Spin dynamics of dimerized Heisenberg chains

Abstract

We study numerically the dimerized Heisenberg model with frustration appropriate for the quasi-1D spin-Peierls compound CuGeO3. We present evidence for a bound state in the dynamical structure factor for any finite dimerization δ and estimate the respective spectral weight. For the homogeneous case (δ = 0) we show that the spin-wave velocity vs is renormalized by the n.n.n. frustration term α as vs = π/2 J(1 − bα) with b ≈ 1.12 78.20.Ls Quantum 1D spin systems may show a variety of instabilities. Of particular interest is the spin-Peierls (SP) phase due to residual magnetoelastic couplings [1], which leads to the opening of a gap in the spin excitation spectrum. The discovery [2] of the spin-Peierls transition below T SP = 14 K in an inorganic compound, CuGeO 3 , has attracted widespread attention.The spin-dynamics of CuGeO 3 is being studied intensively [3][4][5]. Above the spin-Peierls transition the onemagnon excitation spectrum, as measured by neutron scattering [6], forms a broad continuum. The form of the continuum is in good agreement with the continuum expected for one-dimensional antiferromagnetic Heisenberg chains [7]; it is also seen in the magnetic Raman spectrum [8,9]. The physics behind the continuum in the one-magnon excitation spectrum lies on the fact that the elementary excitations of the one-dimensional Heisenberg chain are spinons (also called solitons or Bloch walls), each magnon being made up of two solitons. The resulting "two-spinon" continuum has been seen experimentally also in other quasi-1D antiferromagnets [10].The exact form of the magnetic excitation spectrum in the dimerized state below T SP is still being investigated. A two-spinon continuum is observed [5,6] with large spectral weight at the lower edge. The dispersion of the lower edge has been used to extract the spin-wave velocity [3]. Muthukumar et al. have pointed out recently [9] that the experimental magnetic Raman intensity indicates a well defined magnon mode in the spin-Peierls state of CuGeO 3 and that the origin of this magnon could not be determined on the basis of the Raman scattering data obtained numerically for a single chain.The existence of a well defined magnon mode, i.e. a two-spinon bound state which splits of the continuum, has also been addressed recently by Uhrig and Schulz [11] within an RPA approach. A recent neutron scattering experiment [12], has been interpreted as indicative of such a bound-state.In this context it is an important question to address whether other techniques can shed light on the magnetic excitation spectrum of the dimerized Heisenberg model. Here we present data for the dynamical structure factor S(k, ω) obtained by applying the recursion method [13] to calculate the excitation spectrum of the hamiltonian given below. This approximate method in particular gives very accurate results for the low-lying excitaions. We find evidence for a bound-state for any dimerization δ > 0, independently of the amount of frustration α present. The finite-size corrections of the data is, for certa...

Electronic structure and magnetic properties of the linear chain cupratesSr2CuO3andRösner1, Eschrig2, Hayn3 et al. 1997Phys. Rev. B

“…[44] and r = 1.12 according to Ref. [45]. Recently, Stephan and Penc [46] predicted a strong narrow excitonic peak in the density-density response function N (q, ω) of the EHM in the strong coupling limit at the zone boundary q = π/b:…”

Magnon-magnon interactions in the spin-Peierls compoundCuGeO3

“…6 for various values of α as a function of δ. The data are obtained for N s = 24, the finite-size corrections are very small (compare also [9]). The experimental possible values 1.49-1.78 are indicated as the shaded region in Fig.…”

Magnetic structure ofLi2CuO2: Fromab initiocalculations to macroscopic simulations

“…sensitive to J ʈ -at least not in the expression of Schulz-J b,2 can either be neglected or the relation J ʈ ϭJ b,1 ϪrJ b,2 can be applied with rϭ1 or rϭ1.12. 43,50,51 For the interchain interaction, we follow the strategy previously adopted by other authors, 43,52 which consists in taking the average of the interactions perpendicular to the chain as the effective J Ќ . For CASPT2, we have used J Ќ ϭ͓J a,1 ϩ1/2(J c,1 ϩJ c,2 )͔/2 ϭϪ11.8 K, and for DDCI, J Ќ ϭ (J a,1 ϩJ c,1 )/2ϭϪ2.5 K.…”