Skyrmion interactions and lattices in chiral magnets: analytical results

Ross, Calum; Sakai, Norisuke; Nitta, Muneto

doi:10.1007/jhep02(2021)095

Cited by 15 publications

(9 citation statements)

References 35 publications

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“…The absolute ground states of the model are, unfortunately, not among these special states. Ross et al [26] extended these efforts beyond the exactly solvable point. They showed that two skyrmions interact via a repulsive potential decaying as a power of the distance.…”

Section: Historical Notementioning

confidence: 99%

Chiral magnetism: a geometric perspective

2021

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We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.

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Section: Historical Notementioning

confidence: 99%

Chiral magnetism: a geometric perspective

2021

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“…In addition, it also opens up interesting ways to study the dynamics of vortex and skyrmion field configurations on spin lattices in various dimensions (for recent approaches, see, e.g., Refs. [51,[66][67][68][69]). We leave this for future work.…”

Section: Discussionmentioning

confidence: 99%

Exploring instantons in nonlinear sigma models with spin-lattice systems

Schenk

Spannowsky

2021

Phys. Rev. B

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Instanton processes are present in a variety of quantum field theories relevant to high energy as well as condensed matter physics. While they have led to important theoretical insights and physical applications, their underlying features often remain elusive due to the complicated computational treatment. Here, we address this problem by studying topological as well as nontopological instantons using Monte Carlo methods on lattices of interacting spins. As a proof of principle, we systematically construct instanton solutions in O(3) nonlinear sigma models with a Dzyaloshinskii-Moriya interaction in (1 + 1) and (1 + 2) dimensions, thereby resembling an example of a chiral magnet. We demonstrate that, due to their close correspondence, Monte Carlo techniques in spin-lattice systems are well suited to describe topologically nontrivial field configurations in these theories. In particular, by means of simulated annealing, we demonstrate how to obtain domain walls, merons, and critical instanton solutions.

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“…[29] that there are subtle contributions from infinity (the boundary) to the energy of the skyrmion (hedgehog) solutions in the case of two-dimensional chiral magnets along the solvable line 2A = B. Subsequently it has been realized that the additional total derivative term in the energy density is needed to make the variational principle well-defined, in deriving the field equations for the skyrmion [31].…”

Section: Boundary Termsmentioning

confidence: 99%

“…In the two dimensional solvable case, the boundary energy functional gives a finite and crucial negative energy contribution to the skyrmion energy. This fact leads to the instability of the polarized ferromagnetic background solution and a phase transition to other phases, such as the skyrmion lattice phase, below the critical value of potential parameters [31].…”

Section: Boundary Termsmentioning

confidence: 99%

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Exact ground states and domain walls in one dimensional chiral magnets

Ross

Sakai

Nitta

2021

J. High Energ. Phys.

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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, n3, with a Zeeman (linear with the coefficient B) term and an anisotropy (quadratic with the coefficient A) term, constrained so that 2A ≤ |B|. 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 (n3 = ±1) and canted (n3 ≠ ±1) ferromagnetic phases is found to be second order.

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Skyrmion interactions and lattices in chiral magnets: analytical results

Cited by 15 publications

References 35 publications

Chiral magnetism: a geometric perspective

Chiral magnetism: a geometric perspective

Exploring instantons in nonlinear sigma models with spin-lattice systems

Exact ground states and domain walls in one dimensional chiral magnets

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