Magnon Frequency Research Articles

Inelastic Neutron Scattering from MnF2in the Critical Region

Detailed inelastic neutron-scattering measurements have yielded the behavior of both the transverse and longitudinal spin fluctuations throughout the critical region of the uniaxial antiferromagnet Mn${\mathrm{F}}_{2}$. The static susceptibilities, both transverse and longitudinal, are found to be adequately described by Ornstein-Zernike expressions, both above and below ${T}_{N}$, with ${\ensuremath{\kappa}}_{\ensuremath{\perp}}$ remaining finite, while ${\ensuremath{\kappa}}_{\ensuremath{\parallel}}$ approaches zero as ${T}_{N}$ is approached from either side. Magnons are observed below ${T}_{N}$, the energy gap decreasing as $T\ensuremath{\rightarrow}{T}_{N}^{\ensuremath{-}}$ in a way which closely approximates the behavior of the sublattice magnetization. At a given $Tl{T}_{N}$, the ratio of the magnon frequency to the magnon width decreases with increasing wave vector $q$. Above ${T}_{N}$, heavily damped magnonlike behavior is observed at large $q$, the peaks merging with decreasing $q$. The longitudinal fluctuation is always characterized by a single peak centered at $\ensuremath{\omega}=0$. Above ${T}_{N}$, the half-widths ${\ensuremath{\Gamma}}_{\ensuremath{\parallel}} (q,T)$ define a dynamical scaling function ${\ensuremath{\Omega}}_{+} (\frac{q}{{\ensuremath{\kappa}}_{\ensuremath{\parallel}}})$. In particular, the staggered ($q=0$) mode relaxation rate is approximately proportional to $T\ensuremath{-}{T}_{N}$ for $Tg{T}_{N}$. However for $Tl{T}_{N}$, ${\ensuremath{\Gamma}}_{\ensuremath{\parallel}}$ appears to vanish as $q\ensuremath{\rightarrow}0$ at all temperatures. Although the $Tl{T}_{N}$ data for ${\ensuremath{\Gamma}}_{\ensuremath{\parallel}} (q,T)$ can also be described by a second scaling-function branch, the experimental accuracy and the range of $\frac{q}{{\ensuremath{\kappa}}_{\ensuremath{\parallel}}}$ values spanned by the data at a given temperature are more restricted than above ${T}_{N}$. The behavior below ${T}_{N}$ and at low wave vectors may possibly be associated with thermal diffusion within the spin system. At reduced temperatures below about 0.95, the numerical value of the observed longitudinal staggered susceptibility is consistent with the value calculated on the basis of the local energy-density fluctuations.

Temperature Dependence of Short-Wavelength Magnon Frequencies: Relation to Heat Capacity

A relation between the temperature dependence of the energies of short-wavelength magnons and the heat capacity is presented. This relation, which has no adjustable parameters, is in perfect agreement with all available data for $T\ensuremath{\lesssim}0.7{T}_{N}$. For Ni${\mathrm{F}}_{2}$, agreement is up to ${T}_{N}$. The relation can be used to determine the magnon contributions to the heat capacity of magnetic solids.

Time dependent longitudinal spin pair correlation in isotropic antiferromagnets

We consider the Fourier transform Pq and Mq of the order parameter and of the magnetization in a Heisenberg antiferromagnet. <P0//0z. For q ≈ 0 and anyT < TN, the spectral function ∫∞-∞ dt e iωt<Pz-qPzq (t)> has 2 sharp peaks for |ω| = ωq (magnon frequency); the relaxation time of Mzq is τM,zq ∼ q-32. We also find, as already known, <PzqPzq ∼ q-1 and the magnon lifetime τq ∼ q-z. The ferromagnet ic case is briefly discussed. Nous considérons les transformées de Fourier Pq et Mq du paramètre d'ordre et de l'orientation dans un antiferromagnétique de Heisenberg < P0// 0z). Pour q ∼ 0, à toutes températures T < TN, nous trouvons que la fonction spectrale ∫∞-∞ dt eiωt < Pz-qPzq (t)a deux pics aig us pour |ω| = ωq (fréquence de magnon). Le temps de relaxation de Mzq est en q-32. Nous trouvons <Pz-qPzq∼ q-1 et une durée de vie des magnons τq ∼ q-2. Le cas ferromagnétique est aussi discuté brièvement.

Surface Effects in the Heisenberg Antiferromagnet

We have investigated the effect of a free (100) surface on low-temperature properties of a Heisenberg antiferromagnet of the CsCl structure. It is found that a surface magnon branch occurs in the excitation spectrum, with an excitation energy less than the frequency of a bulk magnon of the same wavelength. In the limit of infinite wavelength, the surface magnon frequency for this geometry is ${({H}_{E}{H}_{A}+{{H}_{A}}^{2})}^{\frac{1}{2}}$, compared to ${(2{H}_{E}{H}_{A}+{{H}_{A}}^{2})}^{\frac{1}{2}}$ for bulk magnons of infinite wavelength. In the limit ${H}_{E}\ensuremath{\gg}{H}_{A}$, the surface magnon frequency is found to be insensitive to changes in exchange constants or anisotropy fields near the surface. The surface modes may be observed in the infrared absorption spectrum of the material, and will affect the low-temperature thermodynamic properties of the system. By means of a Green's-function method, we have examined the influence of the surface on the infrared absorption spectrum, the specific heat, and the low-temperature form of the parallel susceptibility and mean sublattice deviation. Numerical estimates indicate that the surface corrections of the thermodynamic quantities may be observable when ${k}_{B}T\ensuremath{\ll}{(2{H}_{E}{H}_{A})}^{\frac{1}{2}}$.

Interaction of Optical Phonons with Spin Waves in Ionic Crystals

AbstractOptical phonon effects on the magnon resonance (FMR and AFMR) are shown to be negligible in ferromagnetic insulators and most antiferromagnets in present day laboratory fields (H ⪅ 2 × 105 G). In these fields the magnon frequency lies lower than the optical phonon frequency so that the coupling is to a polarization mode which is mainly photon‐like. However, at the band edge, the wavelength‐dependence of the magnon and optical phonon dispersion may allow crossing in low fields. Also, in metamagnetic systems where the anisotropy field is much larger than the exchange field, the resonance in the paramagnetic phase may occur in a frequency range such that the polarization mode will contain a relative large fraction of optical phonons. The theory developed in this paper can also be applied to optical phonon‐spin resonance in paramagnetic salts. This type of resonance should occur in attainable magnetic fields for materials with large g factors.

Parallel-Pumped Magnon Instabilities in a Two-Sublattice Ferrimagnetic Crystal

Instability thresholds for parallel-pumped magnons in a two-sublattice ferrimagnet are derived by means of a perturbation method. Cases are considered in which the pump frequency is twice a particular magnon frequency or else the sum of two distinct magnon frequencies—one belonging to each branch of the spinwave dispersion relation. The calculations are made within the molecular field approximation for a single crystal of ellipsoidal shape, and include the effects of the volume dipolar energy as well as those due to unequal g factors of the sublattices. The thresholds appropriate to an ``unflopped'' antiferromagnet are also given when the dc magnetic field is applied parallel to the anisotropy axis. The prospects for experimentally reaching the thresholds, particularly those occurring at submillimeter wavelengths, are evaluated insofar as is possible; in such cases the possibility exists of utilizing a laser for the pump.

Temperature Dependence of the Exchange Stiffness in Ferrimagnets

The temperature dependence of magnon frequencies is studied for ferrimagnets. The magnon frequency increases for the acoustical branch and decreases for the optical branch, both in low-temperature regions. Temperature variations obey the ${T}^{\frac{5}{2}}$ law. In high-temperature regions, both acoustical- and optical-magnon frequencies decrease with increasing temperature. The sign change of the temperature variation of acoustical-magnon frequencies is due to optical-magnon population which increase with temperature. The sign change occurs at a lower temperature for a magnon with a shorter wavelength. This feature is in accordance with Riste's neutron-scattering experiments performed with magnetites. The second-order shift has proved to be small at low temperatures. In the course of its calculation, we give a simple expression for the matrix element of a magnon interaction. This bears a close relationship to Dyson's dynamical interaction in ferromagnets.