Exotic clock magnetism observed for the first time in an atomically thin crystal

Mar 03, 2026

Physicists confirmed the full two-dimensional six-state clock model in atomically thin nickel phosphorus trisulfide, observing both the BKT and clock phases.

(Nanowerk News) Physicists have experimentally confirmed a complete sequence of magnetic phase transitions in a two-dimensional material, fully realizing a theoretical model of clock magnetism that was first proposed nearly five decades ago. The discovery, reported in Nature Materials (“Six-state clock physics in an atomically thin antiferromagnet”), could open pathways toward ultracompact magnetic technologies operating at the nanoscale.

Key Findings

A team led by physicists at the University of Texas at Austin worked with nickel phosphorus trisulfide (NiPS3), a van der Waals antiferromagnet that can be exfoliated down to a single atomic layer. When the researchers cooled an atomically thin sheet of this material to temperatures between approximately minus 150 and minus 130 degrees Celsius, it entered the BKT phase, a state in which the magnetic moments of individual atoms arrange themselves into swirling vortex patterns. These vortices form in bound pairs that wind in opposite directions, one clockwise and one counterclockwise. When researchers at UT Austin coaxed an atomically thin sheet of nickel phosphorus trisulfide to enter a special magnetic phase, called the BKT phase, the magnetic orientations of individual atoms formed swirling patterns called vortices. (Illustration: Ella Maru Studios) The BKT transition is named after the theorists Vadim Berezinskii, J. Michael Kosterlitz, and David Thouless. Kosterlitz and Thouless received the 2016 Nobel Prize in Physics for their theoretical description of this class of topological phase transition. While the BKT phase and the ordered phase that follows it at lower temperatures had each been observed individually in prior experiments, no study had demonstrated both transitions occurring in sequence within a single two-dimensional system. Edoardo Baldini, assistant professor of physics at the University of Texas at Austin and leader of the study, noted that the magnetic vortices in the BKT phase are predicted to be exceptionally stable while remaining confined to extremely small dimensions, just a few nanometers in lateral extent within a single atomic layer. This combination of robustness and miniature scale makes them attractive candidates for controlling magnetism at the nanoscale and for probing universal topological physics in two-dimensional systems. As the material was cooled further below the BKT regime, it transitioned into a six-state clock ordered phase. In this state, the magnetic moments of individual atoms lock into one of six discrete orientations related by the crystal symmetry. The observation of both phases in sequence establishes the first complete experimental realization of the two-dimensional six-state clock model, confirming the theoretical predictions made in the 1970s about how magnetic ordering develops in strictly two-dimensional systems. Baldini said the work demonstrates the full progression of phases expected under the six-state clock model and establishes the conditions under which nanoscale magnetic vortices naturally form in a purely two-dimensional magnet. Future research will focus on identifying material properties that could stabilize these magnetic phases at progressively higher temperatures, potentially reaching room temperature. The current observation provides the experimental baseline for those efforts. The results also suggest that a broader family of two-dimensional magnetic materials may harbor unexplored magnetic phases beyond those found in NiPS3. This could open new directions both for fundamental physics research and for the development of nanoscale device concepts based on topological magnetic states. The three senior authors, Baldini, Allan MacDonald, and Xiaoqin Li, are all physicists at the University of Texas at Austin and members of the Texas Quantum Institute, which Li co-directs. The co-first authors are Frank Y. Gao, a postdoctoral fellow in physics at the University of Texas at Austin and incoming assistant professor of chemistry at the University of Wisconsin-Madison, and Dong Seob Kim, a former graduate student now at Columbia University. Additional contributors came from the Massachusetts Institute of Technology, Academia Sinica, and the University of Utah.