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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.
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We study two-body interactions of magnetic skyrmions on the plane and apply them to a (mostly) analytic description of a skyrmion lattice. This is done in the context of the solvable line, a particular choice of a potential for magnetic anisotropy and Zeeman terms, where analytic expressions for skyrmions are available. The energy of these analytic single skyrmion solutions is found to become negative below a critical point, where the ferromagnetic state is no longer the lowest energy state. This critical value is determined exactly without the ambiguities of numerical simulations. Along the solvable line the interaction energy for a pair of skyrmions is repulsive with power law fall off in contrast to the exponential decay of a purely Zeeman potential term. Using the interaction energy expressions we construct an inhomogeneous skyrmion lattice state, which is a candidate ground states for the model in particular parameter regions. Finally we estimate the transition between the skyrmion lattice and an inhomogeneous spiral state.
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. 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 then 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 ($n_3 ot=pm 1$) ferromagnetic phases is found to be second order.
We develop the effective field theoretical descriptions of spin systems in the presence of symmetry-breaking effects: the magnetic field, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. Starting from the lattice description of spin systems, we show that the symmetry-breaking terms corresponding to the above effects can be incorporated into the effective field theory as a combination of a background (or spurious) $SO(3)$ gauge field and a scalar field in the symmetric tensor representation, which are eventually fixed at their physical values. We use the effective field theory to investigate mode spectra of inhomogeneous ground states, with focusing on one-dimensionally inhomogeneous states, such as helical and spiral states. Although the helical and spiral ground states share a common feature of supporting the gapless Nambu-Goldstone modes associated with the translational symmetry breaking, they have qualitatively different dispersion relations: isotropic in the helical phase while anisotropic in the spiral phase. We also discuss the magnon production induced by an inhomogeneous magnetic field, and find a formula akin to the Schwinger formula. Our formula for the magnon production gives a finite rate for antiferromagnets, and a vanishing rate for ferromagnets, whereas that for ferrimagnets interpolates between the two cases.
Magnetic singularities, also known as magnetic monopoles or Bloch points, represent intriguingphenomena in nanomagnetism. We show that a pair of coupled Bloch points may appear as alocalized, stable state in cubic chiral magnets. Detailed analysis is presented of the stability of suchobjects in the interior of crystals and in geometrically confined systems.
In chiral magnets a magnetic helix forms where the magnetization winds around a propagation vector $mathbf{q}$. We show theoretically that a magnetic field $mathbf{B}_{perp}(t) perp mathbf{q}$, which is spatially homogeneous but oscillating in time, induces a net rotation of the texture around $mathbf{q}$. This rotation is reminiscent of the motion of an Archimedean screw and is equivalent to a translation with velocity $v_{text{screw}}$ parallel to $mathbf{q}$. Due to the coupling to a Goldstone mode, this non-linear effect arises for arbitrarily weak $mathbf{B}_{perp}(t) $ with $v_{text{screw}} propto |mathbf{B}_{perp}|^2$ as long as pinning by disorder is absent. The effect is resonantly enhanced when internal modes of the helix are excited and the sign of $v_{text{screw}}$ can be controlled either by changing the frequency or the polarization of $mathbf{B}_{perp}(t)$. The Archimedean screw can be used to transport spin and charge and thus the screwing motion is predicted to induce a voltage parallel to $mathbf{q}$. Using a combination of numerics and Floquet spin wave theory, we show that the helix becomes unstable upon increasing $mathbf{B}_{perp}$ forming a `time quasicrystal which oscillates in space and time for moderately strong drive.
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