Magnon Pairs Research Articles

Raman study of one-dimensional spin fluctuations in the spin-1 Heisenberg-chain compound Y2BaNiO5: Contrast with simple expectations.

Spin fluctuations in the Haldane ground state should exhibit a quantum spin gap observable with Raman scattering. The Raman spectra of single-crystalline ${\mathrm{Y}}_{2}$${\mathrm{BaNiO}}_{5}$, a linear spin-1 Heisenberg antiferromagnet, exhibit broad continuum scattering between \ensuremath{\sim}200 and \ensuremath{\sim}800 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in the energy range expected for magnetic excitations (\ensuremath{\sim}J=224 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Numerous weak and broad features superimposed on this continuum scattering possibly result from quantization of the magnon continuum by local molecular fields from nearby chains. A strong and relatively narrow mode at \ensuremath{\sim}680 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, near 3J, unrelated to lattice vibrations, may also be of magnetic origin. All of these features are strongly resonant in the red (${\ensuremath{\lambda}}_{\mathit{L}}$=6328 \AA{}), disappearing for shorter excitation wavelengths. These spectra provide a view of the Haldane spin system excitations complementary to that given by inelastic neutron scattering. Modeling the excitations with Schwinger bosons or spin waves predicts a highly asymmetric scattering feature with a sharp onset near 2\ensuremath{\Delta}(\ensuremath{\sim}0.8J), gradually diminishing toward higher energies. The observed spectra disagree with this theoretical expectation, perhaps due to spin-phonon coupling which may provide an efficient decay channel for the magnon pairs.

Influence of weak localization on the threshold of the parametric excitation of magnons in low-dimensional magnets.

The influence of multiple elastic scattering on the magnon parametric excitation in low-dimensional magnets is studied. The multiple-scattering results in the strong backscattering of magnons. This backscattering can interfere with the parametric excitation because both phenomena involve pairs of magnons with opposite momenta. It is shown that the influence of the backscattering on the threshold of parametric excitation in two-dimensional systems is proportional to the logarithm of the size, even if it exceeds the inelastic mean free path. The possibilities of experimental observation of the effect are discussed.

Influence of radiation damping on the threshold of auto-oscillations in YIG under parallel pumping

Nonlinear magnon relaxation above the threshold of magnon instability is influenced by radiation damping as well as internal processes of magnon-magnon and magnon-phonon damping. Parametrically excited magnon pair disappears with creating a microwave cavity photon whose damping is given by a quality factor Q. Influence of microwave cavity mode damping on the instability and auto-oscillations of magnons is discussed on the basis of the S-theory.

Pressure dependence of two-magnon Raman scattering in NiO.

We report on the pressure dependence of Raman scattering by magnon pairs in NiO for the range 0--30 GPa. The data are in excellent agreement with Bloch's empirical law describing the dependence of superexchange on volume. Using Anderson's theory, we find that the pressure depencence of the antiferromagnetic exchange constant is mainly determined by the hopping parameter of a Hubbard model involving Ni(${\mathit{e}}_{\mathit{g}}$)-O(2p) hybridization. The implications of these results to high-temperature superconductors and early Raman data are discussed.

Dynamics of spin fluctuations in lanthanum cuprate.

Raman scattering studies of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ have revealed a high-frequency component (\ensuremath{\sim}3000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) which we interpret as due to scattering by magnon pairs. Comparison of the spectra with those of ${\mathrm{K}}_{2}$${\mathrm{NiF}}_{4}$ leads to a value of J\ensuremath{\sim}1100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for the exchange interaction. The two-dimensional nature of the fluctuations suggested by earlier neutron scattering work is indicated here by the insensitivity of the spectra to temperature as well as to departures from stoichiometry which strongly influence the three-dimensional ordering temperature ${T}_{N}$.

Theoretical aspects of magnon–magnon interactions in Heisenberg ferromagnets

Spin-wave interactions in ferromagnetic insulators have a well-established theoretical foundation, in contrast to the situation for antiferromagnets. These interactions may be classified into two groups according to whether the dominant aspects are of one- or two-magnon character. The weak interactions between spin waves excited at low temperatures are responsible for the success of "free" (or noninteracting) spin-wave calculations in explaining low-temperature thermodynamic properties. In contrast, the two-magnon aspects appear in connection with two-magnon Raman scattering, where pairs of magnons are created in close proximity and consequently interact strongly. Parallels with analogous systems, especially antiferromagnetic spin waves and phonons, are noted in reviewing the ferromagnetic case. Emphasis is placed on the structure of the theory, rather than on the wealth of experimental activity.

Raman scattering from phonons and magnons in antiferromagnetic Fe 3BO 6

Raman scattering by phonons and by magnon pairs has been observed in Fe 3BO 6. Of the predicted 60 Raman-active modes, 39 have been identified and classified according to their symmetries. The two-magnon band shows a strong decrease in intensity with increasing temperature, and almost vanishes close to T N = 508 K. The origin of this effect is attributed to the existence of a nearly dispersionless magnon branch.

Raman scattering from magnon pair excitations in FeF2

Experiments are reported for the temperature dependence of the two-magnon Raman scattering in FeF2 (TN=78K). New results were obtained for the polarisation characteristics of the scattering, which was observed for temperatures up to approximately=4 TN. A theoretical analysis was developed by extending earlier work to include the three dominant exchange interactions in a temperature-dependent formalism valid up to approximately=3/4 TN. The theory and experiment were found to be in good agreement for spectra with (ZX)=(YZ) polarisation. However, the spectra in (YX) and (ZZ) polarisations showed an additional feature at approximately=143 cm-1 that was not purely two-magnon in origin. After subtraction of this band from the (YX) spectrum the authors again obtained agreement with theory. Possible origins of the additional scattering near 143 cm-1 are proposed.

Spin waves in systems with weak exchange fields

Multiboson spin waves are constructed to represent the low-temperature collective states of paramagnets and ferromagnets whose spins are located in strong single-ion anisotropy fields and are coupled by weak exchange interactions. The different sets of bosons are particles excitable to the different eigenstates of the single-ion part of the Hamiltonian, and boson representations of the single-ion spin operators are constructed by a matrix-elements-matching method. The method allows the determination of magnon frequencies and of possible effects of applied oscillatory magnetic fields, and also allows the estimation of boundaries between different magnetic phases. However, it does not establish the form of the single-ion contribution to four-magnon interactions. In addition, it is not applicable to transitional phases where the exchange cannot be treated as a perturbation. The spin-1 system with positive and negative uniaxial and orthorhombic anisotropies in various magnitudes of parallel static magnetic fields is discussed in detail. Results of Ishikawa and Oguchi are obtained and generalized. The presence of orthorhombic anisotropy is predicted to make possible the "parallel" pumping of various magnon pairs, and also to give rise to parallel incoherent resonance absorption between excited states, as well as the usual "perpendicular" coherent $k=0$ ground-state resonance excitation. Magnon relaxation times are extimated in the case of a paramagnet with hard-axis anisotropy in sufficiently small magnetic fields. Typical materials to which this theory applies are hydrated nickel salts.

Magnon pairs and interactions in a disordered two-dimensional antiferromagnet

Magnon-pair modes and their temperature dependence have been studied by inelastic light scattering in the disordered two-dimensional antiferromagnet ${\mathrm{Rb}}_{2}$${\mathrm{Mn}}_{0.5}$${\mathrm{Ni}}_{0.5}$${\mathrm{F}}_{4}$. At 10 K pair modes arising from one-Mn- plus one-Ni-branch magnons, and from two-Ni-branch magnons were observed at 248 and 372 ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively. Surprisingly, the former exhibits a scattering efficiency only \ensuremath{\sim}20% less than the latter, even though the two-Mn-branch magnon pair could not be detected at all. The observed low-temperature pair-mode frequencies and line shapes can be reasonably estimated from the Ising cluster model, using exchange values for ${J}_{\mathrm{NiNi}}$ and ${J}_{\mathrm{NiMn}}$ of 58 and 5.8 ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively. This model accounts well for the dominant effects of disorder. Upon increasing temperature, both pair modes broaden and renormalize in frequency in essentially the same manner as that previously observed in the ordered two-dimensional isomorphs such as ${\mathrm{K}}_{2}$Ni${\mathrm{F}}_{4}$.

Magnetic scattering of light in K(NiMg)F3

The dependence of magnon-pair excitations upon temperature and dilution of the magnetic ion concentration has been examined by inelastic light scattering in the antiferromagnetic compounds KNi1-cMgcF3. Ten values of c were examined, ranging from pure KNiF3, which shows a well defined low-temperature magnon pair at 746 cm-1, up to values above the percolation limit (c=0.68) for the perovskite structure. For increasing values of c between 0 and 0.5, the magnon-pair mode decreases in frequency and increases in linewidth in accordance with expectations based on earlier work in the (MnZn)F2 system. As the Ni concentration is lowered further the results indicate an increasing departure from expected behaviour. In particular, the pair mode continues to broaden but remains relatively constant in frequency. Quantitative magnetic data at higher values of c are precluded by disorder-induced first-order Raman scattering by phonons. A brief discussion of the phonon spectra is included. Detailed temperature dependence between 25K and 300K is also obtained for magnon pairs at several concentrations of magnesium.

Inter-sublattice energy transfer in MnF 2

The magnetically induced circular emission (MCE) of an exciton—magnon pair from the third nearest neighbour impurity trap [Mgσ(III)] in MnF 2 shows an unusual lineshape. The field dependence of the MCE suggests that this is a consequence of a magnon assisted transfer of excitation between sublattices via the intrinsic exciton band.

Two-magnon raman scattering and infrared absorption in (MnZn)F2

Measurements have been made of the Raman scattering and infrared absorption peaks arising from excitation of magnon pairs in the system (Mn1-cZnc)F2. Single crystals were investigated with c varying from 0 to 1. The measurements are compared with predictions of both a mean field model and an Ising cluster model. Approximate mean field values are obtained for the first, second and third moments of the two-magnon peak. The Ising model has been applied in a way that takes account of the proximity in pairs of the manganese atoms responsible for the two-magnon scattering and absorption and it gives a mean frequency that is higher than the mean field result although not quite as high as the experimental results.

Critical Reexamination of First-Order Electronic and Nuclear Spin-Wave Instabilities in Antiferromagnets

The excitation of first-order spin-wave instabilities in an antiferromagnet which may carry a nuclear moment is reexamined. Nuclear, electronic, and mixed magnon pairs can be excited by processes which are analogous to the ferromagnetic case. Various geometries of pumping fields are possible and their critical values are given. Contrary to the assumption of previous authors, we show that when photon pumping fields are applied to a flopped antiferromagnet, the uniform precession is always excited, and its contribution to the threshold amplitude is significant and can never be neglected. This implies that direct magnon excitation in which the linear susceptibility is negligibly small (parallel pumping) does not exist in an antiferromagnet when the weak dipolar effects are ignored. However, when phonon fields are applied, parallel pumping processes are allowed due to the change in symmetry of the effective magnetoelastic pumping field. In particular when a longitudinal wave is propagating parallel (or nearly so) to the dc sublattice magnetizations the effect of the negligibly small linear subsceptibility can be ignored and the process is analogous to parallel pumping in a ferromagnet.

Phonon Energy Spectrum in a Ferromagnet

The magnetoelastic interaction provides a mechanism whereby, in a ferromagnet, a phonon may couple to two magnons. The propagation of phonons in the crystal may thus be modified by emission and reabsorption of pairs of magnons. Since interactions between the magnons may significantly influence the intermediate state, we have included the dominant low-temperature contributions via the two magnon t-matrix and calculated the phonon self-energy. We find for a phonon with wave-vector q, polarization λ, and energy Ωqλ, Σqλ(Ωqλ)=(|gqλ|2/J) {fB(qλ)+Σ[fi(qλ)/(Ωqλ−ωs)]},where gqλ is the magnon-phonon coupling constant. The functions fB(qλ) and fi(qλ) give, respectively, the contributions from the two spin-wave band and the bound states of energy ωi. In addition to the poles at the true bound states, we find resonances in Σ from fB, corresponding to damped bound (resonant) states of two spin-waves within the band. Near these resonances ImΣ (the line-width) becomes anomalously large, just as does the corresponding function for a single magnon. An interesting result is that, due to the transformational properties of the bound states for q along the [111] direction, longitudinal phonons couple only to the singly degenerate (s-wave) bound state and the transverse phonons couple only to the doubly degenerate (d-wave) bound state.

Magnon-Magnon and Exciton-Magnon Interaction Effects on Antiferromagnetic Spectra

Two-magnon absorption and Raman experiments create pairs of magnons in close proximity, and hence, the magnon-magnon interaction has an important effect on the spectral line shape. Green's-function methods have been used to calculate this effect and the results applied the example of cubic antiferromagnets like RbMn${\mathrm{F}}_{3}$. Similar techniques are used to find the effect of exciton-magnon interaction on the sidebands in RbMn${\mathrm{F}}_{3}$; corresponding experimental results are presented.