We report the observation of the $A_{\rm g}$-symmetric one-magnon Raman peak in the magnon Bose-Einstein condensation phase of TlCuCl$_{3}$. Its Raman shift traces the one-magnon energy at the magnetic $Γ$ point, and its intensity is proportional to the squared transverse magnetization. The appearance of the one-magnon Raman scattering originates from the exchange magnon Raman process and reflects the change of the magnetic-state symmetry. Using the bond-operator representation, we theoretically clarify the Raman selection rules, being consistent with the experimental results.
The magnetic properties of the interacting dimer system TlCuCl3 are investigated within a bond-operator formulation. The observed field-induced staggered magnetic order perpendicular to the field is described as a Bose condensation of magnons which are linear combinations of dimer singlet and triplet modes. This technique accounts for the magnetization curve and for the field dependence of the magnon dispersion curves observed by high-field neutron scattering measurements.
Magnetization measurements were performed to investigate the critical behavior of the field-induced magnetic ordering in gapped spin system TlCuCl$_3$. The critical density of the magnons was obtained as a function of temperature and the magnon-magnon interaction constant was evaluated. The experimental phase boundary for $T < 5$ K agrees almost perfectly with the magnon BEC theory based on the Hartree-Fock approximation with realistic dispersion relations. The phase boundary can be described by the power law $[H_{N}(T)-H_{c}] propto T^{phi}$. With decreasing fitting temperature range, the cri…
A quantitative study of the field-induced magnetic ordering in TlCuCl$_3$ in terms of a Bose-Einstein condensation (BEC) of magnons is presented. It is shown that the hitherto proposed simple BEC scenario is in quantitative and qualitative disagreement with experiment. It is further shown that even very small Dzyaloshinsky-Moriya interactions or a staggered $g$ tensor component of a certain type can change the BEC picture qualitatively. Such terms lead to a nonzero condensate density for all temperatures and a gapped quasiparticle spectrum. Including this type of interaction allows us to obtai…
We investigated experimentally and theoretically sound attenuation in the quantum spin system TlCuCl_3 in magnetic fields at low temperatures. Near the point of Bose-Einstein condensation (BEC) of magnons a sharp peak in the sound attenuation is observed. The peak demonstrates a hysteresis as function of the magnetic field pointing to a first-order contribution to the transition. The sound damping has a Drude-like form arising as a result of hardcore magnon-magnon collisions. The strength of the coupling between lattice and magnons is estimated from the experimental data. The puzzling relation…
We extend the self-consistent Hartree-Fock-Popov calculations by Nikuni et al. [Phys. Rev. Lett. 84, 5868 (2000)] concerning the Bose-Eistein condensation of magnons in TlCuCl3 to include a realistic dispersion of the excitations. The result for the critical field as a function of temperature behaves as Hc(T)-Hc(0) T^{3/2} below 2K but deviates from this simple power-law at higher temperature and is in very good agreement with the experimental results. The specific heat is computed as a function of temperature for different values of the magnetic field. It shows a lambda-like shape at the tran…
We have measured the thermal conductivity of a TlCuCl$_3$ single crystal in magnetic fields up to 14 T. It has been found that the temperature dependence of the thermal conductivity exhibits a sharp peak at 4 K in zero field, which is suppressed by the application of magnetic fields up to 7 T. The peak is concluded to be attributable to the enhancement of the thermal conductivity due to phonons because of the formation of a spin-gap state. In high magnetic fields above 7 T, on the other hand, another sharp peak appears around 4 K and this is enhanced with increasing magnetic field. This peak i…
Thallium copper chloride is a quantum spin liquid of S = 1/2 Cu^2+ dimers. Interdimer superexchange interactions give a three-dimensional magnon dispersion and a spin gap significantly smaller than the dimer coupling. This gap is closed by an applied hydrostatic pressure of approximately 2kbar or by a magnetic field of 5.6T, offering a unique opportunity to explore the both types of quantum phase transition and their associated critical phenomena. We use a bond-operator formulation to obtain a continuous description of all disordered and ordered phases, and thus of the transitions separating t…
Specific heat measurements have been performed in the coupled dimer system TlCuCl$_3$, which has a singlet ground state with the excitation gap $Δ\simeq 7.5$K. The cusplike anomaly indicative of the 3D magnetic ordering was clearly observed in magnetic fields higher than the critical field $H_c$ corresponding to the gap $Δ$. The phase boundary determined by the present specific heat measurements coincides with that determined by previous magnetization measurements. The phase boundary can be described by the power law $[ H_{\rm c}(T)-H_{\rm g} ] \propto T^ϕ$ with $ϕ=2.1(1)$. This result support…
Neutron elastic scattering experiments have been performed on the spin gap system TlCuCl$_3$ in magnetic fields parallel to the $b$-axis. The magnetic Bragg peaks which indicate the field-induced Néel ordering were observed for magnetic field higher than the gap field $H_{\rm g}\approx 5.5$ T at $Q=(h, 0, l)$ with odd $l$ in the $a^*-c^*$ plane. The spin structure in the ordered phase was determined. The temperature and field dependence of the Bragg peak intensities and the phase boundary obtained were discussed in connection with a recent theory which describes the field-induced Néel ordering…
Magnetization measurements were performed on TlCuCl$_3$ with gapped ground state. The critical density and the magnetic phase diagram were obtained. The interacting constant was obtained as $U/k_{\rm B} = 313$ K. The experimental phase boundary for $T < 5$ K agrees perfectly with the magnon BEC theory based on the Hartree-Fock approximation with realistic dispersion relations and $U/k_{\rm B} = 320 $ K. The exponent $ϕ$ obtained with all the data points for $T < 5$ K is $ϕ= 1.99$, which is somewhat larger than theoretical exponent $ϕ_{\rm BEC} =3/2$. However, it was found that the exponent con…
In the first part we investigate in detail if the Bose-Einstein condensation scenario for magnons can quantitatively explain the observed field-induced magnetic ordering in TlCuCl$_3$. We use a bond-operator approach to map the spin system onto hard-core bosons and exactly account for the hard-core constraint in the dilute limit. We solve the hard-core model within the Hartree-Fock-Popov approximation and discuss its validity and the consequences of this approximation for the critical properties. In the second part the effects of spin-phonon and spin-orbit coupling are discussed within this fr…
We investigate two-magnon Raman scattering from the $S=1/2$ Heisenberg antiferromagnet on the triangular lattice, considering both the effect of renormalization of the one-magnon spectrum by 1/S corrections and final-state magnon-magnon interactions. The bare Raman intensity displays two peaks related to one-magnon van-Hove singularities. We find that 1/S self-energy corrections to the one-magnon spectrum strongly modify this intensity profile. The central Raman-peak is significantly enhanced due to plateaus in the magnon dispersion, the high frequency peak is suppressed due to magnon damping,…
We study the two-magnon non-resonant Raman scattering in the (pi,pi) and (pi,0) ordered antiferromagnetic phases of a J1x-J1y-J2-Jc Heisenberg model on the tetragonal lattice within the framework of the spin-wave theory. We discuss the effects of various tuning factors to the two-magnon Raman spectra. We find that both the magnetic frustration J2/J1 and the interlayer exchange coupling Jc may significantly affect the spectra in both the B1g and A1g' channels in the (pi,pi) Neel ordered phase. Moreover, we find a splitting of the two-magnon peak in the (pi,0) antiferromagnetic phase. We further…
We calculate the two-magnon Raman scattering spectra in antiferromagnetic phases of several frustrated spin models defined on the honeycomb lattice. These include the Néel antiferromagnetic phase of a $J_1$-$J_2$-$J_3$ model and the stripe phase of the Heisenberg-Kitaev model. We show that both the magnetic frustration and the anisotropy of interactions may significantly affect the Raman spectra. We further discuss the implications of our results to the magnetic excitations of the iron-based compound BaFe$_2$Se$_2$O and show how the magnetic interactions can be extracted from fit to the Raman …
We present a theory for Raman scattering on 2D quantum antiferromagnets. The microscopic Fleury-Loudon Hamiltonian is expressed in terms of an effective $O(3)$ - model. Well within the Néel ordered phase, the Raman spectrum contains a two-magnon and a two-Higgs contribution, which are calculated diagramatically. The vertex functions for both the Higgs and magnon contributions are determined from a numerical solution of the corresponding Bethe-Salpeter equation. Due to the momentum dependence of the Raman vertex in the relevant $B_{1g}+E_{2g}$ symmetry, the contribution from the Higgs mode is s…
Higgs resonance modes in condensed matter systems are generally broad; meaning large decay widths or short relaxation times. This common feature has obscured and limited their observation to a select few systems. Contrary to this, the present work predicts that Higgs resonances in magnetic field induced, three-dimensional magnon Bose-condensates have vanishingly small decay widths. Specifically for parameters relating to TlCuCl$_3$, we find an energy ($Δ_H$) to width ($Γ_H$) ratio $Δ_H/Γ_H\sim500$, making this the narrowest predicted Higgs mode in a condensed matter system, some two orders of …
We evaluate the Raman light scattering intensity for the square lattice Heisenberg antiferromagnet with plaquette ring exchange J_\Box. With the exchange couplings as fixed before from an accurate fit to the spin-wave dispersion in La2CuO4, leading in particular to J_\Box=0.24J, we demonstrate in a parameter free calculation that the inclusion of the plaquette exchange contribution to the dispersion and the magnon-magnon interaction vertex gives a peak position in $B_{1g}$ scattering geometry E_max = 2.71J which is in excellent agreement with the experimental data. Yet, the intrinsic width and…
We investigate the one-magnon Raman scattering in the layered antiferromagnetic La(2)CuO(4) compound. We find that the Raman signal is composed by two one-magnon peaks: one in the B1g channel, corresponding to the Dzyaloshinskii-Moryia (DM) mode, and another in the B3g channel, corresponding to the XY mode. Furthermore, we show that a peak corresponding to the XY mode can be induced in the planar (RR) geometry when a magnetic field is applied along the easy axis for the sublattice magnetization. The appearance of such field-induced mode (FIM) signals the existence of a new magnetic state above…
We investigate the resonant two-magnon Raman scattering in two-dimensional (2D) Mott insulators by using a half-filled 2D Hubbard model in the strong coupling limit. By performing numerical diagonalization calculations for small clusters, we find that the Raman intensity is enhanced when the incoming photon energy is not near the optical absorption edge but well above it, being consistent with experimental data. The absence of resonance near the gap edge is associated with the presence of background spins, while photoexcited states for resonance are found to be characterized by the charge degr…
We suggest a family of spin-ladder models with exact singlet-rung vacuum. In addition to the terms describing interactions along legs and rungs the Hamiltonian has frustration and cyclic terms. Using coordinate Bethe ansatze all one- and two-dimensional states are constructed. The explicit formula for zero-temperature Raman scattering cross section is derived. The corresponding line-shapes are strongly asymmetric and have no more than one van-Hove singularity. The results are in good agreement with experimental data.
In the first part we discuss how the BEC picture for magnons is modified by anisotropies induced by spin-orbit coupling. In particular we focus on the effects of antisymmetric spin interactions and/or a staggered component of the $g$ (gyromagnetic) tensor. Such terms lead to a gapped quasiparticle spectrum and a nonzero condensate density for all temperatures so that no phase transition occurs. We contrast this to the effect of crystal field anisotropies which are also induced by spin-orbit coupling. In the second part we study the field-induced magnetic ordering in TlCuCl$_3$ on a quantitativ…
We investigate the resonant two-magnon Raman scattering in the two-dimensional (2D) and ladder-type Mott insulators by using a half-filled Hubbard model in the strong coupling limit. By performing numerical diagonalization calculations for small clusters, we find that the model can reproduce the experimental features in the 2D that the Raman intensity is enhanced when the incoming photon energy is not near the absorption edge but well above it. In the ladder-type Mott insulators, the Raman intensity is found to resonate with absorption spectrum in contrast to the 2D system. The difference betw…
We investigate the two-magnon Raman scattering from an anisotropic S=1/2 triangular Heisenberg antiferromagnet Cs2CuCl4. We find that the Raman response is very sensitive to magnon-magnon interactions and to scattering geometries, a feature that is in remarkable contrast with the polarization-independent Raman signal from the isotropic triangular Heisenberg antiferromagnet. Since a spin-liquid ground state gives rise to a similar rotationally invariant Raman response, our results on the polarization dependence of the scattering spectrum suggest that Raman spectroscopy provides a useful probe, …
We consider a three-dimensional quantum antiferromagnet in the vicinity of a quantum critical point separating the magnetically ordered and the magnetically disordered phases. A specific example is TlCuCl$_3$ where the quantum phase transition can be driven by hydrostatic pressure and/or by external magnetic field. As expected two transverse and one longitudinal magnetic excitation have been observed in the pressure driven magnetically ordered phase. According to the experimental data, the longitudinal magnon has a substantial width, which has not been understood and has remained a puzzle. In …
In a magnetic substance the gap in the Raman spectrum, Delta_R, is approximatively twice the value of the neutron scattering gap, Delta_S, if the the magnetic excitations (magnons) are only weakly interacting. But for CuGeO_3 the experimentally observed ratio Delta_R/Delta_S is approximatively 1.49-1.78, indicating attractive magnon-magnon interactions in the quasi-1D Spin-Peierls compound CuGe_3. We present numerical estimates for Delta_R/Delta_S from exact diagonalization studies for finite chains and find agreement with experiment for intermediate values of the frustration parameter alpha. …
Measurement and control of magnetic order and correlations in real time is a rapidly developing scientific area relevant for magnetic memory and spintronics [1,15]. In these experiments an ultra-short laser pulse (pump) is first absorbed by excitations carrying electric dipole moment. These then give their energy to the magnetic subsystem monitored by a time-resolved probe. A lot of progress has been made in investigations of ferromagnets but antiferromagnets are more challenging. Here we introduce time-resolved two-magnon Raman scattering as a novel real time probe of magnetic correlations es…
We present the Raman-scattering spectra of CaV2O5 and MgV2O5. The magnetic contribution in the Raman spectra of CaV2O5 is found in the form of a strong asymmetric line, centered at 2Delta, with a tail on the high-energy side. Our analysis of its spectral shape shows that the magnetic ordering in CaV2O5 can be described using a S=1/2 two-leg ladder Heisenberg antiferromagnetic model with Jparallel/Jperp = 0.1, and a small interladder exchange. The spin gap and exchange constant are estimated to be Delta = 400 cm-1 (570 K) and Jperp = 640 K. No magnon bound states are found. In contrast to CaV2O…
Using Raman spectroscopy, we investigate the lattice phonons, magnetic excitations, and magneto-elastic coupling in the distorted triangular-lattice Heisenberg antiferromagnet alpha-SrCr2O4, which develops helical magnetic order below 43 K. Temperature dependent phonon spectra are compared to predictions from density functional theory calculations which allows us to assign the observed modes and identify weak effects arising from coupled lattice and magnetic degrees of freedom. Raman scattering associated with two-magnon excitations is observed at 20 meV and 40 meV. These energies are in gener…
We argue that the Raman intensity in a spin S two-leg spin-ladder has a pseudo-resonance peak, whose width is very small at large S. The pseudo-resonance originates from the existence of a local minimum in the magnon excitation spectrum, and is located slightly below twice the magnon energy at the minimum. The physics behind the peak is similar to the excitonic scenario for the neutron and Raman resonances in a d-wave superconductor.
The effects of phonon anharmonicity, phonon-magnon and electron-phonon interactions on the temperature dependence of Raman optical phonon modes are theoretically investigated. Besides of the Klemens result for the phonon width due to anharmonicity, the corresponding lineshift is derived. We argue that the phonon decay into two magnons has very low intensity in ferromagnets with low Curie temperatures. Therefore, the electron interband transitions accompanied with the ferromagnetic ordering are included in considerations to get a good quantitative agreement with experiments.
The relation between the electronic excitation and the magnetic excitation for the superconductivity in Bi2Sr2Ca{1-x}YxCu2O{8+δ} was investigated by wide-energy Raman spectroscopy. In the underdoping region the B1g scattering intensity is depleted below the two-magnon peak energy due to the "hot spots" effects. The depleted region decreases according to the decrease of the two-magnon peak energy, as the carrier concentration ncreases. This two-magnon peak energy also determines the B1g superconducting gap energy as $2Δ\approx α\hbar ω_{\rm Two-Magnon} \approx J_{\rm effective}$ $(α=0.34-0.41)$…
Nuclear spin-lattice relaxation in one-dimensional Heisenberg ferrimagnets is studied by means of a modified spin-wave theory. We consider the second-order process, where a nuclear spin flip induces virtual spin waves which are then scattered thermally via the four-magnon exchange interaction, as well as the first-order process, where a nuclear spin directly interacts with spin waves via the hyperfine interaction. We point out a possibility of the three-magnon relaxation process predominating over the Raman one and suggest model experiments.
We investigated temperature dependent Raman spectra of the one-dimensional spin-ladder compound SrCu2O3. At low temperatures a two-magnon peak is identified at 3160+/-10 cm^(-1) and its temperature dependence analyzed in terms of a thermal expansion model. We find that the two-magnon peak position must include a cyclic ring exchange of J_cycl/J_perp=0.09-0.25 with a coupling constant along the rungs of J_perp approx. 1215 cm^(-1) (1750 K) in order to be consistent with other experiments and theoretical results.
We reported two-magnon Raman scattering from La_{1.9}Sr_{0.1}CuO_4, which has a suppressed Tc=12 K, as the temperature is lowered below 37 K and an ordered spin phase is formed. The two-magnon Raman intensity increases with decreasing temperature. The magnetic scattering in La_{1.9}Sr_{0.1}CuO_4 is totally different from that reported in the parent compound La_2CuO_4. We analyze the line shape of the two-magnon scattering within the traditional Loudon-Fleury theory and find the superexchange constant J=1052 cm^{-1}. The calculation of the frequency moment suggests that the quantum fluctuations…
We present and analyze Raman spectra of the Mott insulator Ca$_2$RuO$_4$, whose quasi-two-dimensional antiferromagnetic order has been described as a condensate of low-lying spin-orbit excitons with angular momentum $J_{eff}=1$. In the $A_g$ polarization geometry, the amplitude (Higgs) mode of the spin-orbit condensate is directly probed in the scalar channel, thus avoiding infrared-singular magnon contributions. In the $B_{1g}$ geometry, we observe a single-magnon peak as well as two-magnon and two-Higgs excitations. Model calculations using exact diagonalization quantitatively agree with the…
We study field-induced magnetic order in cubic lattices of dimers with antiferromagnetic Heisenberg interactions. The thermal critical exponents at the quantum phase transition from a spin liquid to a magnetically ordered phase are determined from Stochastic Series Expansion Quantum Monte Carlo simulations. These exponents are independent of the interdimer coupling ratios, and converge to the value obtained by considering the transition as a Bose-Einstein condensation of magnons, alpha_(BEC) = 1.5. The scaling results are of direct relevance to the spin-dimer systems TlCuCl_3 and KCuCl_3, and …
Although the parent iron-based pnictides and chalcogenides are itinerant antiferromagnets, the use of local moment picture to understand their magnetic properties is still widespread. We study magnetic Raman scattering from a local moment perspective for various quantum spin models proposed for this new class of superconductors. These models vary greatly in the level of magnetic frustration and show a vastly different two-magnon Raman response. Light scattering by two-magnon excitations thus provides a robust and independent measure of the underlying spin interactions. In accord with other rec…
Unconventional peak structure in the Raman spectra due to magnon excitation at low temperature is observed in spinel magnet ${\rm MnV_2O_4}$, where a noncollinear spin state is realized by geometrical frustration. We propose a new mechanism to induce such a Raman scattering process due to a one-magnon excitation of the noncollinear spin state. Novel features of the scattering such as selection rules and peak position observed experimentally in ${\rm MnV_2O_4}$ can be explained quite naturally by considering the present one-magnon process. We also discuss that such one-magnon process may exist …
Nuclear spin-lattice relaxation in one-dimensional Heisenberg ferrimagnets is studied by means of a modified spin-wave theory. Calculating beyond the first-order mechanism, where a nuclear spin directly interacts with spin waves through the hyperfine coupling, we demonstrate that the exchange-scattering-enhanced three-magnon nuclear relaxation may generally predominate over the Raman one with increasing temperature and decreasing field. Recent proton spin-lattice relaxation-time (T_1_) measurements on the ferrimagnetic chain compound NiCu(C_7_H_6_N_2_O_6_)(H_2_O)_3_2H_2_O suggest that the majo…
We have used Raman scattering to investigate the magnetic excitations and lattice dynamics in the prototypical spin-orbit Mott insulators Sr2IrO4 and Sr3Ir2O7. Both compounds exhibit pronounced two-magnon Raman scattering features with different energies, lineshapes, and temperature dependencies, which in part reflect the different influence of long-range frustrating exchange interactions. Additionally, we find strong Fano asymmetries in the lineshapes of low-energy phonon modes in both compounds, which disappear upon cooling below the antiferromagnetic ordering temperatures. These unusual pho…
Signature of Magnon-Raman Phonon-Polariton Condensation in a Cavity via Transverse Pumping
Birla Institute of Technology and Science, Pilani-Dubai Campus（比拉理工学院，皮拉尼-迪拜校区）；Birla Institute of Technology and Science, Pilani, Hyderabad Campus（比拉理工学院，海德拉巴校区）
We performed Raman studies and a dielectric characterization of the pseudo-kagome Cu3Bi(SeO3)2O2X (X = Cl, Br). These compounds share competing nearest-neighbour ferromagnetic exchange and frustrating next-nearest-neighbour antiferromagnetic exchange as well as highly noncollinear magnetic ground state. However, at low temperature they differ with respect to the existence of inversion symmetry. For both compounds there exists a pronounced interplay of polar phonon modes with quantum magnetic fluctuations. A novel Raman mode appears for temperatures below the Neel temperature with a Fano linesh…
Inelastic light scattering spectra of several members of the RFe3(BO3)4 family reveal a cascade of phase transitions as a function of temperature, starting with a structural, weakly first order, phase transition followed by two magnetic phase transitions. Those consist of the ordering of the Fe-spin sublattice revealed by all the compound, and a subsequent spin-reorientational transition for GdFe3(BO3)4. The Raman data evidence a strong coupling between the lattice and magnetic degrees of freedom in these borates. The Fe-sublattice ordering leads to a strong suppression of the low energy magne…
We used a combination of polarized Raman spectroscopy and spin wave calculations to study magnetic excitations in the strong spin-orbit-coupled (SOC) bilayer perovskite antiferromagnet $Sr_3Ir_2O_7$. We observed two broad Raman features at ~ 800 $cm^{-1}$ and ~ 1400 $cm^{-1}$ arising from magnetic excitations. Unconventionally, the ~ 800 $cm^{-1}$ feature is fully symmetric ($A_{1g}$) with respect to the underlying tetragonal ($D_{4h}$) crystal lattice which, together with its broad line shape, definitively rules out the possibility of a single magnon excitation as its origin. In contrast, the…
We measure Raman scattering in an interacting spin-dimer system KCuCl3 under hydrostatic pressures up to 5 GPa mediated by He gas. In the pressure-induced quantum phase, we observe a one-magnon Raman peak, which originates from the longitudinal magnetic excitationand is observable through the second-order exchange interaction Raman process. We report the pressure dependence of the frequency, halfwidth and Raman intensity of this mode.
We have measured the doping and temperature dependence of lattice vibrations and magnetic excitations in the prototypical doped spin-orbit Mott insulator Sr$_{2-x}$La$_x$IrO$_4$ (x=0, 0.015, and 0.10). Our findings show that the pseudospin-lattice coupling -- responsible for the renormalization of several low energy phonon modes -- is preserved even when long-range magnetic order is suppressed by doping. In our most highly doped sample, the single magnon (Gamma-point) excitation disappears while the two-magnon mode softens and becomes heavily damped. Doping induced electron-phonon coupling is …
(Sr$_{2}$,Ba$_{2}$)Cu$_{3}$O$_{4}$Cl$_{2}$ are antiferromagnetic insulators which are akin to the parent compounds of the cuprate superconductors but with two distinct magnetic ordering temperatures related to two magnetic Cu$_{I}$ and Cu$_{II}$ spin sublattices. Here we present a study of these materials by means of Raman spectroscopy. Following the temperature and polarization dependence of the data we readily identify two distinct features at around 3000 cm$^{-1}$ and 300 cm$^{-1}$ that are related to two-magnon scattering from the two sublattices. The estimated spin-exchange coupling const…
The B1g Raman spectrum of the two-dimensional S=1/2 Heisenberg model is discussed within Loudon-Fleury theory at both zero and finite temperature. The exact T=0 spectrum for lattices with up to 6*6 sites is computed using Lanczos exact diagonalization. A quantum Monte Carlo (QMC) method is used to calculate the corresponding imaginary-time correlation function and its first two derivatives for lattices with up to 16*16 spins. The imaginary-time data is continued to real frequency using the maximum-entropy method, as well as a fit based on spinwave theory. The numerical results are compared wit…
The effect of exchange bond randomness on the ground state and the field-induced magnetic ordering was investigated through magnetization measurements in the spin-1/2 mixed quantum spin system (Tl$_{1-x}$K$_{x}$)CuCl$_3$ for $x<0.36$. Both parent compounds TlCuCl$_3$ and KCuCl$_3$ are coupled spin dimer systems, which have the singlet ground state with excitation gaps $Δ/k_{\rm B}=7.7$ K and 31 K, respectively. Due to bond randomness, the singlet ground state turns into the magnetic state with finite susceptibility, nevertheless, the excitation gap remains. Field-induced magnetic ordering, whi…
Raman selection rules for electronic and magnetic excitations in BaFe2As2 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. 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 sy…
We revisit the theory of magnetic Raman scattering in Mott insulators with strong spin-orbit coupling, with a major focus on Kitaev materials. We show that Kitaev materials with bond-anisotropic interactions are generally expected to show both one- and two-magnon responses. It is further shown that, in order to obtain the correct leading contributions to the Raman vertex operator $\mc{R}$, one must take into account the precise, photon-assisted microscopic hopping processes of the electrons and that, in systems with multiple hopping paths, $\mc{R}$ contains terms beyond those appearing in the …
We compare the theoretical predictions of the previous article [L. Benfatto and M. B. Silva Neto, cond-mat/0602419], with Raman spectroscopy experiments in Sr(2)CuO(2)Cl(2) and untwinned La(2)CuO(4) single crystals. We construct the magnetic point group for the magnetically ordered phase of the two compounds, Sr(2)CuO(2)Cl(2) and La(2)CuO(4), and we classify all the Raman active one-magnon excitations according to the irreducible co-representations for the associated magnetic point group. We then measure the evolution of the one-magnon Raman energies and intensities for low and moderate magnet…
Two magnon excitations and the nodal spin density wave (SDW) gap were observed in BaFe2As2 by Raman scattering. Below the SDW transition temperature (TSDW) nodal SDW gap opens together with new excitations in reconstructed electronic states. The two-magnon peak remains above TSDW and moreover the energy increases a little. The change from the long-range ordered state to the short-range correlated state is compared to the cuprate superconductors.
