Longitudinal Excitations in Bipartite and Hexagonal Antiferromagnetic Spin Lattices

Abstract

Abstract. Based on our recently proposed magnon-density-waves using the microscopic manybody approach, we investigate the longitudinal excitations in quantum antiferromagnets by including the second order corrections in the large-s expansion. The longitudinal excitation spectra for a general spin quantum number using the antiferromagnetic Heisenberg Hamiltonian are obtained for various spin lattice models. For bipartite lattice models, we find that the numerical results for the energy gaps for the longitudinal modes at q → 0 and the magnetic ordering wavevector Q are reduced by about 40-50 % after including the second order corrections. Thus, our estimate of the energy gaps for the quasi-one-dimensional (quasi-1D) antiferromagnetic compound KCuF3 is in better agreement with the experimental result. For the quasi-1D antiferromagnets on hexagonal lattices, the full excitation spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We find two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. We compare our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and also find good agreement after the higher-order contributions are included in our calculations. introductionThe dynamics of the two-dimensional (2D) and three-dimensional (3D) quantum antiferromagnetic systems with long-ranged order at low temperature can be considered as that of a dilute gas of weakly interacting spin-wave quasiparticles (magnons) with its density given by the quantum correction to the classical Néel order [1,2,3]. These magons are transverse modes with spin S = ±1. The longitudinal fluctuations with spin S = 0 present in these systems consist of the multi-magnon continuum [4]. The question concerning long-lived, well-defined longitudinal modes in quantum antiferromagnetic systems with long-ranged order remains open. This is our main focus in this paper.In case of the quantum antiferromagnetic systems without long-ranged order, the triplet excitation states (two transverse and one longitudinal) of the spin-1 Heisenberg chain with nonzero gap, first predicted by Haldane [5], are well known. This theoretical prediction of an energy gap separating the singlet ground state from the triplet excitation states has been confirmed experimentally in the quasi-1D antiferromagnetic compounds such as CsNiCl 3 and RbNiCl 3 of the spin-1 [6]. Some subsequent experimental investigations [7,6,8,9, 10] and theoretical calculations [11,12,13,14,3] also support Haldane's conjecture. In these experiments, the temperature is high enough so the quasi-1D systems have no long-ranged magnetic order and

The Effects of Three Magnons Interactions in the Magnon-Density Waves of Triangular Spin Lattices

“…The logarithmic behavior of the structure factor and the energy spectrum of the triangular lattice model is similar to that of the square lattice model investigated earlier [39,42,46,47]. We have identified these gapless modes of the 2D models as quasi-gapped modes because any finite size effect or anisotropy will induce a large energy gap when compared with the counterparts of the spin-wave spectrum.…”

“…In this theory the longitudinal excitations are identified as the collective modes of the magnon-density waves, and the corresponding wave functions are constructed by employing the magnon-density operator S z in similar fashion to Feynman's theory on the low-lying excited states of the helium-4 superfluid where the particle density operator is used [40]. In our earlier calculations for the quasi-1D hexagonal structures of CsNiCl 3 and RbNiCl 3 and tetragonal structure of KCuF 3 , we find that, after the inclusion of the higher-order contributions from the quartic terms in the large-s expansion, the energy gap values at the magnetic wavevector are in good agreement with experimental results [41,42].…”

Chern-Simons superconductors and their instabilities

“…The Feynmann's ansatz above has been proposed by Ref. [139] to study the longitudinal mode in Heisenberg spin models. Here, we apply the method to the XY antiferromagnets whose longitudinal mode has no ambiguity because the underlying Lorentz invariance that forbids the decay into a pair of Goldstone modes as discussed above.…”

Longitudinal modes of spin fluctuations in iron-based superconductors

“…In quantum antiferromagnet, the longitudinal modes are the amplitude fluctuation of the ordered moments S z , essentially, magnon density. Different from the itinerant approach 27 and nonlinear-σ model 18,26 , LM can also be viewed as two magnon resonance 30 or magnon density wave 31 in Holstein-Primakov theory. Following Feynman's approach to the helium superfluid 32 , the LM can be defined as:…”