnetic thin film technology. It is expected that in this material the magnetoelastic coupling of the magnetization to the epitaxial film strain does not produce undesired magnetic anisotropy, because the linear magnetoelastic bulk coefficient B₁ of Permalloy is near-zero. It is shown by means of the ab initio density functional electron theory that the nonvanishing nonlinear magnetoelastic couplings also do not lead to a considerable anisotropy. Explicit values for two of the nonlinear magnetoelastic coupling coefficients are given.     

A study on magnetoelastic properties of Tb3 (Fe28−xCox) V1.0 (x=0, 3, 6) compounds

In this work, The magnetoelastic properties of polycrystalline samples of Tb₃ (Fe_28−xCo_x) V_1.0 (x=0, 3, 6) intermetallic compounds are investigated by means of linear thermal expansion and magnetostriction measurements in the temperature range of 77–515 K under applied magnetic fields up to 1.5 T. The linear thermal expansion increases with the Co content. The well-defined anomalies observed in the linear thermal expansion coefficients for Tb₃ (Fe_28−xCo_x) V_1.0 (x=0, 3, 6) compounds are associated with the magnetic ordering temperature for x=0 and spin reorientation temperatures for x=3, 6. Below transition temperatures, the value of the longitudinal magnetostriction (λ_Pa) at 1.6 T increases with Co content.     

Stress effects on the anisotropic thermal expansions of “martensitic” A15 compounds

Precision capacitance dilatometry provides a sensitive measure of the thermal strain developed in a sample undergoing a structural distortion with its varying temperature. The A15 structure compounds, V₃Si and Nb₃Sn, are well known to undergo distortion from their cubic structures at room temperature to tetragonal structures (c/a > 1 for V₃Si and c/a < 1 for Nb₃Sn) at low temperatures. In the past, highly anomalous thermal expansion behaviour recorded for these materials has been attributed to a strongly anharmonic lattice potential manifesting itself in unusually high, and strongly temperature-dependent, Grüneisen parameters. Further studies on polycrystalline material revealed this anomalous expansion to be highly anisotropic at temperatures for which, according to conventional diffraction data, the materials are cubic. This behaviour was linked to control of sample morphology by a residual stress field resulting from sample preparation.

More recent experiments, in which the transformation morphology has been controlled by the application of external stresses to single crystal V₃Si and polycrystalline samples of Nb₃Sn and Nb₃(Sn_1-x Sb _x ), have confirmed the occurrence of significant anisotropy in the thermal strain in the cubic phase, well above the structural transformation.

We link this departure from cubic symmetry with the well-known soft-mode character of these materials and the associated “central peak” scattering which is also observed well above the transformation temperature. We are led to propose that the “central peak” is the precursor to a Bragg reflection for the transformation structure. This coincidence between “central peak” scattering and the reciprocal lattice for the transformed phase in Ti-Ni has been termed a “ghost lattice”.