Thermodynamic theory of square skyrmion lattice in tetragonal frustrated antiferromagnets

TL;DR

This paper develops a thermodynamic model for square skyrmion lattices in tetragonal frustrated antiferromagnets, revealing how various interactions stabilize these structures and align with experimental phase diagrams.

Contribution

It introduces a comprehensive analytical framework incorporating multiple interactions to explain and predict skyrmion lattice stability in tetragonal antiferromagnets.

Findings

Square skyrmion lattice stability is enhanced by combined interactions.

The model reproduces key features of experimental phase diagrams.

Higher-order harmonics are crucial for skyrmion stabilization.

Abstract

High-temperature part of the phase diagram of tetragonal frustrated antiferromagnets is discussed within the framework of the mean-field approach. Based on recent experimental findings, we generalize previous theoretical studies by considering a model that includes frustrated Heisenberg exchange, biquadratic exchange, magnetodipolar interaction, anisotropic exchange, and single-ion anisotropy. It is analytically demonstrated that a subtle interplay among these interactions results in a variety of phase diagrams in the temperature-magnetic field plane. We argue that one of the proposed diagrams reproduces all crucial features of the phase diagram experimentally observed for~\gdru~compound. Besides magnetodipolar interaction and additional easy-axis contribution, it requires moderate biquadratic exchange. We show that despite the remarkable square skyrmion lattice being stable even if only magnetodipolar interaction/compass anisotropy or biquadratic exchange is included, their ``symbiosis'' allows for greatly enhancing its stability region. It is also demonstrated that higher-order harmonics play an important role in the stabilization of the square skyrmion lattice. The developed analytical approach can be useful for the refinement of the microscopic model parameters when comparing its predictions with experimental findings.