Novel topological magnet exhibits quantum effects

An international team led by researchers at Princeton University has uncovered a new class of magnet exhibiting novel quantum effects that extend to room temperature.

The researchers discovered a quantized topological phase in a pristine magnet. Their findings provide insights into a 30-year-old theory of how electrons spontaneously quantize and demonstrate a proof-of-principle method for discovering new topological magnets, which are promising platforms for dissipationless current, high storage capacity and future green technologies. The researchers report their findings in a paper in Nature.

The discovery's roots lie in the workings of the quantum Hall effect – a form of topological effect that was the subject of the Nobel Prize in Physics in 1985. This represented the first time that a branch of theoretical mathematics called topology would fundamentally change how scientists describe and classify the matter that makes up the world around us. Ever since, topological phases have been intensely studied in science and engineering.

Many new classes of quantum materials with topological electronic structures have been found, including topological insulators and Weyl semimetals. However, while some of the most exciting theoretical ideas require magnetism, most materials explored have been nonmagnetic and show no quantization, leaving many tantalizing possibilities unfulfilled.

"The discovery of a magnetic topological material with quantized behavior is a major step forward that could unlock new horizons in harnessing quantum topology for future fundamental physics and next-generation device research" said Zahid Hasan, professor of physics at Princeton University, who led the research team.

Important theoretical concepts about 2D topological insulators were put forward in 1988 by Duncan Haldane, professor of mathematical physics and of physics at Princeton. In 2016, Haldane was awarded the Nobel Prize in Physics for theoretical discoveries of topological phase transitions and topological phases of matter. Subsequent theoretical developments showed that magnetism in a topological insulator with a special atomic arrangement known as a kagome lattice should play host to some bizarre quantum effects.

Ever since their discovery of the first examples of 3D topological insulators, Hasan and his team have been on a decade-long search for a topological magnetic quantum state that may also operate at room temperature. Recently, they found a materials solution to Haldane's conjecture in a kagome lattice magnet that is capable of operating at room temperature and which also exhibits the much desired quantization.

"The kagome lattice can be designed to possess relativistic band crossings and strong electron-electron interactions. Both are essential for novel magnetism. Therefore, we realized that kagome magnets are a promising system in which to search for topological magnet phases as they are like the topological insulators that we studied before," said Hasan.

For a long time, direct material and experimental visualization of this phenomenon remained elusive. The team found that most of the kagome magnets were too difficult to synthesize, the magnetism was not sufficiently well understood, no decisive experimental signatures of the topology or quantization could be observed, or they operated only at very low temperatures.

"A suitable atomic chemistry and magnetic structure design coupled to first-principles theory is the crucial step to make Duncan Haldane's speculative prediction realistic in a high-temperature setting," said Hasan. "There are hundreds of kagome magnets, and we need both intuition, experience, materials-specific calculations and intense experimental efforts to eventually find the right material for in-depth exploration. And that took us on a decade-long journey."

Following several years of intense research on several families of topological magnets, the team gradually realized that a material made of the metallic elements terbium, magnesium and tin (TbMn₆Sn₆) combined the ideal crystal structure with chemically pristine, quantum mechanical properties and spatially segregated kagome lattice layers. Moreover, it uniquely features a strong out-of-plane magnetization.

Once this ideal kagome magnet was successfully synthesized at the large single crystal level by collaborators from Shuang Jia's group at Peking University in China, Hasan's group began systematic state-of-the-art measurements to check whether the crystals are topological and, more importantly, feature the desired exotic quantum magnetic state. For this, they used an advanced technique known as scanning tunneling microscopy, which is capable of probing the electronic and spin wavefunctions of a material at the sub-atomic level with sub-millivolt energy resolution. Under these fine-tuned conditions, the researchers identified the magnetic kagome lattice atoms in the crystal, findings that were further confirmed by state-of-the-art angle-resolved photoemission spectroscopy with momentum resolution.

"The first surprise was that the magnetic kagome lattice in this material is super clean in our scanning tunneling microscopy," said Songtian Sonia Zhang, a co-author of the paper who earned her PhD at Princeton earlier this year. "The experimental visualization of such a defect-free magnetic kagome lattice offers an unprecedented opportunity to explore its intrinsic topological quantum properties."

The real magical moment came when the researchers turned on a magnetic field. They found that the electronic states of the kagome lattice modulate dramatically, forming quantized energy levels in a way that is consistent with Dirac topology. By gradually raising the magnetic field to 9 Tesla, which is hundreds of thousands of times higher than the Earth's magnetic field, they systematically mapped out the complete quantization of this magnet.

"It is extremely rare – there has not been one found yet – to find a topological magnetic system featuring the quantized diagram. It requires a nearly defect-free magnetic material design, fine-tuned theory and cutting-edge spectroscopic measurements" said Nana Shumiya, a graduate student at Princeton and co-author of the paper.

The quantized diagram measured by the team revealed that the electronic phase matches a variant of the Haldane model. It confirms that the crystal features a spin-polarized Dirac dispersion with a large Chern gap, as expected by the theory for topological magnets.

However, one piece of the puzzle was still missing. "If this is truly a Chern gap, then based on the fundamental topological bulk-boundary principle, we should observe chiral (one-way traffic) states at the edge of the crystal," Hasan said.

The final piece fell into place when the researchers scanned the boundary of the magnet. They found a clear signature of an edge state only within the Chern energy gap. Propagating along the side of the crystal without apparent scattering (which reveals its dissipationless character), the state was confirmed to be the chiral topological edge state. Imaging of this state was unprecedented in any previous study of topological magnets.

The researchers used other tools to check and reconfirm their findings of the Chern-gapped Dirac fermions, including electrical transport measurements of anomalous Hall scaling, angle-resolved photoemission spectroscopy of the Dirac dispersion in momentum space and first-principles calculations of the topological order in the material family. The data provided a complete spectrum of inter-linked evidence all pointing to the realization of a quantum-limit Chern phase in this kagome magnet.

"All the pieces fit together into a textbook demonstration of the physics of Chern-gapped magnetic Dirac fermions," said Tyler Cochran, a graduate student at Princeton and co-first author of the paper.

The theoretical and experimental focus of the group is now shifting to the dozens of compounds with similar structures to TbMn₆Sn₆ that host kagome lattices with a variety of magnetic structures, each with their own individual quantum topology. "Our experimental visualization of the quantum limit Chern phase demonstrates a proof-of-principle methodology to discover new topological magnets," said Jia-Xin Yin, a senior postdoctoral researcher at Princeton and another co-first author of the paper.

"This is like discovering water in an exoplanet – it opens up a new frontier of topological quantum matter research our laboratory at Princeton has been optimized for," Hasan said.

This story is adapted from material from Princeton University, with editorial changes made by Materials Today. The views expressed in this article do not necessarily represent those of Elsevier. Link to original source.