Researchers at the University of Texas at Austin have observed a sequence of exotic magnetic phases in an ultrathin material, validating a theoretical model from the 1970s. The experiment involved cooling nickel phosphorus trisulfide to low temperatures, revealing swirling magnetic vortices and a subsequent ordered state. This discovery could inform future nanoscale magnetic technologies.
In a study published in Nature Materials in 2026, physicists led by Edoardo Baldini at the University of Texas at Austin examined the magnetic behavior of an atomically thin sheet of nickel phosphorus trisulfide (NiPS3). The material was cooled to temperatures between -150 and -130 °C, entering a Berezinskii-Kosterlitz-Thouless (BKT) phase. In this phase, magnetic moments form pairs of vortices, one spinning clockwise and the other counterclockwise, confined to a few nanometers laterally and a single atomic layer thick.
The BKT phase is named after Vadim Berezinskii and Nobel laureates J. Michael Kosterlitz and David Thouless, who described such transitions in their 1970s work, earning the 2016 Nobel Prize in Physics. Baldini noted, "The BKT phase is particularly intriguing because these vortices are predicted to be exceptionally robust and confined to just a few nanometers laterally while occupying only a single atomic layer in thickness. Because of their stability and extremely small size, these vortices offer a new route to controlling magnetism at the nanoscale and provide insight into universal topological physics in two-dimensional systems."
As temperatures dropped further, the material transitioned into a six-state clock ordered phase, where magnetic moments align in one of six symmetric directions. This sequence confirms the two-dimensional six-state clock model proposed in the 1970s. Baldini added, "At this stage, our work demonstrates the full sequence of phases expected for the two-dimensional six-state clock model and establishes the conditions under which nanoscale magnetic vortices naturally emerge in a purely two-dimensional magnet."
The research, supported by the National Science Foundation and others, involved co-first authors Frank Y. Gao and Dong Seob Kim, with senior authors Baldini, Allan MacDonald, and Xiaoqin "Elaine" Li. Contributors came from institutions including MIT, Academia Sinica, and the University of Utah. Future efforts aim to stabilize these phases at higher temperatures for potential applications in compact magnetic devices.
