Two-magnon Raman Spectra Research Articles

Spin-wave approach to the two-magnon Raman scattering in aJ1x−J1y−J2−Jcantiferromagnetic Heisenberg model

We study the two-magnon nonresonant Raman scattering in the $(\ensuremath{\pi},\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in-plane ordered antiferromagnetic phases of a spin-$S{J}_{1x}\text{\ensuremath{-}}{J}_{1y}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{c}$ Heisenberg model on the tetragonal lattice within the framework of the spin-wave theory. We show that magnon-magnon interactions may significantly change the shape of spectra even in large-$S$ cases. We discuss the effects of various tuning factors to the two-magnon Raman spectra. We find that both the magnetic frustration ${J}_{2}/{J}_{1}$ and the interlayer exchange coupling ${J}_{c}$ may significantly affect the spectra in both the ${B}_{1g}$ and the ${A}_{1g}^{\ensuremath{'}}$ channels in the $(\ensuremath{\pi},\ensuremath{\pi})$ N\'eel ordered phase. Moreover, we find a splitting of the two-magnon peak in the $(\ensuremath{\pi},0)$ collinear antiferromagnetic phase. We further discuss the implications of our results to the ${\mathrm{BaMnBi}}_{2}$ and iron pnictide systems.

Spin-Density-Wave Gap with Dirac Nodes and Two-Magnon Raman Scattering in BaFe2As2

Raman selection rules for electronic and magnetic excitations in BaFe 2 As 2 were theoretically investigated and applied them to the separate detection of the nodal and anti-nodal gap excitations at the spin density wave (SDW) transition and the separate detection of the nearest and the next nearest neighbor exchange interaction energies. Raman spectra are composed of magnetic excitations with gradually decreasing intensity toward far above the SDW transition temperature ( T SDW ) and electronic excitations induced by the Brillouin zone folding below T SDW . The SDW gap has Dirac nodes, because many orbitals participate in the electronic states near the Fermi energy. Using a two-orbital band model the electronic excitations near the Dirac node and the anti-node are found to have different symmetries. Applying the symmetry difference to Raman scattering the nodal and anti-nodal electronic excitations are separately obtained. The low-energy spectra from the anti-nodal region have critical fluctuation just above T SDW and change into the gap structure by the first order transition at T SDW , while those from the nodal region gradually change into the SDW state. Magnetic excitations are observed as a very broad peak in all polarization configurations. The selection rule for two-magnon scattering from the stripe spin structure was obtained. Applying it to the two-magnon Raman spectra it is found that the magnetic exchange interaction energies are not presented by the short-range superexchange model, but the second derivative of the total energy of the stripe spin structure with respect to the moment directions. The selection rule and the peak energy are expressed by the two-magnon scattering process in an insulator, but the large spectral weight above twice the maximum spin wave energy is difficult to explain by the decayed spin wave. It may be explained by the electronic scattering of itinerant carriers with the magnetic self-energy in the localized spin picture or the particle–hole excitation model in the itinerant spin picture. The magnetic scattering spectra are compared to the insulating and metallic cuprate superconductors whose spins are believed to be localized.

Phonon Effects on Two-Magnon Raman Spectra in Layered Cuprate Systems

We have analyzed the anomalous line shapes of the two-magnon Raman spectra of undoped high T c cuprates, using the spin wave theory in a two-dimensional Heisenberg antiferromagnet. In order to describe a shoulder peak structure near 4 J , which is primarily associated with magnetic excitations of B 1 g symmetry, we have explored the phonon contribution to the Raman spectra. Incorporating the magnon-phonon Hamiltonian due to the modulated exchange interaction by phonons, we have evaluated the two-magnon Raman spectral function coming from the lowest order magnon-phonon-magnon scattering. It is found that the magnon-phonon-magnon scattering gives rise to a phonon-induced shoulder peak near 4 J besides the dominant two-magnon peak near 3 J , in good agreement with experiments.

Effect of spin-phonon interaction on the Raman spectra of quasi-two-dimensional Heisenberg antiferromagnets.

Using the Dyson-Maleev representation of the spin opertors, the two-magnon Raman spectra (${\mathit{B}}_{1\mathit{g}}$ geometry) in quasi-two-dimensional Heisenberg antiferromagnets at finite temperatures are calculated. The two-magnon spectrum is computed in a self-consistent manner within the framework of a renormalized harmonic approximation, which is correct up to order 1/S in the 1/S expansion of perturbation theory. Including a renormalization of the one-magnon spectral function due to the intrinsic spin part of the model up to order 1/${\mathit{S}}^{2}$ and due to spin-phonon interaction up to order 1/S, it is shown that spin-phonon interaction generates a significant broadening of the one-magnon spectral function at the Brillouin-zone boundary in the regime where sound velocities are small compared to magnon velocities. In that regime it dominates the spectral feature of the two-magnon Raman line. Based on that result, the anomalous broadening of the two-magnon spectrum, observed in light-scattering experiments on antiferromagnets with large maximum magnon energies such as, e.g., the spin-1/2 compound ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ and the spin-1 compound ${\mathrm{Pr}}_{2}$${\mathrm{NiO}}_{4}$, can be described mainly as a consequence of spin-phonon interaction. This effect is absent in systems with smaller exchange integrals such as, e.g., ${\mathrm{La}}_{2}$${\mathrm{NiO}}_{4}$ or ${\mathrm{K}}_{2}$${\mathrm{NiF}}_{4}$, respectively. Accordingly, it is safe to postulate that the broad spectral feature observed experimentally is generated by spin-phonon interaction. In order to explain the line shape in the cuprates completely, especially the high-energy tail, four-magnon contributions due to nearest-neighbors spin-pair excitations and higher contributions in the effective Raman-scattering Hamiltonian due to the resonant enhancement of the Raman cross section have to be considered and will be discussed on a qualitative basis.

Raman Scattering from Magnon Excitations in RFeO3

Raman scattering from one- and two-magnon excitations in various rare-earth orthoferrites are studied. The magnetic in-plane and out-of-plane anisotropy energies of these systems are obtained and discussed based on the two-sublattice model of ironspins. Detailed temperature dependence of the frequencies of two \(k{\cong}0\) magnons are also examined on YFeO 3 , ErFeO 3 , SmFeO 3 , Er 0.7 Sm 0.3 FeO 3 and DyFeO 3 . It is shown that the softening behaviors of one-magnon peak frequencies are different between the rotational- and abrupt-type spin-reorientation (SR) systems. This is explained by different anisotropy terms which contribute to the magnon softening associated with SR transitions. The exchange interactions between the iron and rare-earth ions are considered to interpret the magnon softening in the vicinity of SR temperatures. The temperature and polarization properties of two-magnon Raman spectra are also discussed.

The effect of two-magnon two-phonon interactions on the two-magnon Raman spectra of antiferromagnets

An effect of magnon-phonon interactions on two-magnon Raman spectra is studied using Green function methods developed by Elliott and Thorpe. Green functions associated with two-phonon states are included. Two-magnon two-phonon interactions modify the shape of two-magnon Raman spectra appreciably.

Spin-wave analysis in the two-dimensional antiferromagnetK2FeF4. II. Raman scattering

Two-magnon Raman spectra in the two-dimensional basal-plane antiferromagnet ${\mathrm{K}}_{2}$Fe${\mathrm{F}}_{4}$ are investigated in the temperature range 2 to 45 K. The spectra are reduced in terms of the spin-wave description developed in the preceding paper. The method used is the equations of motion of Green's functions. The spectrum calculated with first-order decoupling agrees with the one observed at 2 K. In second order, the magnon damping is evaluated rigorously, but within the zone-boundary maximum-dispersion approximation. The damping appears to be strongly dependent on the energy transfer in the scattering process. Calculated second-order spectra account for the line shift in the entire range of temperatures studied.

THEORETICAL ANALYSIS OF THE TWO-MAGNON RAMAN SPECTRA OF RbNiF3

Two-magnon Raman spectra of RbNiF3 are calculated for the temperature range between 0 K to Néel point TN(= 133 K). From considerations of the general symmetry principle and the experimental results, we have derived the Hamiltonian of interaction between the magnetic system and the radiation field. The method of the equation of motion of retarded Green's function is used to obtain the analytic expression of the two-magnon Raman scattering intensity. In the two-magnon propagator, both the effects of energy renormalization and the life time have been taken into account. Finally, quantitative calculations are performed with proper approximations using computer. Although there are no adjustable parameters, the results account very well for the observed temperature dependence of both the. peak position and the line width in the range from 0 K up to TN.

Two-magnon Raman scattering in quadratic double-layer antiferromagnets

Two-magnon Raman spectra of the quadratic double-layer antiferromagnet ${\mathrm{K}}_{3}$${\mathrm{Mn}}_{2}$${\mathrm{F}}_{7}$ (${T}_{N}=58.3$ K) have been investigated from 2 K up to beyond the ordered regime. Following an analysis of the Raman-scattering Hamiltonian on the basis of symmetry, the spectra are interpreted in terms of a two-dimensional four-sublattice spin-wave theory appropriate to the double layer. The method used is the equation of motion of Green functions. It appears essential to include those quartic terms in the spin-wave Hamiltonian that couple the lower and upper magnon branches, but in the random-phase approximation do not contribute to renormalization of the magnon dispersion. Spectra calculated with first-order decoupling agree well with the spectra observed at 2 K. In second order, the damping of magnons near the zone boundary is expressed in an approximate analytical form. The computed second-order spectra account for the observed temperature dependence of both the peak position and the width of the scattering up to 1.1 ${T}_{N}$. Fits to spectra of ${\mathrm{K}}_{3}$${\mathrm{Mn}}_{2}$${\mathrm{F}}_{7}$, with the anisotropy set at $\ensuremath{\Delta}=g{\ensuremath{\mu}}_{\mathrm{B}}\frac{{H}_{A}}{5}|J|S=0.002$, yield a nearest-neighbor exchange $J=\ensuremath{-}7.68\ifmmode\pm\else\textpm\fi{}0.07$ K, in agreement with findings from the sublattice magnetization and susceptibility. From the low-temperature spectrum of the isomorphic ${\mathrm{K}}_{3}$${\mathrm{Ni}}_{2}$${\mathrm{F}}_{7}$ taken from the literature, we derive $J(1+1.04\ensuremath{\Delta})=\ensuremath{-}95.4\ifmmode\pm\else\textpm\fi{}0.5$ K.

Two-magnon Raman scattering in quadratic double-layer antiferromagnets

Two-magnon Raman spectra of ordered K3Mn2F7 are interpreted in terms of a two-dimensional four-sublattice spin-wave theory. In solving the equation of motion of the Green functions it is essential to include terms of the spin-wave Hamiltonian coupling the two magnon branches.

Resonances in two-magnon Raman spectra and the effect of several exchange parameters

Resonances in two-magnon Raman spectra and the effect of several exchange parameters