The planar Hall effect is a tabletop diagnostic tool for special quantum properties useful in basic research and technological applications. Or so it was thought, because careful calculation by Kobe University researchers clarifies the conditions under which this effect may also appear in classical materials. This makes the diagnostic more meaningful and enables more purposeful design.
In the hunt for materials with properties that are useful for quantum computing or spintronics, researchers have used the "planar Hall effect" as a tabletop diagnostic tool: The researchers send a current through a thin, flat sample and observe whether an electric voltage is produced in response to a magnetic field in the same plane as the sample. If it is, the pattern of how the voltage responds to rotating the magnetic field in the plane of the sample tells researchers about the properties of the material.
"In solid-state physics, beautiful laws underpinned by symmetry hold true. For example, in a crystal with the symmetry of a square, that same symmetry is usually reflected in its physical response. However, the problem we tackled this time is a bit different," says Kobe University quantum solid state physicist FUSEYA Yuki. In some materials, the pattern the voltage exhibits when the magnetic field is rotated repeats every 120 degrees. "That is, even if the crystal doesn't have triangular symmetry, its electrical response to a magnetic field may exhibit the same symmetry as a triangle," explains Fuseya. Researchers have taken this to hint at unusual quantum properties of the material because such a pattern could not be explained with classical models of how electrons move through crystals. Fuseya says, "I was drawn to the intriguing nature of this exception, so I wanted to tackle the problem."
In the journal Physical Review B, the Kobe University physicist and his team now show that, simply put, people hadn't taken their math far enough. More careful analysis at a higher order of the 70-year-old classical theory showed that threefold symmetry can, in fact, be expected for classical materials. Their result therefore hands physicists sharper diagnostic tools for the identification of unusual quantum properties. The study's first author YAMADA Akiyoshi says: "A phenomenon previously considered a rare response in a magnetic field may in fact be occurring in many places, making this research a breakthrough that has uncovered a blind spot in both theory and experiment."
Furthermore, the Kobe University team could show under what conditions the special voltage pattern should appear in classical materials and why it has appeared in previous experiments with classical materials. "The point is alignment: The crystal-probe orientation dictates the threefold component, with applicability across a wide class of materials," the researchers write in their paper. Yamada adds: "What is particularly striking is that the response reflects mirror symmetry rather than much rarer rotational symmetry." This means that, if fabricated with a certain crystal orientation, a wide range of materials are expected to show threefold symmetry.
Thus, the new result is enabling rather than negating. On top of giving researchers more accurate tools for analysis, it also tells those who want to use the planar Hall effect with threefold symmetry for magnetic sensors or other devices that they can use a much wider class of materials instead of just exotic ones, how to produce them and which materials are likely to show the largest effects. Yamada sums up the results, saying: "This study demonstrates that by deciphering the hidden regularities of the electron flow, information regarding microscopic crystal symmetry and electronic structure can be extracted from macroscopic electrical measurements. It is an important step toward advancing research on advanced next-generation materials based on more reliable measurements and interpretations."
This research was funded by the Japan Society for the Promotion of Science (grants 23H04862, 23H00268, 22K18318, 25K23360).
Kobe University is a national university with roots dating back to the Kobe Higher Commercial School founded in 1902. It is now one of Japan's leading comprehensive research universities with over 16,000 students and over 1,700 faculty in 11 faculties and schools and 14 graduate schools. Combining the social and natural sciences to cultivate leaders with an interdisciplinary perspective, Kobe University creates knowledge and fosters innovation to address society's challenges.
