Instantons in chiral magnets

Abstract

We exhaustively construct instanton solutions and elucidate their properties in one-dimensional anti-ferromagnetic chiral magnets based on the O(3) nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.

Gauged sigma models and magnetic Skyrmions

“…This result was derived in [8] for |Q| = 1 in more general rank one models. Example solutions of solvable rank one models and their properties are discussed in [10] and also [16]. We note that a similar reformulation in terms of a flat gauge field was recently applied to a rather different ferromagnetic model in [17].…”

Exploring instantons in nonlinear sigma models with spin-lattice systems

“…However, in fact, as the field takes values on a sphere, there exists a mapping that transforms (1) into a much simpler theory. As was pointed out in [26], the DM interaction can be completely removed by a simple rotation in field space,…”

“…As a first example, let us consider solitonic field configurations of a Lagrangian field theory that models the continuum limit of a one-dimensional chiral magnet evolving in time. This is given by the O(3) nonlinear sigma model in Euclidean space-time (see also [26]),…”

“…[25]. With respect to our example of the O(3) nonlinear sigma model of a chiral magnet, a set of instanton solutions have already been derived for a spin chain in (1 + 1) dimensions [26]. These will serve as a test bed to validate our approach using MC simulations.…”

Skyrmion interactions and lattices in chiral magnets: analytical results

“…Some further studies of BPS magnetic skyrmions and instantons in chiral magnets have been made in refs. [27][28][29].…”