Exact Ground States and Domain Walls in One Dimensional Chiral Magnets

TL;DR

This paper exactly characterizes the phase diagram of a one-dimensional chiral magnet with Dzyaloshinskii-Moriya interaction, revealing spiral, ferromagnetic, and domain wall solutions, and analyzing phase transitions between them.

Contribution

It provides an exact analytical solution for the phase structure, including spiral and domain wall states, in a one-dimensional chiral magnet with specific interactions and potential terms.

Findings

Existence of a continuum of spiral solutions with varying periods.

Divergence of spiral period at phase boundary, leading to domain wall solutions.

Second-order phase transitions between different magnetic phases.

Abstract

We determine exactly the phase structure of a chiral magnet in one spatial dimension with the Dzyaloshinskii-Moriya (DM) interaction and a potential that is a function of the third component of the magnetization vector, $n_3$, with a Zeeman (linear with the coefficient $B$) term and an anisotropy (quadratic with the coefficient $A$) term, constrained so that $2A\leq \vert B\vert$. For large values of potential parameters $A$ and $B$, the system is in one of the ferromagnetic phases, whereas it is in the spiral phase for small values. In the spiral phase we find a continuum of spiral solutions, which are one-dimensionally modulated solutions with various periods. The ground state is determined as the spiral solution with the lowest average energy density. As the phase boundary approaches, the period of the lowest energy spiral solution diverges, and the spiral solutions become domain wall solutions with zero energy at the boundary. The energy of the domain wall solutions is positive in the homogeneous phase region, but is negative in the spiral phase region, signaling the instability of the homogeneous (ferromagnetic) state. The order of the phase transition between spiral and homogeneous phases and between polarized ($n_3=\pm 1$) and canted ($n_3\not=\pm 1$) ferromagnetic phases is found to be second order.