In magnets, the magnetic moments of electrons, known as spins, usually align in an ordered pattern. However, in a spin liquid, the spins never settle into a fixed arrangement. Instead, they continue to fluctuate collectively even at very low temperatures. In a chiral spin liquid, these fluctuations have a preferred handedness, similar to the difference between left and right hands or clockwise and anticlockwise rotation.

This research focuses on the pyrochlore lattice, a three-dimensional structure made of interconnected tetrahedra. Because of this geometry, the spins cannot all simultaneously satisfy their preferred interactions, making the system “frustrated”. This frustration can prevent conventional magnetic order and create the conditions needed for spin-liquid behaviour.

The researchers classified all possible chiral spin-liquid states allowed by the symmetries of the pyrochlore lattice. They then built theoretical models and performed simulations to predict how these states would appear in experiments. One unusual feature of spin liquids is that the collective motion of the spins can behave as if it creates emergent gauge fields, which resemble electromagnetic fields. The researchers found that some chiral spin liquids are dominated by these emergent gauge fields, while others are influenced more strongly by the spin-like excitations themselves.

The researchers showed that different chiral spin liquids have distinct signatures, providing a way to distinguish them experimentally. Their results offer a roadmap for identifying and classifying elusive three-dimensional chiral spin liquids in real materials.

Do you want to learn more about this topic?

Dynamical quantum phase transitions: a review by Markus Heyl (2018)