Spin-pair Excitations Research Articles

Scaling behavior in the optical conductivity of two-dimensional systems of strongly correlated electrons based on the U(1) slave-boson approach to thet−JHamiltonian

The U(1) holon-pair boson theory of Lee and Salk [Phys. Rev. B 64, 052501 (2001)] is applied to investigate the quantum scaling behavior of optical conductivity in the two-dimensional systems of strongly correlated electrons. We examine the role of both the gauge field fluctuations and spin pair excitations on the $\ensuremath{\omega}∕T$ scaling behavior of the optical conductivity. It is shown that the gauge field fluctuations but not the spin pair excitations are responsible for the scaling behavior in the low-frequency region $\ensuremath{\omega}∕T⪡1$. The importance for the contribution of the nodal spinons to the Drude peak is discussed. It is shown that the $\ensuremath{\omega}∕T$ scaling behavior is manifest in the low-frequency region at low hole concentrations close to a critical concentration at which superconductivity arises at $T=0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

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.

Two-magnon Raman scattering in cuprates: Evidence for antiferromagnetic fluctuations in cuprate superconductors

We report observation and resonance-Raman studies of spin-pair excitations in Y Ba 2 Cu 3 O 6+ x (0.37 < x < 0.7) and YBa 2 Cu 4 O 8 superconductors. These citations at energy ∼ 3 J (2700±150 cm −1), similar to two-magnon excitations in insulators, are evidence that antiferromagnetic fluctuations with spatial extent of at least three lattice constants are not overdamped in the underdoped superconductors. With optimal hole doping, where T c >80 K, and in the overdoped TlBa 2 CuO 6 superccconductors the two-magnon peak can no longer be seen above the flat Raman continuum.

Two-magnon Raman scattering in cuprate superconductors: Evolution of magnetic fluctuations with doping.

We report observation and resonance Raman studies of spin-pair excitations in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6+\mathit{x}}$ (0.37x0.7) and ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ superconductors. These excitations at energy \ensuremath{\sim}3J (2700\ifmmode\pm\else\textpm\fi{}150 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$), similar to two-magnon excitations in insulators, are evidence that antiferromagnetic fluctuations with spatial extent of at least three lattice constants are not overdamped in the underdoped superconductors. With optimal hole dopings, where ${\mathit{T}}_{\mathit{c}}$&gt;80 K, the two-magnon peak can no longer be seen above the flat Raman continuum. Photoluminescence and the origin of the broad-spectrum Raman continuum are also discussed.

Raman scattering in FeBO3 at high pressures: Phonon coupled to spin-pair fluctuations and magneto-deformation potentials.

The first direct measurement of the modulation of the magnetic superexchange parameter J by optical phonons is reported. High-pressure Raman scattering studies of the model compound FeBO 3 reveal an unexpectedly large interaction between a (BO 3 ) 3- internal mode and spin-pair excitations. By pressure tuning J, resonant decay of the phonon into the two-magnon continuum and associated mixing were observed yielding a phonon-magnon-pair coupling constant g≃(0.15-0,20)J

Quantum spin nematics: Moment-free magnetism.

Treating antiferromagnetism as a spin superfluid, we discuss the possibility of moment-free magnetism. Specifically we show that large quantum fluctuations induce an anisotropy in Heisenberg spiral structures, driving a biaxial-uniaxial transition to a spin nematic; this state is characterized by tensor spin order and a gapless Goldstone mode of spin-pair excitations. Experimental signatures and realizations of this phenomena are suggested.

Temperature-dependent lifetime of spin excitations in RBa2Cu3O6 (R=Eu, Y).

We have measured the light scattering by spin-pair excitations in single crystals of R${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6}$ (R=Y,Eu) for several polarization directions in the temperature range of 10 to 700 K. A strong broadening of the ${\mathit{B}}_{1\mathit{g}}$ and an enhancement of the ${\mathit{A}}_{1\mathit{g}}$ component is observed with increasing temperature. For all temperatures agreement between calculations and experimental light-scattering data has been obtained with J=810 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and a zone-edge spin-excitation damping \ensuremath{\Gamma} which changes from 184\ifmmode\pm\else\textpm\fi{}50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (T=10 K) to 913\ifmmode\pm\else\textpm\fi{}100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (T=600 K). We conjecture that spin-lattice interaction significantly decreases the spin-excitation lifetime.

Light scattering from quantum spin fluctuations in R2CuO4 (R=La, Nd, Sm).

Raman spectra reveal spin fluctuation scattering over the energy range 0--8000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ (0--1 eV) in single crystal ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ (T phase), ${\mathrm{Nd}}_{2}$${\mathrm{CuO}}_{4}$, and ${\mathrm{Sm}}_{2}$${\mathrm{CuO}}_{4}$ (T' phase). From the ${B}_{1g}$ symmetry spectra, values of the exchange parameter J for these crystals are determined to be 1030\ifmmode\pm\else\textpm\fi{}50, 871\ifmmode\pm\else\textpm\fi{}50, and 888\ifmmode\pm\else\textpm\fi{}50 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively. All three materials also exhibit broad spectral features of ${A}_{1g}$ and ${B}_{2g}$ symmetry, which are forbidden within the classical spin-pair excitation model, but allowed by quantum fluctuations. The line shapes for spectra of all three symmetries agree with recent model calculations for the planar quantum antiferromagnet. While the spectra for crystals with the T' structure are nearly identical, subtle differences from the spectra of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ (T structure) indicate a sensitivity to the structure outside of the ${\mathrm{CuO}}_{2}$ planes.

Raman measurements of energy gap and spin pair excitations in single crystal YBa2Cu3O7

We measured the electronic contribution to the polarized raman scattering of high quality superconducting YBa2Cu3O7 single crystals. For all samples we find a broad background scattering intensity, which is a superposition of two different contributions. The nearly temperature independent background in both Ag and B1g symmetry peaks at about 500cm−1 and is attributed to double magnon excitations. in addition we find a temperature dependent raman signal of Ag symmetry, which at low temperatures is attributed to quasiparticle excitations above the gap. From this electronic scattering we deduce a gap value of 225±50cm−1, approximately equivalent with 3.5 kBTc and consistent with previous tunneling-, far infrared- and Andreev scattering results. The present results indicate for the first time the coexistence of spin waves and superconductivity in YBa2Cu3O7.

Magnetic excitations in La2CuO4

We compare the experimentally observed magnetic excitations in La2CuO4 with those calculated for a square lattice spin-12 Heisenberg antiferromagnet. We find that the short-wavelength spin-pair excitation spectrum deduced from light scattering, and the long wavelength spin-wave dispersion deduced from neutron scattering are both consistent with a nearest neighbor model with the exchange constant J of about 1500 K.

Observation of magnetic excitations in antiferromagnetic TlYBa 2Cu 2O 7 by inelastic light scattering

Polycrystalline samples of the antiferromagnetic insulator TlYBa 2Cu 2O 7 have been prepared and characterized by X-ray diffraction. Raman spectroscopy, magnetization and resistivity measurements. Magnetization data are consistent with a primary antiferromagnetic phase plus a small concentration of paramagnetic copper impurity phases. The room-temperature Raman spectrum has a strong and broad peak around 2625 cm −1 resulting from magnetic spin-pair excitations in the antiferromagnetic phase. The Raman-active phonons of TlYBa 2Cu 2O 7 are similar to those of the closely related compounds TlCaBa 2Cu 2O 7 (Tl-1122) and YBa 2Cu 3O 7− x (Y-123).

Quantitative determination of quantum fluctuations in the spin-1/2 planar antiferromagnet.

Frequency moments of the light-scattering spectrum from spin-pair excitations are calculated for the spin-\textonehalf{} planar Heisenberg antiferromagnet. The quantitative agreement with the experimental ${B}_{1g}$ spectrum in ${\mathrm{La}}_{2}$Cu${\mathrm{O}}_{4}$ demonstrates that the observed linewidth is dominated by quantum fluctuations and yields a value for the exchange parameter $J$ of 1030\ifmmode\pm\else\textpm\fi{}50 ${\mathrm{cm}}^{\ensuremath{-}1}$. Quantum fluctuations also permit light scattering due to diagonal-next-neighbor spin-pair excitations. Observed spectral features in the ${A}_{1g}$ and ${B}_{2g}$ symmetries are consistent with those calculated for this process.

OBSERVATION OF SPIN FLUCTUATIONS IN Bi-Sr-Ca-Cu-O SYSTEMS

Following the observations of spin-pair excitations in La 2 CuO 41 and YBa 2 Cu 3 O 6+δ,2 similar results in Bi-Sr-Ca-Cu-O systems are obtained. The center frequencies of the excitations are about 1900–2300 cm −1, which correspond to the value of the exchange constant J~690–840 cm −1. The extraordinary similarity suggests the same origin of superconductivity of these three kinds of copper oxides superconductors. This means that any theory of superconductivity in copper oxides should account explicitly for these highly energetic spin fluctuations.

High-frequency Raman scattering in the superconducting and semiconducting phases of Ba2YCu3Ox-type single crystals and ceramics.

We report the high-frequency Raman spectra ($\ensuremath{\Delta}\ensuremath{\omega}&gt;1000$ ${\mathrm{cm}}^{\ensuremath{-}1}$) of ${\mathrm{Ba}}_{2}\mathrm{Y}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$ and various analogs, measured at room temperature. In semiconducting single crystals and ceramics of ${\mathrm{Ba}}_{2}\mathrm{Y}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$ ($x\ensuremath{\approx}6$) and semiconducting single crystals of ${\mathrm{Sr}}_{2}\mathrm{Y}{\mathrm{Cu}}_{2.4}{\mathrm{Al}}_{0.6}{\mathrm{O}}_{x}$ we find a peak at 1220 ${\mathrm{cm}}^{\ensuremath{-}1}$ (${A}_{1g}$ symmetry) and a broadband at 2600 ${\mathrm{cm}}^{\ensuremath{-}1}$ (${B}_{1g}$). The 1220-${\mathrm{cm}}^{\ensuremath{-}1}$ peak can be interpreted as scattering from excitations of single spins near defects or two-phonon scattering. The 2600-${\mathrm{cm}}^{\ensuremath{-}1}$ band is attributed to scattering from spin-pair excitations. In the spectra of superconducting ${\mathrm{Ba}}_{2}\mathrm{Y}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$ crystals and ceramics ($x\ensuremath{\approx}7$) these bands are not present. In all samples, semiconductors and superconductors, we observe flat and featureless spectral intensity (${A}_{1g}$ symmetry) extending up to $\ensuremath{\Delta}\ensuremath{\omega}=5000$ ${\mathrm{cm}}^{\ensuremath{-}1}$, the origin of which is not understood at present. The similarity between the high-frequency spectra of ${\mathrm{Ba}}_{2}\mathrm{Y}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$ ($x\ensuremath{\sim}6$) and ${\mathrm{Sr}}_{2}\mathrm{Y}{\mathrm{Cu}}_{2.4}{\mathrm{Al}}_{0.6}{\mathrm{O}}_{x}$ [Al on Cu(1)-chain sites] shows that the magnetic scattering is determined by the structure of the Cu(2)-O planes and is not affected by the distance between the planes or by the Cu(1)-chain structure.

MAGNETIC SUSCEPTIBILITY OF YBa2Cu3O7−Δy

Magnetic properties of YBa 2 Cu 3 O 7−Δy was investigated by dc- and ac-magnetic susceptibility as a function of oxygen deficiency Δy. The susceptibility in the normal state at low temperatures is dominated by the Curie-Weiss law, while the susceptibility at high temperatures deviates from the Curie-Weiss law. The deviations were successfully explained by assuming the triplet spin-pair excitation from the antiferromagnetically coupled Cu 2+ ions in the ground state.

Spin fluctuations and superconductivity in Ba2YCu

We report observation of spin-pair excitations in Ba/sub 2/YCu/sub 3/O/sub 6+//sub delta/, with delta in the range 0.0--0.9. The frequency of the excitations, and hence the value of the exchange constant, J = 950 cm/sup -1/, is similar to that reported recently for (nonsuperconducting) La/sub 2/CuO/sub 4/. The present observation of magnetic excitations in a superconducting material, and of their evolution as a function of delta, demonstrate a large influence of carrier concentration on the spin-fluctuation dynamics.

Dynamics of two-magnon resonances in the absence of bound states

Spectral intensity distributions are calculated for different types of spin-pair excitations in a simple-cubic Heisenberg ferromagnet with next-nearest-neighbor (nnn) exchange interactions. The ratio of next-nearest- to nearest-neighbor (nn) exchange interaction ($\ensuremath{\eta}$) is chosen to be large enough to prevent the formation of bound states, by containing all pair excitations in the continuum, but without being too far removed from the nn case. Calculations have been performed using $\ensuremath{\eta}=\frac{1}{8}$ and $S=1$ for single-ion, nn and nnn pair excitations for total pair wave vectors ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$) along the [111] direction. An understandable picture of the excitations follows the study of resonance peaks in the computed spectra and their comparison with those of the nn case. The changes due to the relaxation of the exact Ising-like limit of the nearest-neighbor case at the zone boundary in the [111] direction are largely due to states which were formerly bound states having become resonances for all values of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$.