Magnetic excitations in quasi-one dimensional helimagnets: Magnon decays and in uence of the inter-chain interactions

TL;DR

This paper develops a unified spin-wave expansion approach to study magnetic excitations, magnon decays, and inter-chain effects in quasi-one-dimensional helimagnets, revealing complex quantum fluctuation phenomena and providing analytical tools for experimental analysis.

Contribution

It introduces a comprehensive torque equilibrium spin-wave framework to analyze magnon decay and spin Casimir effects in frustrated quasi-one-dimensional systems with inter-chain couplings.

Findings

Magnon decay effects significantly modify the excitation spectrum.

Spin Casimir effects alter the ordering vector and sublattice magnetization.

The developed analytical structure factor aids experimental neutron scattering analysis.

Abstract

We present a comprehensive study of the magnetic properties of the long-range ordered quasi-one dimensional $J_{1}$-$J_{2}$ systems with a newly developed torque equilibrium spin-wave expansion approach, which can describe the spin Casimir and magnon decay effects in a unified framework. While the framework does not lose the generality, our discussion will be restricted to two representative types of inter-chain coupling systems: $J_{3}$- or $J_{4}$-system respectively. In spite of the long-range spiral order, the dynamical properties of these systems turn out to be highly nontrivial due to the incommensurate noncollinear spin configuration and the strong quantum fluctuation effects enhanced by the frustration and low-dimensionality. Both the systems show prominent spin Casimir effects induced by the vacuum fluctuation of the spin waves and related modification of the ordering vector, Lifshitz point's position and sublattice magnetization. Significant and spontaneous magnon decay effects are manifested in the quantum corrections to the excitation spectrum. By adjusting the strength of magnetic anisotropy and varying the approximation scheme, it is revealed that these striking distinct features are quite robust and have deep connection with both the spin Casimir and the magnon decay effects. Thus these special consequences of the inter-chain coupling on the spin wave dynamics may be served as a set of probes for different types of inter-chain couplings in experiments. At last, to guide experimental measurements such as inelastic neutron scattering in realistic materials and complement our theoretical framework, we develop the analytical theory of the dynamical structure factor within the torque equilibrium formulism and provide the explicit results of the quasi-one dimensional $J_{1}$-$J_{2}$ systems.