Towards a universal phase diagram of planar chiral magnets

Bernd Schroers; Martin Speight; Thomas Winyard

doi:10.48550/arXiv.2512.19590

Towards a universal phase diagram of planar chiral magnets

Bernd Schroers
, Martin Speight
, Thomas Winyard

Mathematics

Research output: Working paper/Preprint › Preprint

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Abstract

In planar chiral magnets, the competition of the positive definite Heisenberg exchange and Zeeman energies with the indefinite Dzyaloshinskii-Moriya interaction (DMI) energy allows for the possibility of negative energy ground states, and leads to an intricate dependence of the ground states on the parameters of the theory. In this paper, we consider arbitrary spiralization tensors for the DMI interaction and arbitrary directions for the external magnetic field, and study the nature of the ground states in this parameter space, using a combination of analytical and numerical methods. Classifying ground states by their symmetry into ferromagnetic (invariant under under arbitrary translations in the plane), spiral (invariant under arbitrary translations in one direction) and skyrmion lattice ground states (invariant under a two dimensional lattice group), we give a complete description of the phase diagram of this class of theories.

Original language	English
Publisher	arXiv
Number of pages	31
DOIs	https://doi.org/10.48550/arXiv.2512.19590
Publication status	Published - 22 Dec 2025

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Name	arXiv
Publisher	Cornell University

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PreprintSubmitted manuscript, 3.67 MBLicence: CC BY

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title = "Towards a universal phase diagram of planar chiral magnets",

abstract = "In planar chiral magnets, the competition of the positive definite Heisenberg exchange and Zeeman energies with the indefinite Dzyaloshinskii-Moriya interaction (DMI) energy allows for the possibility of negative energy ground states, and leads to an intricate dependence of the ground states on the parameters of the theory. In this paper, we consider arbitrary spiralization tensors for the DMI interaction and arbitrary directions for the external magnetic field, and study the nature of the ground states in this parameter space, using a combination of analytical and numerical methods. Classifying ground states by their symmetry into ferromagnetic (invariant under under arbitrary translations in the plane), spiral (invariant under arbitrary translations in one direction) and skyrmion lattice ground states (invariant under a two dimensional lattice group), we give a complete description of the phase diagram of this class of theories.",

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N2 - In planar chiral magnets, the competition of the positive definite Heisenberg exchange and Zeeman energies with the indefinite Dzyaloshinskii-Moriya interaction (DMI) energy allows for the possibility of negative energy ground states, and leads to an intricate dependence of the ground states on the parameters of the theory. In this paper, we consider arbitrary spiralization tensors for the DMI interaction and arbitrary directions for the external magnetic field, and study the nature of the ground states in this parameter space, using a combination of analytical and numerical methods. Classifying ground states by their symmetry into ferromagnetic (invariant under under arbitrary translations in the plane), spiral (invariant under arbitrary translations in one direction) and skyrmion lattice ground states (invariant under a two dimensional lattice group), we give a complete description of the phase diagram of this class of theories.

AB - In planar chiral magnets, the competition of the positive definite Heisenberg exchange and Zeeman energies with the indefinite Dzyaloshinskii-Moriya interaction (DMI) energy allows for the possibility of negative energy ground states, and leads to an intricate dependence of the ground states on the parameters of the theory. In this paper, we consider arbitrary spiralization tensors for the DMI interaction and arbitrary directions for the external magnetic field, and study the nature of the ground states in this parameter space, using a combination of analytical and numerical methods. Classifying ground states by their symmetry into ferromagnetic (invariant under under arbitrary translations in the plane), spiral (invariant under arbitrary translations in one direction) and skyrmion lattice ground states (invariant under a two dimensional lattice group), we give a complete description of the phase diagram of this class of theories.

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M3 - Preprint

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BT - Towards a universal phase diagram of planar chiral magnets

PB - arXiv

ER -

Towards a universal phase diagram of planar chiral magnets

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