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Physicist Maps Quantum Criticality Where Electrons Follow Different Sets of Rules

Qimiao Si, a theoretical physicist at Rice University, has been mapping quantum criticality for more than 10 years. Now, he has finally identified a traveler that can cross the ultimate frontier.

A simplified representation of a unified phase diagram depicting an ordered antiferromagnetic phase (gray) and a disordered paramagnetic phase (blue) that describe the correlated electronic behavior of heavy fermions and other known types of quantum materials. Researchers from Rice University, the Max Planck Institute for Chemical Physics of Solids and the Chinese Academy of Sciences used a combination of geometrical frustration, pressure and magnetic field to drive an alloy of cerium palladium and aluminum across a region (green) where physicists had previously only been able to speculate about the rules that govern electron behavior. (Image credit: Rice University)

Here, the traveler is essentially an alloy of aluminum and cerium palladium. Si, who is also the director of the Rice Center for Quantum Materials (RCQM), and collaborators in Japan, China, and Germany have described the journey of this alloy in a study recently published online in Nature Physics.

The physicist’s map is a graph known as a phase diagram — a tool that is often used by condensed-matter physicists to figure out what exactly takes place when the phase of a material changes, similar to how a hard block of ice thaws into liquid water.

The regions found on Si’s map are areas in which electrons obey varied sets of rules. The study demonstrates how the scientists used the atoms’ geometric arrangement in the alloy together with numerous magnetic fields and pressures to modify the path of the alloy and bring it into a specific region. Researchers have only been able to guess the rules that control the behavior of electrons in this region.

That’s the corner, or portion, of this road map that everybody really wants to access,” stated Si, pointing toward the top left side of the phase diagram, and high up the vertical axis labeled G. “It has taken the community a huge amount of effort to look through candidate materials that have the feature of geometrical frustration, which is one way to realize this large G.”

However, the fact that cerium atoms are arranged in a sequence of equilateral triangles within the alloy creates frustration. The kagome lattice arrangement is named after the conventional Japanese kagome baskets, because the former has similar patterns as those of the latter. The triangular arrangement makes sure that spins — electrons’ magnetic states — do not organize themselves as they usually would under specific conditions.

Such frustration offered an experimental lever that could be used by Si and his colleagues to analyze a new region of the phase diagram. Here, the boundary between two well-understood and well-explored states — one highlighted by a disorderly arrangement of electron spins and the other marked by an orderly arrangement — diverged.

If you start with an ordered, antiferromagnetic pattern of spins in an up-down, up-down arrangement, there are several ways of softening this hard pattern of the spins. One way is through coupling to a background of conduction electrons, and as you change conditions to enhance this coupling, the spins get more and more scrambled.

Qimiao Si, Harry C. and Olga K. Wiess Professor, Department of Physics & Astronomy, Rice University

Si continued, “When the scrambling is strong enough, the ordered pattern is destroyed, and you end up with a non-ordered phase, a paramagnetic phase.”

This journey can be plotted from order to disorder as a line on the phase diagram. In the above example, the line would first start in a region labeled “AF” for antiferromagnetic phase, and then continue across a border into an adjacent region labeled “P” for paramagnetic.

“Quantum critical point” is the border crossing where an unlimited number of electrons act simultaneously, changing their stances to follow the rules of the regime they have now entered.

Si is a top advocate of quantum criticality, a theoretical framework that attempts to elucidate and predict quantum materials’ behavior with respect to these crucial points as well as phase changes.

What the geometrical frustration does is to extend the process where the spin order becomes more and more fragile so that it’s no longer just a point that the system passes through on the way to being disordered. In fact, that point sort of splits out into a separate region, with distinct borders on either side.

Qimiao Si, Harry C. and Olga K. Wiess Professor, Department of Physics & Astronomy, Rice University

Si informed that the research team, which involved co-corresponding authors and RCQM collaborators Frank Steglich from the Max Planck Institute for Chemical Physics of Solids in Dresden, Germany and Peijie Sun from the Chinese Academy of Sciences in Beijing, carried out the experiments. These experiments confirmed that the alloy of cerium palladium and aluminum experiences a pair of border crossings.

Many experiments were performed by physicists to observe how different materials behave in the ordered phase and in the disordered phase, where the alloy started and ended its journey, respectively.

However, according to Si, these are the initial experiments performed to trace a path via the intervening phase facilitated by considerable geometrical frustration.

He added that measurements of the electronic properties of the alloy as it traveled through the region could not be interpreted by conventional theories that elucidate the behavior of metals. This implies that the alloy acted as a “strange” metal in the unknown territory.

The system acted as a kind of spin liquid, albeit a metallic one,” stated Si.

These results indicate that geometrical frustration can be utilized as a design principle to produce strange metals, Si further added.

That is significant because the unusual electronic excitations in strange metals are also the underlying exotic properties of other strongly correlated quantum materials, including most high-temperature superconductors.

Qimiao Si, Harry C. and Olga K. Wiess Professor, Department of Physics & Astronomy, Rice University

Other study co-authors include Hengcan Zhao, Jiahao Zhang, Meng Lyu, Shuai Zhang, Jinguang Cheng, Yi-feng Yang, and Genfu Chen, all from the Chinese Academy of Sciences; Sebastian Bachus, Yoshifumi Tokiwa, and Philipp Gegenwart from the University of Augsburg; and Yosikazu Isikawa from the University of Toyama.

The Ministry of Science and Technology of China, the National Natural Science Foundation of China, the Chinese Academy of Sciences, the Science and Technology on Surface Physics and Chemistry Laboratory, the German Research Foundation, the National Science Foundation, and the Robert A. Welch Foundation supported the study.


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