Two-decade disagreement on quantum spin liquids put to rest with new findings

April 15, 2021
A decades-long dispute over something you've likely never heard of has been settled. (University of Stuttgart/Björn Miksch)

A decades-long dispute over something you've likely never heard of has been settled. (University of Stuttgart/Björn Miksch)

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A fresh experiment on an extreme state of matter has settled nearly 20 years of contradictory results about its ground state in one material, using direct measurements of electron spins unprecedented to the material to advance understanding of an almost five-decade-old physics problem.

Publishing their findings April 15 in Science, a team of physicists found that an ultracooled material that approximates a quantum spin liquid — a group of particles with highly disordered magnetic arrangements — requires energy to flip the spin of electrons in its ground state. Better understanding this "spin gap" brings researchers one step closer to developing high-temperature superconductors with the unusual quantum state.

Senior author Martin Dressel, a professor of physics at the University of Stuttgart, said clearing up the ambiguity of the experimental results will aid further theory-based research into quantum spin liquids.

"My theory colleagues, they are very much excited about it: 'Oh, now we know where to go and how to do it,' and so on," Dressel said.

The "spin" in quantum spin liquids refers to an intrinsic property of subatomic particles such as electrons. In quantum mechanics, spin carries a meaning more abstract than simply physical rotation, though it is still a form of angular momentum.

Particles with spin also generate magnetic fields, which can be oriented differently relative to one another. The particles' magnetic fields — more specifically, their magnetic moments — point in arbitrary directions in nonmagnetic materials, while they are broadly aligned in the same dimension in magnets, granting them their large-scale magnetic fields. The first kind of material can be described as a more disordered state than the second, though at very cold temperatures, most materials become magnetically ordered.

This is not the case with quantum spin liquids, a theoretical system of particles first devised in 1973 by Nobel laureate Philip Anderson. Even when approaching absolute zero, quantum spin liquids would remain magnetically disordered, with the particles' spins continuously fluctuating. They are also quantum-entangled with each other to an unusually high degree, making the states of the individual particles dependent on each other.

For decades, this exotic state of matter was explored only in theory, but in recent years, materials tested in the lab have been found to display approximate properties of quantum spin liquids. 

Yet physicists have produced conflicting results about the ground state of an organic compound known as κ-(BEDT-TTF)₂Cu₂(CN)₃, what the new study's authors describe as the best real-world candidate for the exotic quantum state. Since 2003, at least five different experimental methods have disagreed on whether the material's ground state has a spin gap, an energy requirement for changing a particle's spin between up and down.

Dressel said previous experiments have relied on indirect measurements and model assumptions, with some employing potentially disruptive high-strength magnetic fields. But his team developed a new multifrequency electron-spin resonance technique to directly measure the spins of electrons in the material for the first time. 

The experiment required "two Ph.D. theses just to build the setup and really go to a parameter range that was not accessible before, and also cover wide frequency data, which was not accessible before," Dressel said. "Then you really can now directly probe the spins."

Dressel and his co-authors cooled the system down to thousandths of a degree above absolute zero, or -273.15 degrees Celsius. They found evidence of a spin gap once temperatures dropped below about 6 degrees Celsius above absolute zero and the material's spin susceptibility fell rapidly.

The team also concluded that the material took the form of a valence bond solid, a quantum spin liquid-like structure. On a repeated triangular grid created with κ-(BEDT-TTF)₂Cu₂(CN)₃, electrons with opposite spins created nonmagnetic pairs, though some unpaired electrons remained.

The newly developed method allowed the researchers to determine which measurements were from unpaired electrons, which contaminate observations of the otherwise quantum spin liquid-like behaviors of the system. 

Valence bond solids have been proposed as possible high-temperature superconductors. Fourteen years after he formulated the unusual state of matter, Anderson suggested that the kind of material could conduct electricity with no resistance while being substantively warmer than absolute zero. Modern superconductors can operate at temperatures as high as -196 degrees Celsius, although developing superconductors at room temperature has been a longtime technological goal for scientists.

"I feel that making progress on the spin liquid eventually might help to solve the problem of high-temperature superconductivity," Dressel said. "Not directly, but it is maybe a step."

The Stuttgart professor is interested in exploring whether the ground state of quantum spin liquids is similar in other materials, such as inorganic-based triangular lattices and lattices of other shapes. The organic compound used in the recent study may also be useful to test the limitations of the ground state by deforming its relatively "soft" triangle lattices, the physics professor said.

And in the paper, the authors said their technique of low-temperature electron-spin resonance could be used to investigate the spin gaps and other properties of different quantum spin liquid candidates.

The study, "Gapped magnetic ground state in quantum spin liquid candidate κ-(BEDT-TTF)₂Cu₂(CN)₃," published April 15 in Science, was authored by Björn Miksch, Mojtaba Rahim, Ralph Hübner, Marc Scheffler and Martin Dressel, University of Stuttgart; Andrej Pustogow, University of Stuttgart and University of California, Los Angeles; Andrey A. Bardin, Russian Academy of Sciences; Kazushi Kanoda, University of Tokyo; and John Schlueter, Argonne National Laboratory and National Science Foundation.