Lagrangian spin-wave theory of frustrated antiferromagnets: Application toABX3compounds

Abstract

A theory of magnetic excitations formulated within the framework of the Lagrange equations of motion is used to study spin waves in stacked triangular antiferromagnets. As a consequence of geometrical frustration, a longitudinal mode parasitically coupled to transverse excitations is predicted. The model demonstrates good agreement with inelastic neutron scattering data for spin-1 CsNiCh and RbNiCh, as well as spin-y CsMnli, in contrast with results based on the Haldane conjecture and with standard spin-wave theory. This formalism has general relevance to all frustrated spin systems.PACS numbers: 75.30.Ds, 75.50.Ee, 76.50.+g Discrepancies between existing theory and experimental results for spin excitations in a class of quasi-onedimensional hexagonal ABX3 antiferromagnets are becoming increasingly clear. Of particular interest is the possibility to observe effects associated with the integerspin Haldane conjecture in spin-1 CsNiC^ and RbNiC^. It is now evident that the field-theory model proposed by Affleck [1,2] does not provide convincing agreement with experimental results [3-6] to support the existence of this novel quantum state at temperatures well below the onset of long-range magnetic order, 7V It may be that other manifestations of the Haldane proposal are responsible for the failure of conventional spin-wave theory to explain the inelastic neutron diffraction data of these Ni compounds; however, related discrepancies also exist for the non-Haldane spin-f system CsMnl3 [7]. In the present work we suggest that standard spin-wave theory fails to fully account for effects associated with the geometrical frustration inherent to triangular antiferromagnets. A theory of magnetic excitations based on the Lagrangian approach introduced by Dzyaloshinskii and Kukharenko [8] (DK) is shown to give a satisfactory explanation of the observed magnon dispersions for CsNiCh, RbNiCl 3 , and CsMnh. The proposed model has general relevance for all frustrated spin systems.Much of the general formalism relevant to this work has already been presented in our study of a phenomenological Lagrangian model of longitudinal spin fluctuations in CsNiCU [9,10], which reproduced the results of Affleck [1,2]. Conventional spin dynamics are determined by the familiar torque equations [11], as introduced by Landau and Lifshitz [12], which exclude longitudinal (magnitude) fluctuations. In an alternate approach, DK give symmetry arguments to support a Lagrangian formalism based on a kinetic part of the form r-7 X J diinijSiSj+pijSjSj), (1) u where Sj=ds,/dt and p /y must be antisymmetric and an odd function of the spin density s(r). DK remark that although the coefficient p_ has no obvious physical interpretation, rigorous arguments demonstrate that p is related to the gyromatic ratio y and equilibrium spin density. In addition, these authors make the important observation that the equations of motion resulting from (1) with p =0 are very similar, but not necessarily identical, to the conventional torque equations (see below). We examin...

Longitudinal Excitations in Bipartite and Hexagonal Antiferromagnetic Spin Lattices

“…Nevertheless, with a similar analysis as before based on the spinwave ground state, we obtain the L − mode energy gap value of 0.64 THz at the magnetic wavevector Q in the first order approximation, and of 0.47 THz after including the second order contributions. This later value is still much larger than the experimental value of about 0.1 THz by Harrison et al [47], which was used to fit a modified spin-wave theory by Plumer and Cailé [17]. Clearly, for such systems as CsMnI 3 , we need a better ground state than that of the spin-wave theory in our analysis.…”

“…This energy gap was initially explained by a uniaxial single-ion anisotropy but now it is widely accepted that the gapped excited state belongs to longitudinal excitation modes, first proposed by Affleck [in the quasi-1D hexagonal antiferromagnetic compounds of the ABX 3 -type with both spin quantum number s = 1 CsNiCl 3 and RbNiCl 3 [15,16]. A field theory approach focusing on the spin frustrations of the hexagonal antiferromagnetic systems has also been proposed [17]. Clearly, such longitudinal modes are beyond the usual spin-wave theory (SWT) which only predicts the transverse spin-wave excitations (magnons).…”

Excited states of quasi-one-dimensional hexagonal quantum antiferromagnets

“…Nevertheless, with a similar analysis as before based on the spinwave ground state, we obtain the L − mode energy gap value of 0.64 THz at the magnetic wavevector Q in the first order approximation, and of 0.47 THz after including the second order contributions. This later value is still much larger than the experimental value of about 0.1 THz by Harrison et al [30], which was used to fit a modified spin-wave theory by Plumer and Cailé [18]. Clearly, for such systems as CsMnI 3 , we need a better ground state than that of the spin-wave theory in our analysis.…”

Longitudinal excitations in quantum antiferromagnets

“…We notice that in deriving the expressions of Eqs. (17) and (18) for the structure factors, the values for q = 0 are excluded due to the condition q > 0 in the definition of X q from Eqs. (3) and (7).…”

“…(6) and (13) in general forms and by Eqs. (17) and (18) in our approximation using the similar SWT ground state with the anisotropy parameter A = 1. We notice that in Eq.…”