Magnetic polarons in one-dimensional antiferromagnetic chains

We study magnetic polarons in antiferromagnetic chains by using the one-dimensional Anderson-Hasegawa double-exchange discrete model, and find analytically different families of magnetic polaron compactons. To study stability and nontrivial dynamics of the self-trapped magnetic polarons, we generalize the Anderson-Hasegawa model to allow for a finite spin of the lattice, and investigate different types of stationary states with collinear and canted spin structure, revealing the existence of stable nonmobile collinear solutions as well as stable mobile magnetic polarons having a canted structure.

Figure 1

(Color online) Examples of localized magnetic polarons. Shown are the amplitudes of the wave functions $A_n$ and spin subsystem ${\mathbf{S}}_n$ for (a) MF $\left[\frac{2}{1}\right]$; (b) MF $\left[\frac{3}{1}\right]$; (c) SCP $[\circlearrowleft \circlearrowleft \circlearrowleft ]$ for $\alpha =3.5$, $\gamma =0.25$; (d) SCF $[\circlearrowleft \frac{3}{1}\circlearrowleft ]$ for $\alpha =12$.

Figure 2

(Color online) Dependence of the instability growth rate $\mathrm{Re}\left(\lambda \right)$ for (a) MF $\left[\frac{2}{1}\right]$, (b) MF $\left[\frac{3}{1}\right]$, (c) MF $\left[\frac{4}{1}\right]$ vs $\alpha$ for $S=5∕2$ and $N^{\prime }=100$. The insets show the stable mode spectrum $\left[\mathrm{Im}\right(\lambda \left)\right]$ inside the stability window. The panel (d) shows the dependence of the stability window vs $S$ for MFs: the dotted lines (squares) indicate the stability thresholds for $\left[\frac{4}{1}\right]$, the stability area is dashed horizontally; the solid lines (circles) are the same for $\left[\frac{3}{1}\right]$, the stability area is dashed vertically.

Figure 3

(Color online) Stability of the SCP $(S=5∕2)$: (a) instability growth rate vs $\kappa$ (for $N^{\prime }=101$); (b) the profiles of the unstable mode $(\kappa =1.2)$. Lower panels are the visualization of the dynamics of $\mid \psi {\mid }^2$: (c) evolution of the unstable solution induced by the spin-wave scattering ($\kappa =1.2$, $N^{\prime }=501$); (d) example of a stable moving SCP ($\kappa =3$, $N^{\prime }=201$).