Magnetic response of a highly nonlinear soliton lattice in a monoaxial chiral helimagnet

We present a theory of nonlinear magnetic response of a chiral soliton lattice state in a monoaxial chiral helimagnet under an oscillating magnetic field. The chiral soliton lattice is stabilized by a static magnetic field applied perpendicular to the chiral axis. Just below the critical field strength, where an incommensurate-to-commensurate phase transition occurs, the soliton density becomes quite low and almost isolated $2\pi$ kinks are partitioned by vast ferromagnetic regions. We consider this highly nonlinear regime and demonstrate that internal deformations of each kink give rise to the nonlinear response in this regime.

Figure 1

Formation of the chiral soliton lattice for (a) $H/H_c=0.8$, (b) 0.9, (c) 0.978, and (d) 0.999.

Figure 2

(a) Dependence of $C_0$ and $C_1$ on $H/H_c$. They intersect at $H=H^{*}$. (b) Schematic phase diagram where $H_c$ and $H^{*}$ are indicated as functions of $T$. The narrow region $H^{*}<H<H_c$ is identified with highly nonlinear region.

Figure 3

Spatial profiles of the potentials for (a) the $\phi$ fluctuation, (b) $\theta$ fluctuation, and (c) the gap for the $\theta$ fluctuation, for the limiting case $\kappa \to 1$.

Figure 4

Scale behavior of the amplitude $M_{n0}$ ($n=1,2,3$) with a growth of $L/a_0\sim 2N$. The dotted vertical line marks an onset of applicability of the perturbation analysis. The inset shows the spatial profile of a single kink with $l_0=8/\pi q_0$ being the width of the kink localization.

Figure 5

The inverse double well potential for the WKB analysis.

Figure 6

Spatial profiles of the potential $V\left(z\right)$ (red) for the quasilocalized state, the probability density ${\left|u_0\left(z\right)\right|}^2$ (blue) and the corresponding energy $E_0$ (green) obtained by the Numerov's algorithm.