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)     

Influence of the ferromagnetic structure on the speed of propagation of magnetoelastic vibrations

The effect of thermomagnetic treatment temperature on the speed of magnetoelastic vibrations propagating in aFe _81.5 B _13.5 Si ₃ C ₂ metal alloy is investigated. A minimum is found in the plot of the dependence of the speed of magnetoelastic vibrations on the thermomagnetic treatment temperature. No minimum is observed in this dependence for amorphous metal alloys treated without magnetic field. It is found that the dependences of the speed of magnetoelastic vibrations on the external magnetic field differ for samples treated differently. The results obtained are explained based on concepts of reorganization of the domain structure of the samples under study. Irkutsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 46–49, September, 1999.     

Magnetoelastic waves in an in-plane magnetized ferromagnetic plate

The spectrum of magnetoelastic waves propagating along the magnetic field in an in-plane magnetized ferromagnetic plate is numerically investigated in the exchangeless approximation. No restrictions are imposed either on the field pattern of backward volume magnetostatic waves (BVMSWs) or elastic waves supported by a plate of a given geometry across the plate or on the relationship between the sound velocity v _S and the phase velocity of the magnetoelastic waves v=ω/q (ω is the frequency, q is the wave number). The resonance interaction of the BVMSWs and elastic waves is accompanied, as a rule, by the formation of “stop” bands δω that are proportional to the magnetoelastic coupling constant b. When the BVMSWs are in resonance with Lamb and shear elastic modes the values of the magnetoelastic gaps δω at v≈v _S turn out to be of the same order. For v≫v _S , the efficiency of the interaction between the BVMSWs and transverse Lamb modes is almost one order of magnitude higher. If the frequency spacing Δω between the elastic modes is smaller than the mag-netoelastic gap in the spectrum (Δω≤δω), which takes place, particularly, in the region of crowding the elastic mode spectrum (v≈v _S), the resonant interaction results in mixing the dispersion laws for the elastic modes. Namely, a surface mode may transform into a volume one and a shear mode, into the Lamb mode or into a shear mode with another number. The resonance interaction of the shear and Lamb elastic modes not only forms the magnetoelastic gaps δω∼b ² but also changes the efficiency of elastic wave coupling with the magnetic subsystem. This may show up as the coexistence of the effects of “repulsing” both the dispersion laws and the damping decrements of the elastic waves at the resonance frequency. It is shown that magnetostriction splits the cutoff frequencies of both transverse Lamb modes and shear modes, as well as the long-wave (q → 0) frequency limits f ₀ of the BVMSW modes. This may cause the resonance interaction between BVMSW modes of equal evenness in a narrow frequency band Δ∼b near f ₀.     

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.     

Optical phonons of Rare-Earth halides in a magnetic field

A theory is developed which explains the observed magnetic field splitting of doubly degenerateE-phonons in Rare Earth Chlorides. It is based on first and second order magnetoelastic interactions. Quantitative calculations are done for CeCl₃ for which the field dependence of the splitting is derived and estimates of the coupling constants are given.Furthermore we propose a mechanism for the observed reduction of the phononlinewidth in a magnetic field.     

Antiferromagnetic conical refraction of elastic waves in hematite

Conical refraction, which is due to the renormalization of the elastic moduli by the effective magnetoelastic interaction and depends on the static magnetic field, has been experimentally observed in an α-Fe₂O₃ trigonal easy-plane antiferromagnet in addition to the usual internal conical refraction of transverse elastic waves propagating along the trigonal C ₃ axis. It has been shown that the deviation angle θ_η of the energy flux from the C ₃ axis at the internal conical refraction is independent of the magnetic field applied in the basal plane (H ⊥ C ₃) and is a constant determined by the ratio of the elastic moduli C ₁₄ and C ₄₄. The deviation angle of the energy flux at the antiferromagnetic conical refraction increases with the magnetic field and approaches the value θ_η at large H values. The results are well described by the theory of this phenomenon developed by E.A. Turov and confirm its basic conclusions.     

Crystal field effects in rare-earth ferroborates RFe3(BO3)4 with R = Nd, Tb, Dy, or Er

Crystal field effects in rare-earth ferroborates RFe₃(BO₃)₄ with various rare-earth elements are studied theoretically. The rare-earth magnetoelastic interaction Hamiltonian is written in a multipole approximation. The field and temperature dependences of the multipole moments and strain susceptibilities of rare-earth ions in the ferroborate structure are calculated. A comparative analysis of anomalies in the thermal expansion and elastic constants of rare-earth ferroborates with Tb and Dy ions having identical magnetic structure but differing in the degree of anisotropy of the rare-earth ion is performed.     

Crystal field effect in the thermal expansion of hexagonal rare earth compounds

The low temperature thermal expansion in hexagonal rare earth materials exhibits crystal field effects. These are quantitatively explained with a magnetoelastic coupling of Γ₁-symmetry strains to a 1=2 quadrupolar operator of the magnetic ion. For PrNi₅ the temperature dependence of both c- and a-axis thermal expansion is correctly accounted for. For dhcp Pr both the cubic and the hexagonal sites of the Pr-ions contribute to the thermal expansion. The magnetoelastic coupling constants are an order of magnitude larger than for cubic compounds.     

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.     

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.     

Magnetoelectric and magnetoelastic interactions in NdFe3(BO3)4 multiferroics

Complex experimental and theoretical investigations of the magnetic, magnetoelectric, and magnetoelastic properties of neodymium iron borate NdFe₃(BO₃)₄ along various crystallographic directions have been carried out in strong pulsed magnetic fields up to 230 kOe in a temperature range of 4.2–50 K. It has been found that neodymium iron borate, as well as gadolinium iron borate, is a multiferroic. It has a much larger (above 300 μC/m²) electric polarization controlled by the magnetic field and giant quadratic magnetoelectric effect. The exchange field between the rare-earth and iron subsystems (～50 kOe) has been determined for the first time from experimental data. The theoretical analysis based on the magnetic symmetry and quantum properties of the Nd ion in the crystal provides an explanation of the unusual behavior of the magnetoelectric and magnetoelastic properties of neodymium iron borate in strong magnetic fields and correlation observed between them.     

Effect of electric current on the magnetic and magnetoelastic properties of amorphous ferromagnetic alloys

The magnetic and magnetoelastic parameters of Fe₆₄Co₂₁B₁₅ and Fe_81.5B_13.5Si₃C₂ amorphous ferromagnetic alloys treated by direct electric current in air are studied as functions of the applied magnetic field and current density. The samples of the alloy have the form of narrow strips with different lengths. It is found that the magnetoelastic parameters of the dc-treated alloys depend on the magnetic field in a qualitatively different way. From the behavior of the magnetic and magnetoelastic parameters of the alloys in the magnetic field a model of magnetization nonuniform distribution in amorphous ferromagnetic alloys subjected to dc treatment is proposed.     

Investigation of the effect of uniaxial pressure on antiferromagnetic resonance in KFe11O17 Crystals

The deformation dependence of the resonance field in KFe₁₁O₁₇ single crystals was investigated by the AFMR method. The measurements were performed at T=77 K and ν=47.52 GHz for two orientations of the external pressure. The experimental data are discussed in terms of a model of a very simple easy-plane antiferromagnet taking account of the elastic and magnetoelastic contributions to the thermodynamic potential. The magnetostriction, magnetoelastic, and elastic contants are calculated and the results are λ=1.94×10⁻⁵, B ₁=2.75×10⁸ erg/cm³, and C ₁₁−C ₁₂=1.42×10¹³ erg/cm³, respectively. The alues of these constants imply that the origin of the initial gap in the AFMR spectrum is not of magnetoelastic origin. Fiz. Tverd. Tela (St. Petersburg) 40, 513–515 (March 1998)     

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.     

Thermal expansion and magnetostriction of GdAg2, and relations to the magnetoelastic paradox

The antiferromagnet GdAg₂ has been shown to be a good model system for the magnetoelastic paradox (MEP), because it exhibits large symmetry conserving magnetoelastic strains and the antiferromagnetic propagation vector breaks the tetragonal lattice symmetry (therefore a large symmetry breaking magnetoelastic strain can be expected in a single magnetic structure). As in many similar Gd based compounds no symmetry breaking strain has been found in the experiment. In order to investigate this MEP further, we have measured magnetostriction and magnetization on a textured polycrystal. The behaviour closely resembles that of GdNi₂B₂C, the prototype system for the magnetoelastic paradox (MEP). Our forced magnetostriction data indicate that the crystal distorts in applied magnetic field and gives further evidence that the MEP is a low field effect. The observed phase transitions are in agreement with available specific heat and neutron diffraction data. Moreover, the saturation magnetic field was measured in high pulsed magnetic fields and agrees well with the value calculated from the Standard Model of Rare Earth Magnetism (SMREM).     

Magnetic phase transitions in layered intermetallic compounds

Magnetic, magnetoelastic, and magnetotransport properties have been studied for the RMn₂Si₂ and RMn₆Sn₆ (R is a rare earth metal) intermetallic compounds with natural layered structure. The compounds exhibit wide variety of magnetic structures and magnetic phase transitions. Substitution of different R atoms allows us to modify the interatomic distances and interlayer exchange interactions thus providing the transition from antiferromagnetic to ferromagnetic state. Near the boundary of this transition the magnetic structures are very sensitive to the external field, temperature and pressure. The field-induced transitions are accompanied by considerable change in the sample size and resistivity. It has been shown that various magnetic structures and magnetic phase transitions observed in the layered compounds arise as a result of competition of the Mn–Mn and Mn–R exchange interactions.     

Temperature anomalies in the nonlinear magnetoacoustic properties of manganese-zinc spinel single crystals

The absorption of a magnetoelastic wave and the nonlinear resonance interaction of counterpropagating magnetoelastic waves in a manganese-zinc spinel single crystal have been investigated near the conjectured spin-reorientational transition. The convolution signal vanishes near T _tr=291 K; this is explained by the relaxational dynamics of the magnetic mode near the transition. The increase in the strength of the field corresponding to the maximum of the convolution with decreasing temperature is explained by a change in the demagnetizing field. Fiz. Tverd. Tela (St. Petersburg) 39, 652–655 (April 1997)     

Dynamic stress sensitivity of Fe73.5Cu1(Ta or W)3Si15.5B7 ribbons after heat treatments in vacuum

Summary The effects of heat treatments in vacuum on magnetic permeability, Young's modulus and magnetoelastic wave amplitude were investigated in the amorphous ferromagnetic alloys Fe_73.5Cu₁Ta₃Si_15.5B₇ and Fe_73.5Cu₁W₃Si_15.5B₇ where tantalum or tungsten replaces niobium, which was generally used with the same atomic fractions of the other elements. The stress sensitivity coefficient was also theoretically deduced in its developmentvs. the applied magnetic bias field. Structural relaxation and crystallization consequences are evidenced. Moreover an already predicted relation between the maximum of magnetoelastic wave amplitude and the minimum of stress sensitivity coefficient was confirmed.     

Effect of mechanical stresses on the magnetoelastic properties of TmVO4

In this paper the influence of mechanical stress on magnetoelastic properties, i.e., magnetostriction and thermal expansion in the neighborhood of a structural phase transition of the Jahn-Teller crystal TmVO₄ is investigated experimentally and theoretically. It is shown that the magnetoelastic properties of TmVO₄ for a magnetic field H∥[001] do not change the domain structure of the sample, which is rather well described when mechanical stresses in the crystal are taken into account using the parameter . Conversely, for magnetic fields along the direction of spontaneous strain [110] the magnetoelastic properties are primarily caused by reorientation of the Jahn-Teller domains and short-range order effects. It is shown that the “true” magnetostriction of a single-domain crystal for H∥[110] diverges at the phase transition point T _c=2.15 K in the absence of mechanical stresses and is strongly decreased by these stresses. Fiz. Tverd. Tela (St. Petersburg) 40, 701–705 (April 1998)