Physicists at The University of Texas at Austin have experimentally confirmed a decades-old theory describing how magnetism behaves in ultra-thin materials.
By cooling an atomically thin crystal of nickel phosphorus trisulfide, or NiPS3, the team observed a full sequence of exotic magnetic phases predicted in the 1970s but never fully demonstrated in a single system.
The breakthrough centers on two distinct magnetic transitions that occur as the material is cooled toward extremely low temperatures.
While each transition had been seen independently in past experiments, researchers had never captured both in succession, completing the theoretical picture.
The experiments were carried out on sheets of NiPS3 just one atom thick. As the temperature dropped to between –150 and –130 C, the material entered a rare state known as the Berezinskii–Kosterlitz–Thouless, or BKT, phase.
In this state, atomic magnetic moments arrange themselves into swirling vortex patterns.
These vortices form in pairs, rotating in opposite directions, one clockwise and the other counterclockwise. The paired structures remain tightly bound together, creating a unique topological state confined within a single atomic layer.
Swirls at the nanoscale
“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,” said Edoardo Baldini, assistant professor of physics at UT and leader of the research.
“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.”
The BKT phase is named after theorists Vadim Berezinskii and Nobel Prize winners J. Michael Kosterlitz and David Thouless, who described this type of phase transition decades ago. Their work earned the 2016 Nobel Prize in Physics.
As the team cooled the material further, it entered a second magnetic regime known as the six-state clock ordered phase. In this state, the magnetic moments no longer swirl freely but instead lock into one of six symmetry-related directions.
Theory finally realized
“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,” Baldini said.
The six-state clock model has long served as a cornerstone framework in theoretical condensed matter physics.
Proposed in the 1970s, it predicts a specific sequence of magnetic transitions in two-dimensional systems. Until now, no experiment had captured that full progression in a real material.
The findings suggest that other two-dimensional magnetic materials may host similar hidden phases.
Researchers believe the ability to manipulate such nanoscale vortices could eventually support ultracompact devices, potentially shrinking magnetic memory or logic components to unprecedented scales.
Future work will focus on stabilizing these exotic phases at higher temperatures, possibly even approaching room temperature. If achieved, that would move the physics from cryogenic laboratories toward practical technologies.
The study was published in Nature Materials.