Whitham's theory of envelope solitary waves in a monoaxial chiral helimagnet

Nonlinear spin excitations open up new options for microwave signals processing due to their ability to transfer data over large distances without distortions. Our work analyzes on the base of Whitham's theory possible types and stability of such nonlinear excitations in the form of the envelope solitary waves for different phases of the monoaxial chiral helimagnet, namely the conical phase, the forced ferromagnetic phase, and the soliton lattice. We found that only envelope solitons of the dark type can propagate in the monoaxial chiral helimagnet. It is shown that these excitations in the conical phase are stable at any wave numbers but only for the conical angles ${\ensuremath{\theta}}_{0}\ensuremath{\lesssim}{48}^{\ensuremath{\circ}}$ or ${\ensuremath{\theta}}_{0}\ensuremath{\gtrsim}{132}^{\ensuremath{\circ}}$. For the forced ferromagnetic state stable solitary wave of the given wave number $k$ can arise only within the narrow range centered around $q=D/J$, the width of which is determined by the strength of the easy-plane anisotropy $B$, i.e., $|k\ensuremath{-}q|\ensuremath{\le}\sqrt{{q}^{2}+2B}$. In the soliton lattice phase, the quasimomentum domain of the stable solitary waves lies symmetrically inside the magnetic Brillouin zone related to the soliton lattice period, which collapses at the critical field ${H}_{C}$ of the phase transition to the forced ferromagnetic state. This domain of stability rapidly shrinks in size as the field increases so that no stable solitary waves are possible above the threshold value $\ensuremath{\sim}0.48{H}_{C}$.