Different to conventional magnets, which can be described with classical physics even at the atomic level, antiferromagnets such as copper sulfate are quantum systems where electrons behave in a complex cooperative manner. They belong to the field of quantum many-body physics, a branch of science that studies the collective behavior of vast assemblies of interacting particles. Thus far, only very few exact solutions to quantum many-body problems are known and even fewer have been realized experimentally.
In a recent publication in Nature Physics, scientists from EPFL's Laboratory for Quantum Magnetism (LQM) have together with collaborators from Institut Laue Langevin and the University of Amsterdam have measured the collective quantum-mechanical magnetism in crystals of copper sulfate and show how it relates to properties of sub-electron quasiparticles known as spinons.
Copper sulfate pentahydrate is a commonplace material that is often used to keep swimming pools clear of algae. Because it easily grows as large crystals, it is also very popular in schools' chemistry classes where many students across the world have been inspired by their beautiful and intense blue color. But copper sulfate has some other fascinating properties that most of us might not realize.
Schematic representation of the magnetic excitations in a spin-1/2 (Heisenberg) antiferromagnetic chain and overview of the neutron scattering results for CuSO4-5D2O. a) Fully polarized (saturated) state. The creation of a magnon by inelastic scattering of a neutron can be imagined as a single spin flip. The Zeeman energy prevents any growth of the flipped section that propagates like a single entity. This magnon can classically be visualized as a spin wave, a coherent precession of the local spin expectation value around the field direction. b) Zero magnetic field state. Snapshots of large antiferromagnetically correlated regions of the ground state. The spins could be found in a locally antiferromagnetic configuration with equal probability in any direction (for example, the opposite one (shadows)). The neutron acts on the singlet ground state and excites triplet states which we may imagine as a local spin flip surrounded by two domain walls, which individually correspond to a spinon carrying spin-1/2 The spatial extent of a spinon depends on the anisotropy: in the Ising limit, a local spin flip decomposes into two spinons; in the Heisenberg limit, it decomposes into a rapidly converging series of statescontaining two, four and higher even numbers of such spinons c) Intensity maps of the experimental and theoretical magnon dispersion in the fully polarized phase of CuSO4-5D2O for uoH = 5 > OHsat and T 100 mK, above the Neel transition temperature to three-dimensional antiferromagnetic ordering. The two observed branches (flat and cosine-shaped) are associated with two non-equivalent. Cu2C sites in CuSO4-5D2O (Cu1 and Cu2, respectively). The cosine-shaped dispersion corresponds to the excited magnon of the saturated Heisenberg antiferromagnetic Cu1 chain and the flat branch around 0.7 meV is a transition between two local Zeeman levels of the decoupled Cu2 sites. d) Intensity colour maps of the experimental inelastic neutron scattering spectrum of the Cu1 chain spins in the zero-field phase of CuS04-5D2O, and theoretical two- and four- spinon dynamic structure factor.
When cooled down close to absolute zero temperature, this material hosts a fascinating state of matter called a "quantum spin-liquid". Magnetism essentially originates from a material's electrons spins, sometimes referred to as magnetic moments. When conventional magnets (such as ferromagnets) are cooled down to low temperatures, their electrons' spins align together in a simple static pattern. In contrast, in a quantum spin-liquid state like discovered in copper sulfate, the electrons' spins are interrupted from lining up by quantum fluctuations. This causes the spins to constantly change direction as the molecules floating in a liquid. Despite of this constant change in direction, they remain correlated over long distances, a property that is known as quantum entanglement and which is the key property scientist's hope will lead to future quantum computers.
The LQM scientists, led by Henrik M. Rønnow, cooled down a copper sulfate crystal close to absolute zero (about 0.01 K) to turn it into a quantum spin liquid and then used inelastic neutron scattering to investigate the motion of electrons' spins. The experiments reveal that the magnetic properties of copper sulfate can no longer be described by the individual behavior of the magnetic moments carried by each individual electron in the sample. Instead, flipping the magnetic moment of one single electron creates two spatially separated quantum objects called spinons.
The accuracy of the experiments made it possible to detect not only such spinon-pairs but even splitting (also called fractionalization) into four-spinon states. By carefully accounting for the intensity of their experimental signal, the EPFL team thereby proved and quantified the actual existence of states composed of more than two spinons. Their paradigm-shifting discovery is not only expected to affect future physics textbooks, but, more importantly, allows researchers to develop a simple picture for understanding multi-particle excitations in quantum systems.