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Study Presents Experimental Evidence for First-Ever 3D Quantum Spin Liquid

The existence of a three-dimensional “quantum spin liquid” has not been proved so far due to lack of techniques.

Bin Gao, co-lead author of a Nature Physics study about the first possible 3D quantum spin liquid, at the CORELLI beamline of Oak Ridge National Laboratory’s Spallation Neutron Source. (Image credit: ORNL/Genevieve Martin)

Hence, physicists from Rice University and colleagues demonstrated that their cerium zirconium pyrochlore single crystals have the right composition to become the first possible 3D version of the state of matter which was long-sought.

In contrast to its name, a quantum spin liquid is a solid where entanglement—the strange property of quantum mechanics—ensures a liquid-like magnetic state.

In a study published in Nature Physics this week, scientists reported plenty of experimental evidence—including most important neutron-scattering experiments at Oak Ridge National Laboratory (ORNL) and muon spin relaxation experiments at Switzerland’s Paul Scherrer Institute (PSI)—to prove that cerium zirconium pyrochlore, in its single-crystal form, is the first material to qualify as a 3D quantum spin liquid.

A quantum spin liquid is something that scientists define based on what you don’t see,” stated Pengcheng Dai from Rice University, who is the corresponding author of the paper and a member of Rice’s Center for Quantum Materials (RCQM). “You don’t see long-range order in the arrangement of spins. You don’t see disorder. And various other things. It’s not this. It’s not that. There’s no conclusive positive identification.”

The samples developed by the researchers are considered to be the first of their kind: Pyrochlores due to their 2:2:7 ratio of cerium, zirconium, and oxygen, and single crystals since the atoms within them are arranged in an unbroken, continuous lattice.

We’ve done every experiment that we could think of on this compound. (Study co-author) Emilia Morosan’s group at Rice did heat capacity work to show that the material undergoes no phase transition down to 50 millikelvin. We did very careful crystallography to show there is no disorder in the crystal.

Pengcheng Dai, Professor of Physics and Astronomy, Rice University

Dai continued, “We did muon spin relaxation experiments that demonstrated an absence of long-range magnetic order down to 20 millikelvin, and we did diffraction experiments that showed the sample has no oxygen vacancy or other known defects. Finally, we did inelastic neutron scattering that showed the presence of a spin-excitation continuum—which may be a quantum spin liquid hallmark—down to 35 millikelvin.”

Dai, who is a professor of physics and astronomy, gave credits for the success of the research to his collaborators, specifically co-lead authors Bin Gao and Tong Chen and co-author David Tam.

Gao, a Rice postdoctoral research associate, developed the single-crystal samples using a laser floating zone furnace at the lab of Sang-Wook Cheong, a co-author from Rutgers University.

Tong, a PhD student at Rice, assisted Bin in carrying out experiments at ORNL that generated a spin excitation continuum indicative of the existence of spin entanglement that leads to short-range order. Tam, who is also a PhD student at Rice, led the muon spin rotation experiments at PSI.

According to Dai, in spite of the efforts from the researchers, it is not feasible to conclusively say cerium-zirconium 227 is a spin liquid, partially because physicists have not yet come to a consensus on what experimental proof is required to make the declaration, and partially since a quantum spin liquid is defined as a state that occurs at absolute zero temperature, a paradigm beyond the reach of any experiment.

It is considered that quantum spin liquids exist in solid materials formed of magnetic atoms in specific crystalline arrangements. Spin is the intrinsic property of electrons that results in magnetism, and electron spins can only point up or down. In contrast to magnetic materials, in a majority of the materials, spins are jumbled at random similar to a deck of cards.

Spins in the magnets within MRI machines and on refrigerators sense their neighbors and arrange themselves jointly in a single direction. Physicists term this “long-range ferromagnetic order,” and another significant example of long-range magnetic order is antiferromagnetism, in which spins jointly arrange in a recurring, up-down, up-down pattern.

In a solid with a periodic arrangement of spins, if you know what a spin is doing over here, you can know what a spin is doing many, many repetitions away because of long-range order.

Andriy Nevidomskyy, Theoretical Physicist and Study Co-Author, Rice University

Nevidomskyy, who is also an associate professor of physics and astronomy and RCQM member, further stated that “In a liquid, on the other hand, there is no long-range order. If you look at two molecules of water a millimeter apart, for example, there is no correlation whatsoever. Nevertheless, due to their hydrogen-hydrogen bonds, they can still have an ordered arrangement at very short distances with nearby molecules, which would be an example of short-range order.”

Nobel laureate physicist Philip Anderson proposed the concept of quantum spin liquids in 1973 based on the insights that geometric arrangement of atoms in certain crystals could render it impossible for entangled spins to jointly orient themselves in stable arrangements.

In 2017, Philip Ball, an eminent science writer, aptly stated: “Imagine an antiferromagnet—in which adjacent spins prefer to be oppositely oriented—on a triangular lattice. Each spin has two nearest neighbors in a triangle, but the antiparallel alignment cannot be satisfied for all of the trio.”

Ball added, “One possibility is that the spin lattice freezes into a disordered ‘glassy’ state, but Anderson showed that quantum mechanics allows the possibility of fluctuating spins even at absolute zero (temperature). This state is called a quantum spin liquid, and Anderson later suggested that it might be connected to high-temperature superconductivity.”

The probability for quantum spin liquids to account for the high-temperature superconductivity created immense interest among condensed matter physicists from the 1980s. According to Nevidomskyy, the interest increased further when it was “suggested that some examples of so-called topological quantum spin liquids may be amenable to building qubits” for quantum computing.

But I believe part of the curiosity about quantum spin liquids is that it has resurfaced in many incarnations and theoretical proposals. And although we have theoretical models where we know, for a fact, that the result will be a spin liquid, finding an actual physical material that would fulfill those properties has, so far, proven very difficult. There is no consensus in the field, up to now, that any material—2D or 3D—is a quantum spin liquid.

Andriy Nevidomskyy, Theoretical Physicist and Study Co-Author, Rice University

Morosan is a member of RCQM and a professor of physics and astronomy, chemistry, and materials science and nanoengineering at Rice.

RCQM leverages worldwide collaborations and the strengths of over 20 Rice research groups to find solutions to questions related to quantum materials. RCQM is supported by Rice’s offices of the provost and the vice provost for research, the Wiess School of Natural Sciences, the Brown School of Engineering, the Smalley-Curl Institute and the departments of Physics and Astronomy, Electrical and Computer Engineering, and Materials Science and NanoEngineering.

Chien-Lung Huang and Haoyu Hu of Rice; Kalyan Sasmal and Brian Maple, both from the University of California, San Diego; Devashibhai Adroja of the United Kingdom’s Rutherford-Appleton Laboratory; Feng Ye, Huibo Cao, Gabriele Sala, and Matthew Stone, all from the Neutron Scattering Division at ORNL; Christopher Baines and Joel Barker, both from PSI; Jae-Ho Chung of both Rice and Korea University, Seoul; Xianghan Xu of Rutgers; Manivannan Nallaiyan and Stefano Spagna, both from Quantum Designs Inc. in San Diego; and Gang Chen of both the University of Hong Kong and Fudan University, Shanghai are the additional study co-authors of the study.

The Department of Energy, the Robert A. Welch Foundation, the National Science Foundation, the National Research Foundation of Korea, Rutgers University, the Gordon and Betty Moore Foundation’s EPiQS initiative, and the Ministry of Science and Technology of China supported the study.


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