Terahertz anomalous Hall effect in magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$

In the vast landscape of modern physics, a special class of materials known as topological semimetals has captured the imagination of scientists for their unique ability to conduct electricity in ways that defy ordinary rules. Imagine a crystal where electrons do not simply flow like water in a pipe, but instead behave as if they are massless particles called Weyl fermions, moving in straight lines through a three-dimensional grid. These materials are special because their internal structure forces the electrons to organize around specific points in their energy landscape, known as Weyl nodes. When the symmetry of time is broken within these crystals—meaning the material behaves differently if you were to reverse the flow of time—these nodes act as sources and sinks for a hidden geometric property called Berry curvature. This curvature creates a powerful, built-in sideways push for moving electrons, a phenomenon known as the anomalous Hall effect, which generates a transverse voltage without any external magnetic field. Understanding how these materials respond to light, particularly at low energies, is crucial because it reveals the fundamental nature of these electron movements and could pave the way for new technologies in computing and sensing.

A team of researchers has now turned their attention to a specific magnetic crystal, Co3Sn2S2, which is celebrated for exhibiting an exceptionally strong version of this anomalous Hall effect. While previous studies had confirmed the existence of this giant effect in direct current, the behavior of the material when hit with light at lower energies remained a mystery. To solve this, the scientists combined precise measurements using terahertz radiation—a form of light with a frequency between microwaves and infrared—with a simplified theoretical model designed to mimic the material's electronic structure. By shining this specific type of light on the crystal and observing how it rotated the polarization of the light as it passed through, the team was able to probe the low-energy excitations of electrons near the Weyl nodes. Their work provides a clear, transparent explanation for the observed optical phenomena, linking the rotation of light directly to the separation of the Weyl nodes in momentum space, a fundamental property of the crystal's internal geometry.

The researchers focused on the intrinsic optical response of the material, meaning they looked at how the electrons moved on their own without the help of an external magnetic field. They found that the material's ability to conduct electricity along the direction of the light and its ability to conduct electricity sideways are deeply connected to the distance between the Weyl nodes. In their experiments, they measured how the real part of the longitudinal conductivity changed with frequency at various temperatures, ranging from extremely cold to moderately warm. The data showed a clear pattern that matched their theoretical predictions, confirming that the material's behavior is dominated by the movement of electrons close to the chemical potential, a specific energy level within the crystal. By adjusting the parameters in their model to fit the experimental data, they determined that the separation between the Weyl nodes is approximately 0.4 inverse angstroms, a value that aligns well with previous theoretical estimates.

A key discovery in this study was the behavior of the transverse conductivity, which is responsible for the anomalous Hall effect. The researchers observed that the real part of this conductivity remains nearly constant at very low frequencies, a direct result of the fixed separation between the Weyl nodes. As the frequency of the light increased, the conductivity rose to a peak when the energy of the photons matched twice the chemical potential, which was measured at 43 millielectronvolts. Beyond this point, the conductivity dropped and even changed sign, becoming negative at higher frequencies. This complex behavior, including the specific way the imaginary part of the conductivity vanished at low frequencies and then rose sharply, was successfully reproduced by their model. The team also noted that the scattering of electrons, which is influenced by temperature and impurities, played a critical role in shaping these curves, with higher temperatures leading to broader and less distinct features in the data.

The study also examined the Faraday rotation, which is the angle by which the plane of polarized light rotates as it passes through the magnetic material. The researchers found that this rotation angle increased with frequency in the low-energy range, a trend that was consistent across different temperatures. They explained this by noting that while the sideways conductivity remained relatively steady, the conductivity along the direction of the light decreased as the frequency rose, causing the ratio between the two to grow. Furthermore, as the temperature increased, the scattering of electrons changed in a way that reduced the longitudinal conductivity even further, leading to a larger rotation angle. This non-uniform temperature dependence highlighted the delicate interplay between the material's doping profile and the rate at which electrons scatter off phonons, or vibrations in the crystal lattice.

By combining these experimental observations with a physically intuitive model, the researchers were able to place strict constraints on the material's parameters, such as the chemical potential and the energy separation between the Weyl nodes. Their work confirms that the giant magneto-optical response in Co3Sn2S2 is an intrinsic property arising from the topological nature of its electronic band structure. The study does not merely suggest a connection; it provides a robust quantitative match between theory and experiment, demonstrating that the separation of Weyl nodes is the primary driver of the observed effects. This approach offers a powerful method for understanding other magnetic Weyl semimetals, suggesting that similar low-energy models can be used to decode the complex optical signatures of these exotic materials. The findings reinforce the idea that the unique properties of these crystals are not accidental but are rooted in the fundamental geometry of their quantum states, opening new avenues for exploring the potential of topological materials in future technologies.