Multiple-q states and skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields (1109.6161v2)

Abstract: Ordering of the frustrated classical Heisenberg model on the triangular-lattice with an incommensurate spiral spin structure is studied under magnetic fields by means of a mean-field analysis and a Monte Carlo simulation. Several types of multiple-q states including the "skyrmion-lattice" state is observed in addition to the standard single-q state. In contrast to the Dzyaloshinskii-Moriya interaction driven system, the present model allows both skyrmions and anti-skyrmions, together with a new thermodynamic phase where skyrmion and anti-skyrmion lattices form a domain state.

• The paper demonstrates that multiple-q states, including a triple-q skyrmion lattice, emerge in the triangular Heisenberg antiferromagnet under magnetic fields.
• The authors employ mean-field analysis and Monte Carlo simulations to analyze phase transitions among single-q, double-q, and triple-q states with temperature variations.
• Findings suggest that skyrmion lattices can form without Dzyaloshinskii-Moriya interactions, opening new avenues for spintronic applications in frustrated magnets.

Multiple-$q$ States and Skyrmion Lattice in Triangular-Lattice Heisenberg Antiferromagnets

This research provides a comprehensive study of the classical Heisenberg antiferromagnet model on a triangular lattice, exploring its behavior under external magnetic fields. The authors, Tsuyoshi Okubo, Sungki Chung, and Hikaru Kawamura, utilize both mean-field analysis and Monte Carlo simulation techniques to investigate the emergence of multiple-$q$ states and skyrmion lattice structures, which appear due to geometric frustration and competition between nearest and further-neighbor interactions.

Overview and Methodology

The study focuses on two specific models, the $J_1$-$J_3$ and $J_1$-$J_2$ models, where the incommensurate spiral structures are stabilized by ferromagnetic nearest-neighbor interactions ($J_1$) and antiferromagnetic further-neighbor interactions ($J_3$ or $J_2$). The Hamiltonian of the system is given by:

$$\mathcal{H}= -J_1\sum_{\left\langle i,j \right\rangle}\bm{S}_i\cdot\bm{S}_j -J_{2,3}\sum_{\langle\langle i,j \rangle\rangle}\bm{S}_i\cdot\bm{S}_j -H\sum_i S_{i,z}$$

A detailed mean-field analysis reveals that, upon incorporating temperature, several configurations can emerge. These configurations are classified into single-$q$, double-$q$, and triple-$q$ states, characterized by the wavevectors involved in the spin arrangements. Crucially, the triple-$q$ state exhibits a skyrmion lattice, a vortex-like topological structure known to appear in chiral magnets.

Numerical Results and Observations

The Monte Carlo simulations validate the presence of multiple-$q$ states at finite temperatures. The phase diagrams produced in the study reveal that the single-$q$ state is predominantly stable at low temperatures, whereas multiple-$q$ states like the double-$q$ and triple-$q$ states gain stability at intermediate temperatures and specific magnetic field intensities. A key finding is that the skyrmion lattice, appearing in the triple-$q$ state, is produced without the presence of Dzyaloshinskii-Moriya interactions, which are typically responsible for stabilizing skyrmions in chiral magnets.

In addition, the study identifies a novel "Z-phase" where domains of skyrmions and anti-skyrmions coexist, distinguished by a broken mirror symmetry. This phase is noteworthy because it suggests possible conditions for real-world manifestations of skyrmions in frustrated magnetic systems.

Implications and Future Directions

This work shows that skyrmion and multiple-$q$ states can emerge from purely symmetric exchange interactions, expanding the scope of materials that can exhibit skyrmionic behaviors beyond those with inherent chiral interactions. The realization of skyrmions in frustrated magnets could pave the way for novel spintronic devices that utilize the high density and precise arrangement of skyrmions. The implications for applying external fields to control these states suggest potential developments in data storage technologies and others where magnetic textures can be manipulated.

Future studies could explore quantum effects that were not accounted for in this classical model, as well as investigate the effect of disorder and other lattice geometries that may further diversify the phase space of skyrmion-hosting materials. Additionally, examining the interplay between skyrmions and electronic properties in such systems is warranted to fully exploit their technological capabilities.