Angular Modulations in Magnetic Torque Induced by Phase Transitions in the Triangular Supersolid $2H$-AgNiO$_2$

Magnetism is often thought of as a simple force, the invisible pull that makes a compass needle point north or holds a refrigerator note in place. But in the world of solid materials, magnetism can become far more complex, behaving like a crowded room where every person tries to face a different direction at once. This is known as "frustration," a state where the rules of the material prevent the tiny magnetic spins inside from settling into a single, comfortable order. When scientists add a specific kind of crystal structure called a triangular lattice to this mix, the frustration becomes even more intense. In these systems, the spins can sometimes settle into exotic, hybrid states that break the usual rules of physics. One such rare state is called a "supersolid." In a normal solid, atoms are locked in a rigid grid. In a supersolid, the material keeps that rigid grid but also allows its internal magnetic parts to flow freely, as if the solid were a liquid at the same time. Finding and understanding these states is difficult because they are fragile and require very specific conditions to exist, but they offer a glimpse into how nature organizes itself under extreme pressure.

Researchers at the University of Oxford, working with colleagues in the United States and Germany, have taken a closer look at a material called 2H-AgNiO2 to see if it can host these mysterious supersolid states. This material is unique because it is a metal that contains a specific arrangement of nickel atoms. Inside, the nickel atoms form two distinct groups: some are stuck in place, acting like fixed magnets, while others move freely through the crystal like a sea of electrons. The fixed magnets sit on a triangular grid, creating the perfect environment for magnetic frustration. The team wanted to see how this material behaves when they apply a strong magnetic field and slowly rotate the direction of that field. They used a technique called torque magnetometry, which measures how much a material twists when placed in a magnetic field. By rotating the sample in a field as strong as 45 Tesla—more than a million times stronger than the Earth's magnetic field—they could map out exactly how the internal magnetic order changed as the field direction shifted.

The researchers discovered that the material's response to the magnetic field was far more intricate than expected. When they rotated the field near a specific "easy" direction, the twisting force they measured did not change smoothly. Instead, it developed a jagged, sawtooth pattern. This shape is a clear sign that the material's internal magnetic structure is highly sensitive to the direction of the field. As they cooled the material down to just above absolute zero, they found that this sawtooth behavior became more pronounced, indicating that the magnetic order was becoming more rigid and complex. However, the most surprising discovery happened near a temperature of 19 Kelvin. Close to this point, the smooth twisting signal suddenly developed an extra, unexpected wiggle. This new modulation appeared only when the magnetic field was strong and the temperature was just right, suggesting that the material was undergoing a subtle shift between different magnetic phases that had not been seen before.

To make sense of these twisting signals, the team built a computer model of the material's magnetic spins. They simulated how these spins would behave under different conditions, using a simplified version of the material that focused on the fixed magnetic atoms. The simulations confirmed that the jagged sawtooth pattern was caused by the magnetic field forcing the spins to cross over different boundaries between ordered states. The model showed that as the field rotated, the material was switching between a standard magnetic order and a more complex, canted state where the spins lean at an angle. The extra wiggle found near 19 Kelvin was also explained by the model: it represented a transition between the standard order and a different, more fluid magnetic state that only exists at higher temperatures. The researchers found that the experimental data and the computer simulations matched up very well, particularly in how the material responded when the field was tilted away from its preferred direction.

One of the key findings of the study is that the material's behavior is incredibly sensitive to the angle of the magnetic field. When the field was aligned perfectly with the easy direction, the material showed four distinct changes in its magnetic state as the field strength increased. However, as soon as the field was tilted even slightly, two of those changes disappeared, leaving only two. This tells us that the exotic states the researchers were looking for are very delicate; they only exist when the magnetic field is pointing in a very specific direction. The study also clarified the role of the moving electrons in the material. While previous theories suggested that these moving electrons might be the main cause of the strange behavior, the new results show that the fixed magnetic atoms are sufficient to explain most of what was observed. The moving electrons likely play a supporting role, but the core story of the supersolid phases can be told by looking at the fixed spins alone.

The work provides a robust example of how these supersolid magnetic orders can be detected and understood. By combining precise measurements with detailed computer models, the team was able to construct a map of the material's magnetic phases. This map shows exactly where the material switches from one state to another as the magnetic field changes in strength and direction. The researchers did not claim to have solved the entire mystery of supersolids, nor did they suggest immediate applications for this material. Instead, they provided a clear, detailed picture of how a specific, real-world material behaves under extreme conditions. Their findings confirm that 2H-AgNiO2 is a rich system for studying these complex magnetic phenomena, offering a reliable platform for future experiments. The study demonstrates that by carefully watching how a material twists in a magnetic field, scientists can uncover the hidden, shifting landscapes of quantum matter that lie beneath the surface.