Researchers at the Joint Quantum Institute (JQI) in College Park, Maryland, and colleagues, have uncovered evidence for a long-sought-after quantum state of matter: a spin liquid.

The researchers studied what happens when “frustration” (ensembles of interacting components that cannot settle into a state that minimizes each interaction) occurs in materials with a hexagonal (six-sided) unit cell lattice.

These atoms interact via their respective spins. The strength of the interaction between nearest neighbor (NN) atoms is denoted by the parameter J1. Similarly, the force between next nearest neighbors (NNN) — that is, pairs of atoms that have at least one intervening atom between them — is denoted by J2.

The researchers calculated what happens in an array of hexagons consisting of 30 sites where the spins are free to swing about in a two-dimensional plane (this approach is called an XY model). The researchers said that the interactions of atoms can be represented by a matrix with 155 million entries on each side. This huge number corresponds to the different spin configurations that can occur on this honeycomb-structured material.

The researchers found a “kaleidoscope” of phases that represent the lowest-energy states that are allowed given the magnetic interactions. Just as water can exist in different phases — steam, liquid, and ice — as the temperature is changed in the XY model, a change in the strengths of the interactions among the spins (the J1 and J2 parameters) results in different phases. For example, one simple solution is an antiferromagnet, where the spins are anti-aligned.

But one phase turns out to be a true quantum spin liquid having no order at all. When J2 is between about 21% and 36% of the value of J1, frustration coaxes the spins into disorder; the entire sample co-exists in millions of quantum states simultaneously.

What would such a spin liquid material be good for? The materials could support some exotic kind of superconductivity or could organize particle-like entities that possessed fractional electric charge, the researchers said.

Ref.: Christopher N. Varney, et al., Physical Review Letters, Kaleidoscope of Exotic Quantum Phases in a Frustrated XY Model, [DOI: 10.1103/PhysRevLett.107.077201]