Physicists were surprised to discover in 2022 that electrons in magnetic crystals of iron and germanium can spontaneously and collectively organize their charges into a pattern characterized by a standing wave. Magnetism also arises from the collective self-organization of electron spins into ordered patterns, and these patterns rarely coexist with the patterns that produce the standing wave of electrons that physicists call a charge density wave.
In a study published this week in nature physics Rice University physicists Meng Yi and Bingcheng Dai, and several collaborators from the 2022 study, present a body of experimental evidence showing that charge density wave detection was rare, a case in which magnetic and electronic orders not only coexist but are directly related.
“We found that magnetism subtly modulates the landscape of electron energy states in matter in a way that enhances and prepares for charge density wave formation,” said Yi, co-author of the study.
More than a dozen researchers from Rice participated in the study. Oak Ridge National Laboratory (ORNL); SLAC National Accelerator Laboratory. Lawrence Berkeley National Laboratory (LBNL); University of Washington University of California, Berkeley; the Weizmann Institute of Science in Israel; and South China University of Science and Technology.
The iron and germanium materials are Kagome lattice crystals, a much-studied family of materials characterized by two-dimensional arrangements of atoms reminiscent of the weaving pattern in traditional Japanese Kagome baskets, which feature equilateral triangles that touch at the corners.
“Kagome materials have taken the quantum materials world by storm recently,” Ye said. “The cool thing about this structure is that the geometry imposes interesting quantum constraints on the way electrons are allowed to zoom around, somewhat analogous to how traffic vertigo affects the flow of traffic on and off sometimes.”
By their nature, electrons avoid each other. One way to do this is to arrange their magnetic states—the spins that point either up or down—in the opposite direction to the spins of their neighbors.
“When placed on Kagome’s lattices, the electrons can also appear to be in a state where they are stuck and cannot travel anywhere due to quantum interference effects,” said Dai, one of the study’s co-authors.
When the electrons cannot move, the trigonometric arrangement produces a state that each has three neighbors, and there is no way for the electrons to collectively arrange all the neighboring spins in opposite directions. The inherent frustration of electrons in Kagome lattice materials has long been recognized.
The lattice constrains electrons in ways that “could have a direct effect on the observable properties of matter,” Ye said, and the team was able to use that to “dig deeper into the origins of the interference between magnetism and wave charge density” in iron and germanium.
They did this using a combination of inelastic neutron scattering experiments, conducted at ORNL, and angle-angle photoemission spectroscopy experiments conducted at LBNL’s Advanced Light Source and Stanford Synchrotron Radiation Lightsource, as well as in Yi’s lab at Rice.
“These probes allowed us to look at what both the electrons and the lattice were doing while the charge density wave was forming,” she said.
Day said the results confirm the team’s hypothesis that charge order and magnetic order are related in iron and germanium. “This is one of the very few, if not the only, known examples of Kagome matter where magnetism forms first, setting the stage for the formation of charges,” he said.
Ye said the work shows how curiosity and basic research into natural phenomena can eventually lead to applied science.
“As physicists, we are always excited when we find materials that spontaneously form an arrangement of some sort,” she said. “This means there is an opportunity for us to learn about the self-organizing capabilities of the fundamental particles of quantum materials. Only with this kind of understanding can we hope to one day engineer materials with new or exotic properties that we can control at will.”
Day is the Sam and Helen Worden Professor of Physics and Astronomy. Both Dai and Yi are members of the Rice Quantum Initiative and the Rice Center for Quantum Materials (RCQM).
The research at Rice was supported by the EPiQS Initiative of the Gordon and Betty Moore Foundation (GBMF9470), the Welch Foundation (C-2024, C-1839), the Department of Energy (DE-SC0021421) and the National Science Foundation (2100741, 1921847).
