An international team of researchers led by researchers at Princeton University has found that a magnetic material at room temperature allows electrons to behave intuitively and act collectively rather than as individuals. Their collective behavior mimics massless particles and antiparticles that coexist unexpectedly and together form an exotic loop-like structure.
The key to this behavior is topology – a branch of mathematics already known to play a powerful role in dictating the behavior of electrons in crystals. Topological materials may contain massless particles in the form of light or photons. In a topological crystal, the electrons often behave like braked light, but unlike light they have electrical charges.
Topology has rarely been observed in magnetic materials, and the discovery of a magnetic topological material at room temperature is a step forward that could unlock new methods for utilizing topological materials for future technical applications.
"Prior to this work, evidence for the topological properties of three-dimensional magnets was unclear. These new results provide us with direct and conclusive evidence of this phenomenon at the microscopic level," said M. Zahid Hasan, Eugene Higgins professor of physics at Princeton , who led the research. "This work opens up a new continent for the exploration of topological magnets."
Hasan and his team spent more than a decade studying candidate materials in pursuit of a topological magnetic quantum state.
"The physics of bulk magnets has a natural question for us is: Can magnetic and topological properties together produce something new in three dimensions?" Hasan said.
Thousands of magnetic materials exist, but most did not have the right properties, the researchers found. The magnets were too difficult to synthesize, the magnetism was not well understood, the magnetic structure was too complicated to theoretically model, or no crucial experimental signatures of the topology could be observed.
Then came a happy turning point.  "After studying many magnetic materials, we performed a measurement on a class of room temperature magnets and saw unexpected signatures of massless electrons," said Ilya Belopolski, a postdoctoral researcher in Hasan's laboratory and co-author of the study. "It made us on our way to the discovery of the first three-dimensional topological magnetic phase."
The exotic magnetic crystal consists of cobalt, manganese and gallium, arranged in an orderly, repeating three-dimensional pattern. To explore the topological state of the material, the researchers used a technique called angular resolved photo emission spectroscopy. In this experiment, high intensity light shines on the sample and forces electrons to emit from the surface. These emitted electrons can then be measured and provide information on how the electrons behaved when inside the crystal.
"It's an extremely powerful experimental technique, which in this case allowed us to directly observe that the electrons in this magnet behave as if they were massless. These massless electrons are known as Weyl fermions," said Daniel Sanchez, a visitor researchers from Princeton and Ph.D. student at the University of Copenhagen and another first author of the study.
An important insight came as the researchers studied the Weyl fermions more closely and realized that the magnet was host to an infinite series of distinct massless electrons that take the form of a loop, with some electrons mimicking the properties of the particles and some of the antiparticles. This collective quantum behavior of the electrons has been called a magnetic topological Weyl fermion loop.
"It's really an exotic and new system," says Guoqing Chang, a postdoctoral researcher in Hasan's group and co-author of the study. "The collective electron behavior of these particles is unlike what is known to us in our everyday experience – or even the experience of particle physicists studying subatomic particles. Here we are dealing with emerging particles that follow different natural laws."
It turns out that a key driver for these properties is a mathematical quantity that describes the infinite series of massless electrons. The researchers were able to determine the role of the topology by observing subtle changes in the difference in behavior of electrons living on the surface of the sample and deeper in its interior. The technique of demonstrating topological quantities through contrasts of surface and bulk properties was groundbreaking by Hasan's group and was used to detect Weyl fermions, a finding published in 2015. The team recently used an analogous approach to discover a topological chiral crystal, works published in the journal Nature earlier this year who was also led by Hasan's group at Princeton and included Daniel Sanchez, Guoqing Chang and Ilya Belopolski as leading writers.
The relationship between topology and magnetic quantum-particle particles was investigated in the Hasan Group's theoretical predictions published in October 2017 in Physical Review Letters . However, the group's theoretical interest in topological magnets goes back much earlier to theoretical predictions published in Nature Materials 2010. These theoretical works by Hasan's group were funded by the US Department of Energy's Office of Basic Energy Sciences.  "This work represents the culmination of about a decade of trying to realize a topological magnetic quantum phase in three dimensions," Hasan said.
In 2016, Duncan Haldane, Princeton's Sherman Fairchild University professor of physics, won the Nobel Prize in Physics for his theories that predict the properties of one- and two-dimensional topological material.
An important aspect of the result is that the material retains its magnetism up to 400 degrees Celsius – well above room temperature – which fulfills a key requirement for real technical applications.
"Prior to our work, topological magnetic properties were normally seen when the thin films of material were extremely cold – a fraction of a degree above absolutely zero – requiring special equipment simply to achieve the necessary temperatures. Even a small amount of heat would thermally destabilizing the topological magnetic state, "Hasan said. "The quantum magnet studied here exhibits topological properties at room temperature."
A three-dimensional topological magnet reveals its most exotic signatures only on its surface – electron wave functions take the form of drum hairs. This has never been seen before in previously known magnets and constitutes the topological magnet. The researchers observed such drumhole-shaped electronic states in their data, which provided the crucial, decisive evidence that it is a new matter.
Patrick Lee, William & Emma Roger's professor of physics at the Massachusetts Institute of Technology, who was not involved in the study, commented on the importance of the finding. "The Princeton Group has long been at the forefront in discovering new materials with topological features," Lee said. "By extending this work to a room temperature ferromagnetic and demonstrating the existence of a new type of drumhead surfaces, this work opens a new domain for further discoveries."
To understand their results, the researchers found the arrangement of atoms. on the surface of the material using several techniques, such as checking for the correct type of symmetry using the scanning tunnel microscope in Hasan's Laboratory for Topological Quantum Matter and Advanced Spectroscopy located in the basement of Princeton's Jadwin Hall.
An important contributor to the discovery was the pointed spectroscopy equipment used to conduct the experiment. The researchers used a special radiation with photo-emission spectroscopy that was recently built at Stanford Synchrotron Radiation Lightsource, part of the SLAC National Accelerator Laboratory in Menlo Park, California.
"The light used in the SLAC photo emission experiment is extremely bright and focused down to a small spot only several tens of micrometers in diameter," says Belopolski. "This was important for the study."
The work was carried out in close collaboration with the group of Professor Hsin Lin at the Institute of Physics, Academia Sinica in Taiwan, and Professor Claudia Felser at the Max Planck Institute for the Chemical Physics of Solids in Dresden, Germany, including postdoctoral researcher Kaustuv Manna who co.
Driven by the exciting opportunity to apply, the researchers went a step further and applied electromagnetic fields to the topological magnet to see how it would respond. They observed an exotic electromagnetic response up to room temperature, which can be directly traced back to the quantum electrons.
"We have many topological materials, but among them it has been difficult to show a clear electromagnetic response from the topology," Hasan added. "Here we have been able to do that. It creates a whole new field of research for topological magnets."
The Study, "Detecting Topological Weyl fermion Lines and Drum Skin Surfaces in a Room Temperature Magnet," by Ilya Belopolski, Kaustuv Manna, Daniel S. Sanchez, Guoqing Chang, Benedikt Ernst, Jiaxin Yin, Songtian S. Zhang, Tyler Cochran Shumiya, Hao Zheng, Bahadur Singh, Guang Bian, Daniel Multer, Maksim Litskevich, Xiaoting Zhou, Shin-Ming Huang, Baokai Wang, Tay-Rong Chang, Su-Yang Xu, Arun Bansil, Claudia Felser, Hsin Lin and Zahid Hasan appear in the September 19 issue of Science .
Take a look under the hood of topological insulators
"Detecting Topological Weyl Lines and Drum Skin Surfaces in a Room Temperature Magnet" Science (2019). science.sciencemag.org/cgi/doi … 1126 / science.aav2327
Physicists detect topological behavior of electrons in 3-D magnetic material (2019, September 19)
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