Nonlinear magnetoelastic wave dynamics and field tunable soliton excitations in hexagonal multiferroic media

Abstract

We investigate nonlinear magnetoelastic wave dynamics and electrically tunable soliton excitations in hexagonal multiferroic media. By varying the magnetoelastic coupling strength and using a coupled magnetoelastic-ferroelectric continuum model, we found that the system evolves from weakly nonlinear quasiperiodic oscillations to strongly anharmonic yet phase-coherent multimode dynamics. Our results suggest that the dynamics remain bounded and approach distorted limit-cycle behavior rather than chaotic motion despite the enhanced nonlinearity. The excitation spectra and the band dispersion relations reveal that this nonlinear evolution originates from strong magnon-phonon hybridization and coupling-induced renormalization of collective excitation branches, leading to coherent energy exchange among magnetic, elastic, and polarization subsystems. In addition, the coupled dynamics can be reduced to an effective magnetoelastic nonlinear Schrödinger equation and support localized excitations such as bright and dark solitons and Kuznetsov-Ma type breathers. Furthermore, it is found that an external electric field modifies both the effective nonlinear coefficient and the dispersion curvature, enabling continuous control of soliton amplitude, width, and stability. The field also induces a saddle-node bifurcation in the magnetization phase space, defining a critical threshold separating multistable and monostable regimes. Our results establish a theoretical framework for electrically tunable nonlinear spin-lattice excitations and soliton engineering in multiferroic systems.

Figures (9)

• Figure 1: Spatiotemporal evolution of (a,g) the magnetization $m(x,t)$, (c,i) the elastic displacement $u(x,t)$, and (e,k) the polarization $p(x,t)$ for $B_{1}=0.01$ (left panel) and $B_{1}=1$ (right panel). The corresponding phase portraits are shown in (b,h), (d,j), and (f,l), respectively.
• Figure 2: Power spectra of the elastic displacement, magnetization, and polarization modes. for and strong magnetoelastic coupling. The top row shows the frequency-domain response in the weak ($B_1=0.1$) while the bottom row corresponds to the strong ($B_1=1.0$) magnetoelastic coupling regime.
• Figure 3: Dispersion relations of the coupled magnetoelastic system. The top and middle rows show the three-dimensional band surfaces $\omega(\mathbf{k})$ of the magnetic, elastic, and ferroelectric modes in the Brillouin zone for different magnetoelastic coupling strengths $B_1$. The bottom row shows one-dimensional cuts along $k_x$ for $B_1=0.1$ (solid line) and $B_1=1.0$ (dashed line).
• Figure 4: Streamlines of the phase portrait in the $(M,\dot{M})$ plane for (a) $E_0=0$ and (b) $E_0=1$. Stable fixed points are indicated by yellow circles, and the unstable saddle point by red circles. (c) Variation of effective potential $V(M)$ with $M$ for $E_0=0$ (blue) and $E_0=1$ (orange). (d) Bifurcation diagram of the fixed points $M^\ast$ as a function of $E_0$, showing the field-driven annihilation and creation of stable (yellow) and unstable (red) solutions.
• Figure 5: (a) Spatial profiles of the normalized strain component $\tilde{\varepsilon}_{xx}(\xi)$ associated with the soliton for different electric-field strengths $E_0=0$, $0.5$, and $1$. (b) Peak strain amplitude $\tilde{\varepsilon}_{\mathrm{peak}}$ as a function of the electric field $E_0$. (c) Total soliton energy $E_{\mathrm{total}}$ as a function of the soliton width $w$ for different electric fields and (d) Electric field dependence of the nonlinear coefficient $\beta$.