Nonlinear magnetoelastic effects in ultrathin epitaxial FCC Co(0 0 1) films:: an ab initio study

Those linear and nonlinear magnetoelastic coupling coefficients which determine the magnetostrictive stress and the strain-induced out-of-plane magnetic anisotropy in epitaxially grown FCC Co(0 0 1) films are calculated by the ab initio density functional electron theory. The nonlinear couplings have a strong effect on the change Δσ₁^m of the in-plane magnetostrictive stress resulting from a change of the magnetization direction from [0 1 0] to [1 0 0], but a negligibly small effect on the out-of-plane anisotropy e_MCA. The calculations confirm the experimental result that the measured out-of-plane anisotropy cannot be totally attributed to volume magnetoelastic effects. Estimates are given for the nonlinear magnetoelastic coupling coefficients m₁^γ,2 and m₂^γ,2.     

Physical reasons for the emergence of jumps during rotation of the magnetization of a two-sublattice ferrimagnet at low temperatures

It is shown that the contribution of the intersublattice exchange interaction to the magnetic anisotropy energy of a two-sublattice ferrimagnet can come only from higher order constants satisfying the condition 2K₂+3K₃+?>0. For this reason, for different signs of the first anisotropy constants of the sublattices, this contribution may cause a spontaneous spin-reorientation second-order transition, but not first-order transitions and jumps during magnetization rotation, which are associated with such a transition. Such jumps can appear only when the opposite inequality is satisfied, and the corresponding contribution to anisotropy can be ensured only by a fairly strong magnetoelastic interaction.     

Inhomogeneous magnetostriction states in uniaxial ferromagnetic films

Surface magnetoelastic Love waves and nonuniform distributions of the magnetization and elastic strains are investigated in a uniaxial ferromagnetic film on a massive nonmagnetic substrate in a tangential external magnetic field. A new inhomogeneous phase is predicted having spatial modulation of the order parameter, arising from magnetostrictive coupling of the magnetization with lattice strains near the interface of the magnetoelastic and elastic media. It is shown that, at some critical magnetic field H _c, different from the orientational transition field in an isolated sample, a magnetoelastic Love wave propagating parallel to the magnetization vector in the film plane becomes unstable. The frequency and group velocity of the wave vanish at wave number k=k _c≠0 and the wave freezes, forming a domain structure localized in the film and adjoining substrate. Fiz. Tverd. Tela (St. Petersburg) 41, 665–671 (April 1999)     

Ultrasonic velocities near the spin-reorientation transitions in ErFeO3 at high pressure

Longitudinal and shear sound velocities have been measured near the spin-reorientation transitions in ErFeO₃ at hydrostatic pressure up to 2.4 kbar. The results, which are analyzed in terms of a phenomenological theory with magnetoelastic coupling terms, show that hydrostatic pressure has a very small effect on the magnetic anisotropy constants.     

Magnetic and Elastic Vibrations in Manganese–Zinc Spinel Crystals as the Functions of Anisotropy Constant

The amplitudes of magnetic and elastic vibrations for Mn_0.61Zn_0.35Fe_2.04O₄ spinel crystalline slab are calculated by solving the equations describing the magnetic and elastic dynamics. The anisotropy constants, magnetization, second-order elastic constants and magnetoelastic coupling constants for a studied crystal are expressed as the functions of temperature. The magnetization vector and elastic shear components are found as the functions of the first magnetic anisotropy constant at different values of an external constant magnetic field greater than a saturation field. The procession patterns for normally and tangentially magnetized slabs are displayed for two values of the first anisotropy constant. High absolute values of the first anisotropy constant are shown to refer to reorientation of the magnetization vector.     

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.     

Magnetic anisotropy in Co73Mo2Si15B10 and (Co0.89Fe0.11) 72Mo3Si15B10 metallic glasses,induced by stress-annealing

Annealing temperature dependence of the stress-induced magnetic anisotropy in Co₇₃Mo₂Si₁₅B₁₀ (λ_s < 0) and (Co_0.89Fe_0.11) ₇₂Mo₃Si₁₅B₁₀ (λ > 0) metallic glass ribbons has been studied experimentally. The room temperature values of the induced anisotropy constants K depend strongly on the annealing conditions, and reveal a change of sign at annealing temperatures well below T_cryst. It is concluded that transient creep and steady-state creep at the elevated temperature give rise to compressive and tensile stresses, respectively, in the expression for the magnetoelastic coupling energy at room temperature.     

Effect of annealing in an external magnetic field on the microstructure and magnetic properties of the Fe/FePt/Pt multilayer system

The effect of annealing in an external magnetic field applied perpendicular to the plane of the film on the kinetics of Ll ₀ phase transformation of the microstructure and the magnetic properties of the Fe(2 nm)/FePt(20 nm)/Pt(2 nm) multilayer system has been investigated. The relations between the hysteresis loop shape, magnetic correlation length, and structural disorders, which are characteristic of magnetic information carriers, have been analyzed. It has been found that the annealing of the Fe(2 nm)/FePt(20 nm)/Pt(2 nm) multilayer system at a temperature of 470°C in an external magnetic field of 3500 Oe, which is applied perpendicular to the film plane, leads to the formation of a face-centered tetragonal structure of the Ll ₀ phase in the FePt film, which is characterized by the high coercivity H _c , the (001) preferred texture, the magnetic anisotropy perpendicular to the film plane, small sizes of FePt grains in the film, and weak exchange coupling between the particles. The energy of the external magnetic field encourages the process of transformation of the FePt film into the Ll ₀ phase. Thus, a method has been developed for fabricating multilayer films based on the FePt Ll ₀ phase with the parameters necessary for information carrier materials with perpendicular-type magnetic recording.     

Crystal field and quadrupole interaction effects in YbXO4 Zircons (X = V, P)

The magnetic and magnetoelastic properties of YbPO₄ and YbVO₄ crystals are investigated experimentally and theoretically; the crystal field parameters are determined, as well as the magnetoelastic coefficients B ^μ and total quadrupole coupling constants G ^μ for all symmetry modes. It is found that, for H ∥ [100], γ-symmetric quadrupole interactions predominate and are responsible for a significant contribution to the third-order susceptibility, magnetization, magnetostriction, and elastic constant. It is demonstrated that, in the absence of an external field, these interactions do not lead to quadrupole ordering, because the respective deformation susceptibility χ_γ is several times less than the critical value of 1/G ^γ. The influence of an external magnetic field along different symmetry axes on the quadrupole effects and quadrupole interactions in Yb zircons is investigated. It is demonstrated that, for H ∥ [110], the susceptibility χ_γ increases with the field, so that in a fairly strong field in the investigated crystals one can expect a γ-symmetric stimulated phase transition.     

The influence of magnetoelastic interaction on structural phase transitions in cubic ferromagnetics

In the framework of the Landau theory of phase transitions, the influence of the magnetoelastic interaction on structural transitions in cubic ferromagnetics with a positive first magnetic anisotropy constant is analyzed. It is shown that structural transitions are not accompanied by a reorientation of magnetization in this case. The phase diagrams of such ferromagnetics either contain a termination point of the structural transition or a critical point in which the first-order transition is replaced by a second-order one. Magnetoelastic interaction also leads to the appearance of an interval of the ferromagnetic parameters in which a coupled first-order structural-magnetic transition exists. The phase T?x diagram for Heusler Ni_2+x Mn_1?x Ga alloys is calculated, which is in good agreement with the experimental phase diagram of these alloys.     

Entropy and magnetocaloric effects in ferromagnets undergoing first- and second-order magnetic phase transitions

The exchange striction model is invoked to derive an expression for the entropy of ferromagnetic materials undergoing first- and second-order magnetic phase transitions. The magnetocaloric and barocaloric effects are calculated for the ferromagnet La(Fe_0.88Si_0.12)₁₃ undergoing a first-order phase transition. The calculated results are in fair agreement with experimental data. The ferromagnet La(Fe_0.88Si_0.12)₁₃ is used as an example to predict the changes in magnetic and magnetocaloric properties associated with gradual increase in the magnetoelastic coupling constant (i.e., with passage from first- to second-order magnetic transition region). It is shown that stronger magnetoelastic coupling leads to stronger magnetocaloric effects and changes their dependence on magnetic field and pressure. Expressions are obtained for the maximum field- and pressure-induced entropy changes. An analysis is presented of the mechanism responsible for the increase in magnetocaloric and barocaloric effects associated with change from the second- to first-order magnetic phase transition.     

Ferrimagnetic resonance spectra of magnetic bubble films at low microwave frequencies

Magnetic bubble films exhibit a number of ferrimagnetic resonance modes due to the spatial variation of the anisotropy. The resonance frequencies have been measured as a function of the applied bias fieldH ₀. In the lower field range the magnetization of the transient layer, which has negative anisotropy, is not yet parallel toH ₀. In this range the resonance frequencies are shifted to higher values due to pinning effects. In films grown by the vertical dipping method an additional layer on top of the transient layer is observed within which the magnetization rotates from the direction in the transient layer to that of the bulk of the film. In films grown by horizontal dipping no such layer could be detected. Each ferrimagnetic resonance mode excites transverse elastic waves in the film due to the magnetoelastic interaction and thus gives rise to elastic resonances of the whole crystal, film and substrate. These elastic resonances lead to a fine-structure of the ferrimagnetic resonances. The observed fine-structure vanishes periodically with frequency and from this behaviour the thickness of the magnetic film and of the transient layer has been determined.     

Spin wave dispersion of FeBO3 at small wavevectors

Brillouin scattering from thermally excited magnons and ferromagnetic resonance are used to determine the spin wave dispersion of the low-frequency spin wave branch in FeBO₃, a transparent weak ferromagnet. In addition to the dominant exchange and Zeeman contributions, the investigation takes into account magnetic dipole and magnetoelastic interactions. Due to the antisymmetric exchange enhancement the material exhibits a broad spin wave band and a large gap energy at small magnetic fields. Competing directional dependences of the dipole and the exchange energy produce a degeneracy of spin waves with a certain magnitude of the wavevector propagating in different directions. The gap energy is shown to be due to magnetoelastic coupling, whereas the contribution of the anisotropy in the easy plane is negligible atT=300 K.     

Influence of magnetoelastic effects on lattice vibrations in the ferromagnetic invar alloy Fe0.65Ni0.35

Neutron scattering measurements have been made of phonons in a Fe₆₅Ni₃₅ crystal at several temperatures. Marked softening of the [110] acoustic shear modes and a dip in the dispersion relation are found at low temperatures. Above the magnetic ordering temperature T_c, the frequency shift is removed completely, which suggests phonon perturbation by magnetoelastic coupling.     

Effect of crystallization annealing under loading on the magnetic properties and the structure of a soft magnetic FeSiNbCuB alloy doped with chromium

The changes of quasi-static magnetic hysteresis loops and X-ray diffraction patterns of the Fe_73.5Si_13.5B₉Nb₃Cu₁ doped to 10 at % chromium instead of iron have been studied to elucidate the influence of the thermomechanical treatment consisting of annealing and cooling of the alloy under the tensile stress (tensile-stress annealing (TSA)) on the magnetic properties and the structure of these alloys. It is shown that the treatment results in the induction of the magnetic anisotropy of the hard axis type at which the magnetization reversal along the direction of applying the external stress during annealing is hampered. The energy of the induced magnetic anisotropy decreases as the chromium content increases. During TSA, the nanocrystal lattices are deformed, and the deformation is retained after cooling. The interplanar spacings increase along the extension direction and decrease in the transverse direction. The deformation anisotropy is observed for crystallographic directions. The anisotropic deformation of the bcc lattice of nanocrystals with high content of the ordered Fe₃Si phase characterized by a negative magnetoelastic interaction is the cause of formation of the state with the transverse magnetic anisotropy of the hard axis type.     

FMR and SMFMR investigation of epitaxial Fe/GaAs(0 0 1) thin films with Si and Ge overlayer

The magnetic anisotropy and magnetoelastic properties of epitaxial iron films prepared by DC magnetron sputtering on single crystal GaAs(0 0 1) substrate and covered with a protective Si or Ge layer have been investigated by means of the ferromagnetic resonance and strain-modulated ferromagnetic resonance. It has been shown that the uniaxial and cubic anisotropy constants as well as two magnetoelastic constants strongly depend on the thickness of the film. The surface components of the cubic anisotropy and magnetoelastic constants have been determined.     

Magnetostriction of the NdCo5 uniaxial permanent magnet

Magnetostriction measurements, between ≈5 and 300 K, of powder magnetically aligned samples of the hexagonal compound NdCo₅, in strong pulsed magnetic fields up to 15 T are reported. The measurement have been performed parallel, perpendicular and at 45° to the alignment c-axis, for the field also applied in those directions. This set of measurements allows us to determine the six irreducible magnetoelastic modes: λ^α₁₁, λ^α₂₁, related to the strain dependence of the isotropic exchange, and λ^α₁₂, λ^α₂₂, λ^γ, λ^ϵ, related to the strain dependence of the crystalline field anisotropy energy. Anomalies on the strains, associated with the spin reorientation (SR) regime are observed, in particular at the temperatures of beginning, T_SR1, and end, T_SR2, of the SR. The thermal variation of the strains is explained by the standard magnetostriction model, including an ingredients: exchange striction (varying as m²_Nd), single-ion anisotropy (varying as m³_Nd), (where m_Nd is the reduc ed Nd sublattice magnetization), as well as an angular dependence of the form {sin²θ(H, T)−sin²θ(0, T)}, where θ(H, T) and θ(0, T), respectively, are the SR angles under field and spontaneous. The irreducible magnetoelastic coupling constants at 0 K have been estimated, although the point charge model is far from agreement with those results.     

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.     

Brillouin light scattering study of the magnetic hysteresis loop in Fe-Ni/Si(100) film with induced magnetic anisotropy

The magnetic hysteresis of Fe₅₇Ni₄₃/Si(100) with magnetic anisotropy induced by an external field has been studied by Brillouin light scattering (BLS). The results are compared with those of the magneto-optic-Kerr-effect (MOKE) measurement and the vibrating sample magnetometer (VSM). The BLS results show that the sample film has strong in-plane anisotropy. The angle between the magnetization and a 4.6 G applied magnetic field H reaches a maximum value of 45° when H lies along the hard axis. The coercivity and magnetic anisotropy field for the film obtained by the BLS are compared with the values obtained by the VSM and MOKE measurement.