Large diversity of magnetic phases in two-dimensional magnets with spin-orbit coupling and superconductivity
Abstract: We classify the magnetic ground states of a 2D lattice of localized magnetic moments which are coupled to a superconducting substrate with Rashba-spin-orbit coupling. We discover a rich magnetic phase diagram with surprisingly complex structures including 2q-spin-spirals, a 2x2-periodic pattern, and skyrmion lattices, self-consistently, using an effective classical spin Hamiltonian and show that the system hosts non-zero 4-spin interactions. Our in-depth analysis of about ten thousand magnetic configurations becomes feasible using contrastive clustering, a recent advanced unsupervised machine learning technique. This work proposes simple few-band systems for non-collinear magnetic states and stimulates further research on topological effects in their self-consistent electronic structure.
- L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging Research Landscape of Altermagnetism, Phys. Rev. X 12, 040501 (2022).
- A. Fert, V. Cros, and J. Sampaio, Skyrmions on the track, Nat. Nanotechnol. 8, 152 (2013).
- E. Y. Vedmedenko, Dynamics of Bound Monopoles in Artificial Spin Ice: How to Store Energy in Dirac Strings, Phys. Rev. Lett. 116, 077202 (2016).
- A. Kitaev, Anyons in an exactly solved model and beyond, Annals of Physics 321, 2–111 (2006).
- I. Martin and C. D. Batista, Itinerant electron-driven chiral magnetic ordering and spontaneous quantum hall effect in triangular lattice models, Phys. Rev. Lett. 101, 156402 (2008).
- K. Ido and T. Misawa, Many-body chern insulator in the kondo lattice model on a triangular lattice (2024), arXiv:2310.07094 .
- Y. Akagi and Y. Motome, Spin chirality ordering and anomalous hall effect in the ferromagnetic kondo lattice model on a triangular lattice, J. Phys. Soc. Jpn. 79, 083711 (2010).
- Y. Akagi, M. Udagawa, and Y. Motome, Hidden multiple-spin interactions as an origin of spin scalar chiral order in frustrated kondo lattice models, Phys. Rev. Lett. 108, 096401 (2012).
- R. Wieser, E. Y. Vedmedenko, and R. Wiesendanger, Entropy driven phase transition in itinerant antiferromagnetic monolayers, Phys. Rev. B 77, 064410 (2008).
- F. A. Gómez Albarracín and H. D. Rosales, Machine learning techniques to construct detailed phase diagrams for skyrmion systems, Phys. Rev. B 105, 214423 (2022).
- F. Albarracín, Unsupervised machine learning for the detection of exotic phases in skyrmion phase diagrams (2024), arXiv:2404.10943 .
- Y. Nambu, Generalized Hamiltonian Dynamics, Phys. Rev. D 7, 2405 (1973).
- K. Binder and D. Heermann, Monte Carlo Simulation in Statistical Physics (Springer, 2002).
- E. Y. Vedmedenko, Feature Article: Influence of the lattice discreteness on magnetic ordering in nanostructures and nanoarrays, Phys. Status Solidi B 244, 1127 (2007).
- E. A. Kearsley and J. T. Fong, Linearly independent sets of isotropic cartesian tensors of ranks up to eight, J. Res. Natl. Bur. Stand., Sect. B 79B, 49 (1975).
- D. P. Kingma and J. Ba, Adam: A method for stochastic optimization (2014), arXiv:1412.6980 .
- Additional material can be found at: https://timmatthies.github.io/latentspaceexplorer/.
- L. Van der Maaten and G. Hinton, Visualizing Data using t-SNE, J. Mach. Learn. Res. 9, 2579 (2008).
- B. Berg and M. Lüscher, Definition and Statistical Distributions of a Topological Number in the Lattice O(3) σ𝜎\sigmaitalic_σ-Model, Nucl. Phys. B. 190, 412 (1981).
- A. Bogdanov and D. Yablonskii, Thermodynamically stable “vortices” in magnetically ordered crystals. The mixed state of magnets, Zh. Eksp. Teor. Fiz 95, 178 (1989).
- B. Braunecker and P. Simon, Interplay between Classical Magnetic Moments and Superconductivity in Quantum One-Dimensional Conductors: Toward a Self-Sustained Topological Majorana Phase, Phys. Rev. Lett. 111, 147202 (2013).
Paper Prompts
Sign up for free to create and run prompts on this paper.
