Solitary magnon excitations in a one-dimensional antiferromagnet with Dzyaloshinsky–Moriya interactions

Abstract

We investigate solitary excitations in a model of a one-dimensional antiferromagnet including a single-ion anisotropy and a Dzyaloshinsky–Moriya antisymmetric exchange interaction term. We employ the Holstein–Primakoff transformation, the coherent state ansatz and the time variational principle. We obtain two partial differential equations of motion by using the method of multiple scales and applying perturbation theory. By so doing, we show that the motion of the coherent amplitude must satisfy the nonlinear Schrödinger equation. We give the single-soliton solution.

Tunable Magnon Interactions in a Ferromagnetic Spin-1 Chain

“…Spin excitations in 1D chains have been studied for both ferromagnetic (FM) and antiferromagnetic (AFM) exchange interactions [4,15,18,30]. For an isolated FM spin-1/2 chain with pure Ising interactions, the excitations (|m z = 1/2 → | − 1/2 ) are domain walls.…”

Intrinsic localized spin waves in an antiferromagnetic spin system with next nearest neighbour interactions

“…Nguenang et al [11,12] studied the solitary excitations including the localized and de-localized structures using the coherent state representation. The magnetic system under semiclassical studies [13] involves exchange interactions between spins and spin anisotropy which are intrinsically nonlinear.…”

Localized spin excitations in a site-dependent antiferromagnetic spin system with D-M interaction

“…But the effect of D-M interaction is less spoken in the literature of nonlinear dynamics of AFMs because of the mathematical complexity. Recently, adopting the method of multiple scales and perturbation theory, Lissouck and Nguenang [20] probed the solitary excitations in onedimensional AFM with D-M interaction and obtained the spatial configuration of the spin which proved the existence of the solitary excitations in the system studied.…”

“…a e-mail: lathaisaac@yahoo.com Intrinsic localized modes are spatially localized timeperiodic nonlinear excitations that can occur due to the interplay of nonlinearity and discreteness. In the past few decades, enormous analytical and numerical works have been focused in many classical atomic lattices [20][21][22][23][24] and spin-lattices [25][26][27][28][29][30][31][32] that show the existence of intrinsic localized modes. The elementary excitations out of the ground state of a Heisenberg magnet named spin waves have been inferred for many decades [33].…”