Spin-wave response in the dilute quasi-one-dimensional Ising-like antiferromagnetCsCo0.83Mg0.17Br

Abstract

Inelastic neutron-scattering profiles of spin waves in the dilute quasi-one-dimensional Ising-like antiferromagnet CsCo 0.83 Mg 0.17 Br 3 have been investigated. Calculations of S xx (Q,), based on an effective spin Hamiltonian, accurately describe the experimental spin-wave spectrum of the 2J mode. The Q dependence of the energy of this spin-wave mode follows the analytical prediction xx (Q)ϭ(2J)(1 -5⑀ 2 cos 2 Qaϩ2⑀ 2 ) 1/2 , calculated by Ishimura and Shiba using perturbation theory.The quantum nature of spin-1/2 one-dimensional magnetic systems manifests itself in a number of interesting properties that have been studied both experimentally and theoretically for many years. 1 The spin-wave excitation spectrum around the pure Ising energy consists of a continuum of states, accompanied by the propagation of domain wall pairs of the soliton response. The existence of a band of spin-wave states and the soliton response have been confirmed within the quasi-one-dimensional system, CsCoM 3 (M ϭBr,Cl), by Satija et al. 2 and Nagler et al. 3 The spin Hamiltonian describing the dynamics of 1D Ising-like antiferromagnets, including the exchange mixing produced by interchain and intrachain interactions, was determined to be 4 ͑1͒Here J is the exchange coupling between nearest-neighbor Co ions in a chain, ⑀ is the parameter that distinguishes the Ising limit (⑀ϭ0) from the Heisenberg limit (⑀ϭ1), and h is an effective ͑staggered͒ field, which arises from exchange mixing and coupling between chains. The Hamiltonian ͑1͒ may also model the case where a nonmagnetic ion ͑Mg͒ is substituted for the magnetic ion ͑Co͒, which gives a distribution of finite length spin chains. Finite length chains are of interest because they allow one to study surface modes with neutron scattering. Moreover, comparison with theory is more rigorous since the full spectrum, S xx (Q,), can be computed exactly for Hamiltonian ͑1͒ in small chains. Nagler et al. 5 measured the spin-wave spectrum of such a dilute one-dimensional chain, CsCo 0.83 Mg 0.17 Cl 3 , with inelastic neutron scattering and carried out a detailed comparison with theoretical results based on such a Hamiltonian. Their results confirmed the necessity of the staggered field. Nonetheless, the calculated spin-wave spectrum at the zone center was in disagreement with experiment, and the relative intensities between the surface mode (ϳJ) and the bulk mode (ϳ2J) were not in quantitative agreement. Furthermore, only two wave vectors were examined, therefore, up until the present, a full experimental study of the spin-wave dispersion has been lacking. Such a dispersion relation was calculated by Ishimura and Shiba ͑IS͒, 7 and it remains an unchallenged prediction relevant to the effective Hamiltonian described above.In this paper, by measuring the spin-wave response for several Q vectors throughout the Brillouin zone, it is shown that a refined calculation of S xx (Q,) quantitatively describes the spin-wave spectrum associated with both the J and the 2J mode, and that the Q dependence of th...