Motivated by various spin-1/2 compounds like Cs2CuCl4 or κ-(BEDT-TTF)2Cu2(CN)3, we derive a Raman-scattering operator à la Shastry and Shraiman for various geometries. For T = 0, the exact spectra are computed by the Lanczos algorithm for finite-size clusters. We perform a systematic investigation as a function of J2/J1, the exchange constant ratio: ranging from J2 = 0, the well known square-lattice case, to J2/J1 = 1 the isotropic triangular lattice. We discuss the polarization dependence of the spectra and show how it can be used to detect precursors of the instabilities of the ground state against quantum fluctuations.Motivated by various spin-1/2 compounds like Cs2CuCl4 or κ-(BEDT-TTF)2Cu2(CN)3, we derive a Raman-scattering operator à la Shastry and Shraiman for various geometries. For T = 0, the exact spectra are computed by the Lanczos algorithm for finite-size clusters. We perform a systematic investigation as a function of J2/J1, the exchange constant ratio: ranging from J2 = 0, the well known square-lattice case, to J2/J1 = 1 the isotropic triangular lattice. We discuss the polarization dependence of the spectra and show how it can be used to detect precursors of the instabilities of the ground state against quantum fluctuations.

Jan 1, 200610 citations

Raman scattering in a Heisenberg S=12 antiferromagnet on the anisotropic triangular lattice

Natalia Borisovna Perkins, Gia-Wei Chern, Wolfram Brenig

We investigate the two-magnon Raman scattering from an anisotropic $S=\frac{1}{2}$ triangular Heisenberg antiferromagnet Cs ${}_{2}$ CuCl ${}_{4}$ . 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, complementary to neutron scattering, of the ground-state properties of Cs ${}_{2}$ CuCl ${}_{4}$ , particularly whether the time-reversal symmetry is broken in the ground state.We investigate the two-magnon Raman scattering from an anisotropic $S=\frac{1}{2}$ triangular Heisenberg antiferromagnet Cs${}_{2}$CuCl${}_{4}$. 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, complementary to neutron scattering, of the ground-state properties of Cs${}_{2}$CuCl${}_{4}$, particularly whether the time-reversal symmetry is broken in the ground state.

arXiv:1212.2286Physical Review BMay 22, 201318 citations

Magnetic Raman Scattering in Two-Dimensional Spin-1/2 Heisenberg Antiferromagnets: Spectral Shape Anomaly and Magnetostrictive Effects

Franco Nori, Roberto D. Merlin, Stephan Haas +2 more

We calculate the Raman spectrum of the two-dimensional spin-1/2 Heisenberg antiferromagnet by exact diagonalization and quantum Monte Carlo techniques on clusters of up to 144 sites. On a 16-site cluster, we consider the phonon-magnon interaction which leads to random fluctuations of the exchange integral. Results are in good agreement with Raman scattering experiments on various high- ${T}_{c}$ precursors, such as ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.2}$ . In particular, our calculations reproduce the broad line shape of the two-magnon peak, the asymmetry about its maximum, the existence of spectral weight at high energies, and the observation of nominally forbidden ${A}_{1g}$ scattering.We calculate the Raman spectrum of the two-dimensional spin-1/2 Heisenberg antiferromagnet by exact diagonalization and quantum Monte Carlo techniques on clusters of up to 144 sites. On a 16-site cluster, we consider the phonon-magnon interaction which leads to random fluctuations of the exchange integral. Results are in good agreement with Raman scattering experiments on various high- ${T}_{c}$ precursors, such as ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.2}$. In particular, our calculations reproduce the broad line shape of the two-magnon peak, the asymmetry about its maximum, the existence of spectral weight at high energies, and the observation of nominally forbidden ${A}_{1g}$ scattering.

arXiv:cond-mat/9505012Physical Review LettersJul 17, 199542 citations

Numerical Study of Magnetic Raman Scattering Spectra in Ladder Antiferromagnets –Exchange Scatterings from the Singlet Ground State–

Shinichiro Tada, Yuhei Natsume, Toshihiko Suzuki

The exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which two-legs with antiferromagnetic bond J c is connected by rungs with antiferromagnetic bond J r . The numerical calculation is made for the system of 12 ×2 sites by Lanczos method. The ratio of J c / J r is considered to be 0.6–1.0 in order to discuss the experimental work for ladders of Cu 2+ ions in oxide compounds Sr 14- x Ca x Cu 24 O 41 . In addition to the Raman edge about J r corresponding twice the singlet-triplet spin gap, the characteristic structure appears around 2 or 3 times of J r i.e. 3 or 5 times the spin-gap. We concentrate our attention on characteristic features of excited levels, transitions to which are Raman-active. In particular, the relationship between correlations for spins in those states and corresponding Raman intensities is discussed in the picture of triplet pairs excited from singlet dimers. By the perturbation theory, the essential dependence of those intensities on distances between triplet dimers is investigated.The exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which two-legs with antiferromagnetic bond J c is connected by rungs with antiferromagnetic bond J r . The numerical calculation is made for the system of 12 ×2 sites by Lanczos method. The ratio of J c / J r is considered to be 0.6–1.0 in order to discuss the experimental work for ladders of Cu 2+ ions in oxide compounds Sr 14- x Ca x Cu 24 O 41 . In addition to the Raman edge about J r corresponding twice the singlet-triplet spin gap, the characteristic structure appears around 2 or 3 times of J r i.e. 3 or 5 times the spin-gap. We concentrate our attention on characteristic features of excited levels, transitions to which are Raman-active. In particular, the relationship between correlations for spins in those states and corresponding Raman intensities is discussed in the picture of triplet pairs excited from singlet dimers. By the perturbation theory, the essential dependence of those intensities on distances between triplet dimers is investigated.

Journal of the Physical Society of JapanAug 15, 20011 citation

Spin- 12 Heisenberg model on the anisotropic triangular lattice: From magnetism to a one-dimensional spin liquid

Dariush Heidarian, Sandro Sorella, Federico Becca

We investigate the anisotropic triangular lattice that interpolates from decoupled one-dimensional chains to the isotropic triangular lattice and has been suggested to be relevant for various quasi-two-dimensional materials such as ${\text{Cs}}_{2}{\text{CuCl}}_{4}$ or $\ensuremath{\kappa}\text{\ensuremath{-}}{(ET)}_{2}{\text{Cu}}_{2}{(\text{CN})}_{3}$. We obtain an excellent accuracy by means of a representation for the resonating valence-bond wave function with both singlet and triplet pairings. This approach allows us to establish that the magnetic order is rapidly destroyed away from the pure triangular lattice and incommensurate spin correlations are short range. A nonmagnetic spin liquid naturally emerges in a wide range of the phase diagram with strong one-dimensional character.We investigate the anisotropic triangular lattice that interpolates from decoupled one-dimensional chains to the isotropic triangular lattice and has been suggested to be relevant for various quasi-two-dimensional materials such as ${\text{Cs}}_{2}{\text{CuCl}}_{4}$ or $\ensuremath{\kappa}\text{\ensuremath{-}}{(ET)}_{2}{\text{Cu}}_{2}{(\text{CN})}_{3}$. We obtain an excellent accuracy by means of a representation for the resonating valence-bond wave function with both singlet and triplet pairings. This approach allows us to establish that the magnetic order is rapidly destroyed away from the pure triangular lattice and incommensurate spin correlations are short range. A nonmagnetic spin liquid naturally emerges in a wide range of the phase diagram with strong one-dimensional character.

Physical Review BJul 16, 2009101 citations

The spin-S Heisenberg antiferromagnet on the orthogonal-dimer lattice

Hiroki Nakano, Tôru Sakai

Abstract The spin-S Heisenberg antiferromagnet on the orthogonal-dimer lattice is studied. In most of the investigations of the antiferromagnet on this lattice beginning with the study by Shastry and Sutherland, the S = 1 / 2 case has intensively been treated. In the present study, the cases of S = 1 and 3/2 are particularly treated by the numerical-diagonalization method based on the Lanczos algorithm applied to finite-size clusters. We successfully capture the edge of the exact-dimer phase and that of the Néel-ordered phase. A significant finding is the existence of an intermediate phase between both the edges irrespective of spin-S.Abstract The spin-S Heisenberg antiferromagnet on the orthogonal-dimer lattice is studied. In most of the investigations of the antiferromagnet on this lattice beginning with the study by Shastry and Sutherland, the S = 1 / 2 case has intensively been treated. In the present study, the cases of S = 1 and 3/2 are particularly treated by the numerical-diagonalization method based on the Lanczos algorithm applied to finite-size clusters. We successfully capture the edge of the exact-dimer phase and that of the Néel-ordered phase. A significant finding is the existence of an intermediate phase between both the edges irrespective of spin-S.

Journal of Physics Condensed MatterAug 13, 20243 citations

We investigate the two-magnon Raman scattering from an anisotropic

S=\frac{1}{2}

triangular Heisenberg antiferromagnet Cs

{}_{2}

CuCl

{}_{4}

. 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, complementary to neutron scattering, of the ground-state properties of Cs

{}_{2}

CuCl

{}_{4}

, particularly whether the time-reversal symmetry is broken in the ground state.

{T}_{c}

precursors, such as

{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}

and

{\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.2}

. In particular, our calculations reproduce the broad line shape of the two-magnon peak, the asymmetry about its maximum, the existence of spectral weight at high energies, and the observation of nominally forbidden

{A}_{1g}

scattering.

{\text{Cs}}_{2}{\text{CuCl}}_{4}

or $\ensuremath{\kappa}\text{\ensuremath{-}}{(ET)}_{2}{\text{Cu}}_{2}{(\text{CN})}_{3}$. We obtain an excellent accuracy by means of a representation for the resonating valence-bond wave function with both singlet and triplet pairings. This approach allows us to establish that the magnetic order is rapidly destroyed away from the pure triangular lattice and incommensurate spin correlations are short range. A nonmagnetic spin liquid naturally emerges in a wide range of the phase diagram with strong one-dimensional character.