Theory of Spin Waves in the Heavy Rare Earth Metals

Goodings, D. A.; Southern, B. W.

doi:10.1139/p71-139

Cited by 29 publications

(6 citation statements)

References 25 publications

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“…1. Throughout the 4° to 77°k range, the measured gap is approximately 40% larger than that calculated from the generally accepted theoretical expression for the frozen lattice model [3,4], viz.,…”

Section: Resultsmentioning

confidence: 60%

Spin-Waves in Ferromagnetic Dysprosium Metal.

Nicklow¹,

Wakabayashi²

1972

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The spin-wave dispersion relations for the [110] and [001] symmetry directions in ferromagnetic dysprosium metal (isotopically enriched 96.8% with 163 Dy) have been studied between 4.7° and 77°K. Throughout this temperature ' range the^ measured temperature dependence of the energy gap at zero wave vector (q = 0) is in fair agreement with that predicted theoretically for the frozen lattice model. However, the magnitude of the total planar anisotropy deduced from these gap measurements is larger by a factor of two than that obtained from macroscopic measurements. The increase o£ the magnon energies with decreasing temperature is much more pronounced at q = 0 than near the Brillouin zone boundaries. Thus the magnitude of the isotropic exchange interaction decreases substantially, about 25% in the [001] direction, between 77° and 4.7°K. Significant magnon-phonon interactions are observed, parti-? cularly in the [110] direction where the acoustic magnon branch is mixed with both the longitudinal and transverse acoustic phonon branches. The peak in the Fourier transform of the exchange interaction, J(q), which at 77°K occurs near the wave vector of the helical-magnetic structure of Dy just above T c , persists down to 4.7°K with shifts to smaller q as the temperature is decreased. At 77°K the optic and acoustic spin-wave branches are degenerate, to within 0.1 meV, at the K-symmetry point of the Brillouin zone. However at 4.7°K this degeneracy is lifted, with AE = 0.8 meV, thereby indicating the existence of a temperature dependent long-range anisotropic magnetic interaction in Dy.

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Section: Resultsmentioning

confidence: 60%

Spin-Waves in Ferromagnetic Dysprosium Metal.

Nicklow¹,

Wakabayashi²

1972

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“…i Formally the single ion Hamiltonian is included in (2) (Go, = 1) by defining J The spin Hamiltonian (2) is now treated by a conventional spin wave technique (Cooper et al 1962, Cooper 1968, Goodings and Southern 1971. The Racah operators are trans-formed (Danielsen and Lindgird 1972, Buckmaster et al 1972) into a coordinate system in which the ordered moment (of the cone) is always along the local z axis.…”

Section: Anisotropic Exchange Interactionmentioning

confidence: 99%

“…In I the spin wave measurements are interpreted by means of the model Hamiltonian generally used for describing the magnetic properties of the heavy rare earth metals (Cooper et al 1962, Cooper 1968. Goodings and Southern 1971.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic exchange interaction in the conical magnetic phase of erbium

Jensen¹

1974

J. Phys. F: Met. Phys.

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From a general two ion spin Hamiltonian, we deduce an expression for the energies of spin waves propagating in a hexagonal solid in which the magnetic moments are ordered in a conical or helical structure. The spin wave dispersion relation in the c direction of Er in its conical magnetic phase at 4.5 K, which has been studied by Nicklow er d (1971) is reanalysed. In this analysis we introduce an alternative kind of anisotropic coupling between the total angular moments (Ji and J i ) on the sites i and j , proportional to the following combination of Racah operators: oz. -*(J,), az, -2(JjX expressed with respect to a coordinate system with the z axis along the c direction. The resulting anisotropy (both the constant and the q dependent part) is reduced by an order of magnitude in comparison with that deduced by Nicklow et a/ (1971). The constant anisotropy is found to be equal to about 20 meV (a rough estimate from magnetization measurements gives 5-10 meV). The anisotropic part of the exchange interaction is found to be of the same order of magnitude as the isotropic part.

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“…The effects of the presence of homogeneous strains upon the magnon energies of the rare earth metals has been discussed in detail by, for example, Turov and Shavrov (1965), Cooper (1968), Goodings and Southern (1971), Vigren and Liu (1972), Marller et a1 (1972), Brooks (1972) and Brooks and Egami (1973b, to be referred to as 11). The effects of the presence of homogeneous strains upon the magnon energies of the rare earth metals has been discussed in detail by, for example, Turov and Shavrov (1965), Cooper (1968), Goodings and Southern (1971), Vigren and Liu (1972), Marller et a1 (1972), Brooks (1972) and Brooks and Egami (1973b, to be referred to as 11).…”

Section: Introductionmentioning

confidence: 99%

Effects of Tilt Angle, DNA Concentration, and Surface Potential on Directed Alignment of DNA Molecule for the Application to Nanodevices

Kim¹,

Hong²

2013

Jpn. J. Appl. Phys.

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A systematic scheme, based upon Roth linearization of many-body equations of motion, is applied to decoupling of the coupled spin-lattice equations of motion of magnetostrictive HCP ferromagnets. Magnetoelastic coupling is characterized by the same microscopic Hamiltonian that gives rise to macroscopic magnetostrictive properties, and magnonphonon coupling is expressed in terms of macroscopic magnetostriction parameters. Both one-and two-ion magnetoelastic coupling is included through the Evenson and Liu localstrain theory. The magnitude of the splitting of magnon and phonon dispersion curves is proportional to appropriate magnetostriction constants divided by the square root of the magnetization, and Jensen's results are recovered in the zero temperature limit.

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Theory of Spin Waves in the Heavy Rare Earth Metals

Cited by 29 publications

References 25 publications

Spin-Waves in Ferromagnetic Dysprosium Metal.

Spin-Waves in Ferromagnetic Dysprosium Metal.

Anisotropic exchange interaction in the conical magnetic phase of erbium

Effects of Tilt Angle, DNA Concentration, and Surface Potential on Directed Alignment of DNA Molecule for the Application to Nanodevices

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