Raman scattering for triangular lattices spin- 1 2 Heisenberg antiferromagnets

Motivated by various spin-1/2 compounds like Cs 2 CuCl 4 or κ - (BEDT - TTF) 2 Cu 2 (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 J 2 / J 1 , the exchange constant ratio: ranging from J 2 = 0, the well known square-lattice case, to J 2 / J 1 = 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 Cs 2 CuCl 4 or κ - (BEDT - TTF) 2 Cu 2 (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 J 2 / J 1 , the exchange constant ratio: ranging from J 2 = 0, the well known square-lattice case, to J 2 / J 1 = 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.

arXiv:cond-mat/0608083Journal of Physics Condensed MatterMar 23, 200723 citations

Magnetic Raman Scattering from 1D Antiferromagnets

Rajiv R. P. Singh, Peter Prelovšek, B. Sriram Shastry

We study Raman scattering from 1D antiferromagnets within the Fleury-Loudon scheme by applying a finite temperature Lanczos method to a 1D spin-half Heisenberg model with nearest-neighbor ( ${J}_{1}$ ) and second-neighbor ( ${J}_{2}$ ) interactions. The low-temperature spectra are analyzed in terms of the known elementary excitations of the system for ${J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ and ${J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ . We find that the low- $T$ Raman spectra are very broad for $|{J}_{2}/{J}_{1}|\ensuremath{\le}0.3$. This broad peak gradually diminishes and shifts with temperature, so that at $T>{J}_{1}$ the spectra are narrower and peaked at low frequencies. The experimental spectra for ${\mathrm{CuGeO}}_{3}$ are discussed in light of our calculations.We study Raman scattering from 1D antiferromagnets within the Fleury-Loudon scheme by applying a finite temperature Lanczos method to a 1D spin-half Heisenberg model with nearest-neighbor ( ${J}_{1}$) and second-neighbor ( ${J}_{2}$) interactions. The low-temperature spectra are analyzed in terms of the known elementary excitations of the system for ${J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ and ${J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$. We find that the low- $T$ Raman spectra are very broad for $|{J}_{2}/{J}_{1}|\ensuremath{\le}0.3$. This broad peak gradually diminishes and shifts with temperature, so that at $T>{J}_{1}$ the spectra are narrower and peaked at low frequencies. The experimental spectra for ${\mathrm{CuGeO}}_{3}$ are discussed in light of our calculations.

Physical Review LettersNov 4, 199612 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

1 The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N = 40 spins

Johannes Richter, J. Schulenburg

We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J c1 2 and J2> J c2 2 separated by a gapful quantum paramagnetic phase. We estimate Jc1 2 ≈ 0.35J1 and J c2 2 ≈ 0.66J1. PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 1We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J c1 2 and J2> J c2 2 separated by a gapful quantum paramagnetic phase. We estimate Jc1 2 ≈ 0.35J1 and J c2 2 ≈ 0.66J1. PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 1

Jan 1, 200991 citations

MAGNETIC ORDERING OF ANTIFERROMAGNETS ON A SPATIALLY ANISOTROPIC TRIANGULAR LATTICE

R. F. Bishop, P. H. Y. Li, DAMIAN J. J. FARNELL +1 more

We study the spin-1/2 and spin-1 [Formula: see text] Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice, using the coupled cluster method. With respect to an underlying square-lattice geometry the model contains antiferromagnetic (J1 > 0) bonds between nearest neighbours and competing [Formula: see text] bonds between next-nearest-neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry the model has two sorts of nearest-neighbour bonds, with [Formula: see text] bonds along parallel chains and with J1 bonds providing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one extreme (κ = 0) and a set of decoupled chains at the other (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For the spin-1/2 [Formula: see text] model, we find a weakly first-order (or possibly second-order) quantum phase transition from a Néel-ordered state to a helical state at a first critical point at κc1 = 0.80 ± 0.01, and a second critical point at κc2 = 1.8 ± 0.4 where a first-order transition occurs between the helical state and a collinear stripe-ordered state. For the corresponding spin-1 model we find an analogous transition of the second-order type at κc1 = 0.62 ± 0.01 between states with Néel and helical ordering, but we find no evidence of a further transition in this case to a stripe-ordered phase.We study the spin-1/2 and spin-1 [Formula: see text] Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice, using the coupled cluster method. With respect to an underlying square-lattice geometry the model contains antiferromagnetic (J1 > 0) bonds between nearest neighbours and competing [Formula: see text] bonds between next-nearest-neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry the model has two sorts of nearest-neighbour bonds, with [Formula: see text] bonds along parallel chains and with J1 bonds providing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one extreme (κ = 0) and a set of decoupled chains at the other (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For the spin-1/2 [Formula: see text] model, we find a weakly first-order (or possibly second-order) quantum phase transition from a Néel-ordered state to a helical state at a first critical point at κc1 = 0.80 ± 0.01, and a second critical point at κc2 = 1.8 ± 0.4 where a first-order transition occurs between the helical state and a collinear stripe-ordered state. For the corresponding spin-1 model we find an analogous transition of the second-order type at κc1 = 0.62 ± 0.01 between states with Néel and helical ordering, but we find no evidence of a further transition in this case to a stripe-ordered phase.

International Journal of Modern Physics BOct 20, 20104 citations

Spectral function of the J1−J2 Heisenberg model on the triangular lattice

Nicholas E. Sherman, Maxime Dupont, Joel E. Moore

Triangular lattice compounds have received extensive attention recently as quantum spin liquid candidates. Here, the authors look at the ${J}_{1}$ - ${J}_{2}$ Heisenberg model on the triangular lattice, and calculate the spectral function relevant for neutron scattering experiments. They find a high-energy spectrum consistent with reports of a spinon Fermi surface state in triangular lattice compounds, although the low-energy spectrum rules out such a phase, and points towards a U(1) Dirac spin liquid. They provide clear signatures to look for in future neutron scattering experiments to distinguish these two phases.Triangular lattice compounds have received extensive attention recently as quantum spin liquid candidates. Here, the authors look at the ${J}_{1}$-${J}_{2}$ Heisenberg model on the triangular lattice, and calculate the spectral function relevant for neutron scattering experiments. They find a high-energy spectrum consistent with reports of a spinon Fermi surface state in triangular lattice compounds, although the low-energy spectrum rules out such a phase, and points towards a U(1) Dirac spin liquid. They provide clear signatures to look for in future neutron scattering experiments to distinguish these two phases.

arXiv:2209.00739Physical review. B./Physical review. BApr 25, 202340 citations

We study Raman scattering from 1D antiferromagnets within the Fleury-Loudon scheme by applying a finite temperature Lanczos method to a 1D spin-half Heisenberg model with nearest-neighbor (

{J}_{1}

) and second-neighbor (

{J}_{2}

) interactions. The low-temperature spectra are analyzed in terms of the known elementary excitations of the system for

{J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

and

{J}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2

. We find that the low-

T

Raman spectra are very broad for $|{J}_{2}/{J}_{1}|\ensuremath{\le}0.3$. This broad peak gradually diminishes and shifts with temperature, so that at

T>{J}_{1}

the spectra are narrower and peaked at low frequencies. The experimental spectra for

{\mathrm{CuGeO}}_{3}

are discussed in light of our calculations.

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.

Triangular lattice compounds have received extensive attention recently as quantum spin liquid candidates. Here, the authors look at the

{J}_{1}

{J}_{2}

Heisenberg model on the triangular lattice, and calculate the spectral function relevant for neutron scattering experiments. They find a high-energy spectrum consistent with reports of a spinon Fermi surface state in triangular lattice compounds, although the low-energy spectrum rules out such a phase, and points towards a U(1) Dirac spin liquid. They provide clear signatures to look for in future neutron scattering experiments to distinguish these two phases.