Existence of localized modes in a frustrated ferromagnetic spin chain with added biquadratic interaction

The analytical study on the 1D frustrated ferromagnetic spin chain with added biquadratic exchange interaction by means of quasi -discrete multiple scale approximation is addressed in this report. It is found that the dynamics of the frustrated spin system is governed by the nonlinear Schrodinger (NLS) equation which admits bright and dark localized modes. We analyze the play roles of biquadratic exchange interaction and frustration parameter on the appearance of the bright and dark solitonic profile. The inclusion of the biquadratic interaction significantly increases the number of unstable/stable domain in the whole Brillouin zone. The linear dispersion curves also shift drastically and the value of the critical point of the frustration parameter changes accordingly. We invoke the extended rational sinh-cosh function method to find the exact soliton solution aided with symbolic computation. The set of soliton solution obtained produces the dark type soliton which depends on the strength of the biquadratic exchange interaction. We further employ an elegant algebraic Hirota bilinearization method to construct multisoliton solution. More interestingly, we explore the elastic collision of two bright solitons in the frustrated spin system which can be exploited for high density data transfer in quantum computing. The impact of biquadratic exchange interaction is found to be crucial in frustrated compounds with edge sharing copper oxides and it strongly favors for stability.