Magnetoelastic Modes Research Articles

Magnetostrictive model for the determination of the energy diagram of dysprosium epitaxial films.

A magnetostrictive model that shows the influence of epitaxy on the magnetic phases of dysprosium is presented. This model takes account of all the relevant magnetoelastic modes (\ensuremath{\alpha} and \ensuremath{\gamma}) and of their thermal dependence. The calculation permits us to investigate their respective roles in the ferromagnetic transition. The spectacular shifts of ${\mathit{T}}_{\mathit{C}}$ recently observed experimentally in dysprosium epitaxial films are explained through these energy diagrams. \textcopyright{} 1996 The American Physical Society.

Magnetic and magnetoelastic properties in tetragonal TbPO4.

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.

Magnetostriction of the NdCo 5 uniaxial permanent magnet

Magnetostriction measurements, between ≈5 and 300 K, of powder magnetically aligned samples of the hexagonal compound NdCo 5, 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 α 11, λ α 21, related to the strain dependence of the isotropic exchange, and λ α 12, λ α 22, 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 m 2 Nd), single-ion anisotropy (varying as m 3 Nd), (where m Nd is the reduc ed Nd sublattice magnetization), as well as an angular dependence of the form {sin 2θ( H, T)−sin 2θ(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.

Abstract: Magnetoelastic modes in amorphous ribbons

Certain kinds of amorphous ribbons (2605SC, for example) are known to undergo huge modulus changes with applied magnetic field at kilohertz frequencies and below. It is to be expected that relatively large changes in ultrasonic velocity will also occur. In order to analyze the field dependence of the ultrasonic velocity and attenuation, an understanding of the nature and dispersion of the normal magnetoelastic propagating waves must be obtained. Magnetoelastic plate-wave dispersion and attenuation have been calculated for models of magnetically saturated insulators. For a description of ribbons, however, the effect of a finite conductivity must be concluded. It is probably necessary to include the effect of the random nature of the parameters determining the velocity, as well. In a future publication we will present the results of calculations of the effect of eddy currents and random magnetic anisotropy on the velocity of ultrasonic waves in ribbon-like amorphous magnetoelastic alloys.

Relation between wave speeds in the crust of dense magnetic stars

By studying, within the relativistic framework, the propagation of so-called infinitesimal discontinuities throughout a magnetized elastic perfect conductor in an initial state of high hydrostatic pressurep0and in the presence of a magnetic field of arbitrary strength, it is proven that there holduniversalrelations (i. e., that donotdepend on theexactequation of state of the body) between the speedsUfandUsof so-called fast and slow magnetoelastic modes. These results, which should hold true in the crust of dense magnetic stars, have the following form. IfA0is the relativistic Alfvén number of the initial state anda0is the sound speed of a fictitious relativistic perfect fluid whose law of compression would yield the initial pressurepo, then (with nondimensional speeds)U2/f= 4/3[U2s(1+A20]+(a20-4/3A20) for a propagation along the magnetic field andU2f(1+A20)=4/3U2s+(a20+A20) for a propagation in a direction orthogonal to the magnetic field. These results generalize previous results obtained in relativistic elasticity by Carter and Maugin.

Excitation of gigahertz magnetoelastic waves in dysprosium films: Frequency dependence

Application of a tunable spin-phonon spectrometer to the study of microwave phonon excitations over more than an octave in frequency in polycrystalline films of dysprosium is shown to provide direct information about the coupled magnetoelastic modes. In particular, experiments demonstrate that a rf magnetic field couples to the "phononlike" branch of the magnetoelastic dispersion curves, and the attenuation of the rf field in the films leads to $q\ensuremath{\ne}0$ momentum conservation. The observed phonon signal intensity at the rf frequency ${\ensuremath{\nu}}_{0}$ is shown to be in excellent agreement with intensities computed from the coupled-mode dispersion relations.

Thermal Conductivity and Magnon-Phonon Resonant Interaction in Antiferromagnetic FeCl2

The thermal conductivities ${K}_{\ensuremath{\perp}}$ and ${K}_{\ensuremath{\parallel}}$ in the $c$ plane and along the $c$ axis, respectively, have been measured in Fe${\mathrm{Cl}}_{2}$ between 1.2 and 80 \ifmmode^\circ\else\textdegree\fi{}K. Both ${K}_{\ensuremath{\perp}}$ and ${K}_{\ensuremath{\parallel}}$ are found to exhibit, in a wide temperature range, an unusual behavior which reveals the presence of a strong spin-phonon coupling. The experimental results in the antiferromagnetic phase are interpreted on the basis of the magnon-phonon resonant interaction arising from single-ion magnetostriction. It is shown that the thermal conductivity of the resulting magnetoelastic modes can reasonably account for the experimental results: In particular, the anomalous behaviors of ${K}_{\ensuremath{\perp}}$ and ${K}_{\ensuremath{\parallel}}$ between 5 and 17 \ifmmode^\circ\else\textdegree\fi{}K are explained by the effect of a large magnon scattering on the mixed modes. This large scattering leads to a negligible contribution of the spin waves to heat transport. From the ${K}_{\ensuremath{\perp}}$ results, the magnetoelastic coupling constant ${G}_{44}$ is found to be 3.5 meV.

Phenomenological Theory of Magnetoelastic Modes in Hexagonal Ferromagnets of Easy-Plane Type

The magnetoelastic-mode theory of easy-plane hexagonal ferromagnets is approached from general principles of small oscillations around the equilibrium configuration. A general formula for normal-mode energies is obtained by diagonalizing the Hamiltonian, properly retaining terms quadratic in magnon-magnon, phonon-phonon, and magon-phonon operators. It is found that magnons and phonons are strongly mixed in the region of small $k$ for transverse waves propagating in certain directions parallel to the hexagonal plane when an external field is applied along the hexagonal hard direction and is close to $\frac{36{K}_{h}}{M}$ (hexagonal anisotropic field). On the other hand, the spin waves propagating along the $c$ axis are well approximated by the Turov-Shavrov frozen-lattice model because the extremely strong axial anisotropy makes the dynamical interaction (quadratic magnon-phonon terms) diminished. The dipolar effect is also discussed; and it is shown that, in the hard-direction case, magnons and phonons are mixed in relatively small amounts for the transverse waves propagating perpendicular to the magnetization, owing to the volume dipolar effect. Application of our theory to Tb is made with the use of numerical values of the temperature-dependent anisotropic and magneto-elastic coupling parameters. The lower-branch magnetoelastic modes may be responsible for the absorption of microwaves in the low-frequency-resonance experiments.

Magnetoelastic bandwidth compression

A bandwidth compression process is described which uses the magnetoelastic normal modes of a ferrimagnetic crystal as independent subharmonic oscillators. The critical power level and mode density for this process are discussed and dynamic range is shown to be strongly dependent upon crystal geometry. Measurements have been made on a device with a 60-MHz input frequency and a 30-MHz output frequency. Spectrograms of voice signals before and after two-to-one bandwidth compression are presented and the possibility of obtaining bandwidth expansion is discussed briefly.

PROPAGATING MAGNETOELASTIC WAVES IN AN INFINITE PLATE

The elastic modes of propagation in an infinite plate are coupled to the propagating magnetostatic modes when the plate material is magnetoelastic. The dispersion relations for these magnetoelastic modes are derived, and the resulting coupled mode spectrum is discussed.

Multiple subharmonic generation in YIG

Simultaneous application of two or more CW signals to a parametric-type frequency-selective limiter results in the generation of corresponding half-frequency subharmonics. This effect may be useful in the design of bandwidth compressors. A preliminary experimental investigation of the subharmonic power spectrum is reported. Parallel pumping of magnetoelastic modes in YIG single crystals was used in these experiments.

Boundary-Value Problem for Magnetoelastic Waves in a Metallic Film

A boundary-value problem using traveling-wave magnetoelastic normal modes is solved for the case of a ferromagnetic metal film attached to a substrate. A specialization is made to certain spin-wave resonance experiments in the vicinity of 57.8 GHz, reported recently by Weber. For the dc magnetic field perpendicular to the plane of the film, the general dispersion relation for coupled electromagnetic, spin-wave, and acoustic modes is described. The effect of damping on the shape of the dispersion curves is discussed. For the choice of conductivity, the eddy-current exchange effects in the magnetoelastic crossover region are shown to be small. An expression for the power absorption by the film as a function of dc magnetic field is calculated assuming that the spins are pinned on the film surfaces. The magnetic field shift of a particular spin-wave resonance peak as a function of frequency through magnetoelastic crossover is computed. Values of the magnetoelastic constant $b$ and the phenomenological phonon relaxation time $\ensuremath{\tau}$ obtained by Weber are adjusted slightly to take into account the effect of the glass substrate: $b$ is decreased from 6.87\ifmmode\times\else\texttimes\fi{}${10}^{7}$ to 6.66\ifmmode\times\else\texttimes\fi{}${10}^{7}$ erg/${\mathrm{cm}}^{3}$, and $\ensuremath{\tau}$ is increased from 0.90\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}10}$ to 1.00\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}10}$ sec.

Scattering of Light by Magnons

Scattering of light by magnons has recently been predicted by calculations, and subsequently verified by experiments. In this paper, theoretical aspects of the problem are reviewed briefly. The spin-Raman effect is treated along the same line as ordinary Raman scattering by phonons. The order of magnitude of one-magnon Raman scattering is estimated from the rotatory power of the magnetic ions. The effect is smaller in antiferromagnets because of opposite spins in different sublattices. In ferrites and antiferromagnets, two-magnon Raman scattering can occur through exchange-type interaction. Raman scattering by magnetoelastic modes should also be observable. The possibility of constructing a tunable light oscillator is discussed.

Second-Order Magnetoelastic Properties of Yttrium Iron Garnet

Second-order (in strain) magnetoelastic properties of yttrium iron garnet (YIG) have been studied using an ultrasonic technique. The group velocity of selected small-amplitude magnetoelastic (dominantly elastic) modes in single-crystal specimens has been measured at a frequency of 30 Mc/sec as a function of magnetic field strength and magnetization orientation. In this manner, first-order and second-order magnetoelastic constants and second-order ``morphic'' constants have been completely determined for YIG. This work reports the first evaluation of second-order magnetoelastic constants and morphic constants. All results have been interpreted using finite deformation magnetoelastic theory. Small strain magnetoelastic theory, valid only to first order in small quantities, leads to incorrect results in the treatment of second-order effects.