In-plane anomalous and third-harmonic Hall response in an easy-plane trigonal magnet

Electricity flowing through a wire usually moves in a straight line, but under the right conditions, it can be forced to turn. In the world of physics, this sideways movement is known as the Hall effect. When a magnetic field is applied to a material carrying an electric current, the moving electrons are pushed to one side, creating a voltage across the width of the material. For decades, scientists have studied this phenomenon in materials where the magnetic field points straight up or down, perpendicular to the flat surface of the sample. However, a more recent discovery revealed that in certain magnetic materials, this sideways voltage can appear even when the magnetic field lies flat within the plane of the material. This is called the in-plane anomalous Hall effect. It is a subtle phenomenon that depends heavily on the internal symmetry of the crystal structure and how easily the material's magnetic properties can be tilted. Understanding how to control this effect is crucial for developing new types of electronic devices that could process information more efficiently, using the magnetic orientation of materials rather than just their charge.

Researchers at the Indian Institute of Technology Kanpur have now uncovered a clear path to making this flat-plane effect much stronger and more complex. By working with a specific type of magnetic crystal called Mn3Si2Te6, which naturally prefers to have its magnetism lie flat within its layers, the team managed to tune the material's internal resistance to magnetic changes. They did this by swapping some of the tellurium atoms in the crystal with selenium atoms. This chemical substitution acted like a fine adjustment knob, weakening the forces that hold the magnetism in a rigid direction. As they reduced this magnetic stiffness, they observed something remarkable: the material began to generate a significant sideways voltage even when the magnetic field was applied flat against the surface. This confirmed the emergence of the in-plane anomalous Hall effect in a controlled way.

The story of their discovery deepens when they looked at how the voltage changed as they rotated the magnetic field. In a typical magnetic material, the voltage would rise and fall in a smooth, single wave as the field turned, much like the gentle rise and fall of a single tide. But in their selenium-rich samples, the voltage behaved differently. Instead of a single wave, the signal developed a complex pattern with three distinct peaks and valleys for every full rotation of the magnetic field. This specific three-part pattern is a direct fingerprint of the crystal's three-fold rotational symmetry, a geometric property where the crystal looks the same if you turn it by one-third of a circle. The researchers found that as they increased the amount of selenium and lowered the temperature, this three-part signal grew stronger, eventually becoming the dominant feature of the electrical response, overshadowing the simpler, single-wave behavior seen in the unmodified material.

To understand exactly what was happening, the team broke down the electrical signal into its different rhythmic components. They found that the strength of this complex, three-part signal grew much faster with increasing magnetic field strength than the standard signal did. In fact, the relationship between the field strength and this new signal followed a specific mathematical rule where the signal grew with the cube of the field, rather than just in a straight line. This cubic growth indicates that the effect is a higher-order phenomenon, a more sophisticated interaction between the electrons and the crystal lattice that only becomes visible when the magnetic anisotropy—the material's resistance to changing its magnetic direction—is sufficiently reduced. The data showed that in the most heavily modified samples, this higher-order effect became so strong that it completely took over the electrical transport at high magnetic fields, proving that the material's internal symmetry was now the primary driver of how electricity moved through it.

The researchers also carefully checked to ensure that this behavior was not caused by simple misalignment of their equipment or by the magnetic field pointing slightly out of the plane. They rotated the field through every possible angle and measured the voltage at different temperatures. They observed that the complex signal vanished as the temperature rose, which is consistent with the thermal energy disrupting the delicate magnetic order required for the effect. Furthermore, the signal appeared and disappeared smoothly as the field was rotated, suggesting that the magnetism was reorienting itself continuously rather than jumping abruptly between different states. This smooth behavior confirmed that the effect was an intrinsic property of the material's symmetry and magnetic structure, not an artifact of the measurement setup.

By combining these observations, the team established a direct link between the material's crystal symmetry, its magnetic stiffness, and the way electricity flows through it. They demonstrated that by simply tuning the chemical composition to reduce the magnetic anisotropy, they could switch the material from a conventional conductor to one that exhibits a strong, symmetry-driven nonlinear response. This finding is significant because it provides a clear, experimental method for engineering higher-order electrical effects in magnetic materials. It shows that the geometry of the crystal lattice, when paired with the right magnetic conditions, can create entirely new pathways for electrons to travel. The work suggests that by carefully designing materials with specific symmetries and tuning their magnetic properties, scientists can unlock new ways to control electrical currents, potentially leading to more advanced electronic components that rely on the intricate dance of symmetry and magnetism.