Pressure-correlation phase diagram unraveling quantum phase transitions in altermagnetic $\epsilon$-FeOOH and realization of piezo-anomalous Hall effect

Deep within the Earth, under crushing weights of rock and heat, minerals behave in ways that seem impossible at the surface. They can shrink, change their internal structure, or even alter how their tiny magnetic parts align. This is the realm of high-pressure physics, a field dedicated to understanding how matter transforms when squeezed. Among the most fascinating materials in this domain are iron oxyhydroxides, minerals that contain iron, oxygen, and hydrogen. These compounds are not just geological curiosities; they are laboratories for quantum physics. When squeezed, the electrons inside them can shift from one state to another, changing the material from a magnet to a non-magnet, or from an insulator that blocks electricity to a conductor that lets it flow. Scientists have long known that pressure can trigger these changes, but the exact map of how these transitions happen, and what forces drive them, has remained a puzzle.

A team of researchers at the Indian Institute of Technology Madras has now drawn a detailed map of these transformations for a specific mineral called epsilon-FeOOH. By using powerful computer simulations to mimic the effects of extreme pressure, they discovered that this mineral does not just change once or twice as it is squeezed; it undergoes a series of distinct, pressure-driven switches. The study reveals that the mineral passes through three critical pressure points where its fundamental nature flips. At the first critical point, the electrons rearrange themselves, causing the material to switch from a high-spin state, where the magnetic moments are large, to a low-spin state, where they are smaller. This shift is not just a magnetic change; it also alters how the material conducts electricity, moving from one type of insulating behavior to another. At a second critical pressure, the mineral's crystal structure itself changes, shifting from a non-symmetrical arrangement to a perfectly symmetrical one. Finally, at a third critical point, the direction in which the material's internal magnetism points changes again.

What makes this discovery particularly exciting is the connection between these internal changes and a phenomenon known as the anomalous Hall effect. In simple terms, this effect describes how a material can generate a voltage across its width when an electric current flows through it, even without an external magnetic field. Usually, this happens in materials with specific magnetic properties. The researchers found that epsilon-FeOOH is special because it can turn this effect on and off, and even change the direction of the voltage, simply by applying pressure. This happens because the material possesses a unique magnetic order called altermagnetism, where the magnetic spins are arranged in a way that allows for this electrical response under certain conditions. The study shows that by squeezing the mineral to different degrees, one can switch the anomalous Hall effect on at a lower pressure and then rotate its direction at a higher pressure. This creates what the authors call a "piezo-anomalous Hall effect," a way to control electricity using mechanical force.

The researchers arrived at these conclusions by building a virtual model of the mineral and subjecting it to increasing levels of pressure in their calculations. They tracked how the electrons moved, how the atoms shifted, and how the magnetic forces changed. They found that the transition from the high-spin to the low-spin state is driven by a competition between two forces: the crystal field, which is the electric environment created by the surrounding atoms, and the Hund's coupling, a quantum rule that favors electrons having parallel spins. As the pressure increases, the crystal field grows stronger, eventually overpowering the Hund's coupling and forcing the electrons into the low-spin state. This transition occurs at a pressure that depends heavily on how strongly the electrons repel each other. In contrast, the structural change from the non-symmetrical to the symmetrical phase happens at a pressure that is largely unaffected by these electron interactions, occurring at around 45 gigapascals. This structural shift aligns with previous experimental observations, giving the researchers confidence in their model.

The study also clarifies the direction of the material's internal magnetism, known as the spin quantization axis. At low pressures, the magnetic moments point in one direction, but as pressure rises past a specific threshold, they flip to point in a different direction. The researchers found that the material only exhibits the anomalous Hall effect when these magnetic moments point along certain axes. When the moments point along one axis, the effect is zero. When they switch to another axis, the effect turns on. When they switch again at a higher pressure, the direction of the effect rotates. This precise control over the electrical response through mechanical pressure suggests that epsilon-FeOOH could be a unique material for future technologies that rely on manipulating magnetic and electrical properties simultaneously. The work provides a complete phase diagram, showing exactly where these transitions occur and how they are linked to the underlying quantum forces.

One of the key contributions of this research is the validation of recent experimental findings while filling in the missing theoretical gaps. Earlier studies had observed structural changes and hints of spin transitions, but the full picture of how these events relate to each other was unclear. The simulations show that the structural change and the spin crossover happen at different pressures, resolving a long-standing ambiguity. Furthermore, the identification of altermagnetism in both the low-pressure and high-pressure phases of the mineral is a significant finding. Altermagnetism is a recently discovered state of matter that combines features of ferromagnetism and antiferromagnetism, and finding it in a pressure-tunable mineral like this opens new avenues for investigation. The researchers emphasize that while their results are based on computer simulations, they align closely with experimental data, such as the specific pressure at which the structural change occurs and the direction of the spin axis at equilibrium.

The implications of this work extend beyond just understanding a single mineral. It demonstrates that pressure can be used as a precise tool to tune quantum properties in correlated electron systems. The ability to switch on a Hall effect and rotate its direction without changing the material's chemical composition is a rare and valuable capability. The researchers suggest that this piezo-anomalous Hall effect could be a new mechanism for designing sensors or memory devices that respond to mechanical stress. However, they remain cautious, noting that these findings are currently theoretical and based on the specific conditions modeled in their study. The true test will come from future experiments that can replicate these high-pressure conditions and measure the predicted electrical responses directly. For now, the study offers a clear, detailed map of a complex quantum landscape, showing how the interplay of pressure, electron repulsion, and crystal structure can be harnessed to create new and controllable physical phenomena.