Shooting neutrons at a crystal and watching how they bounce off. Neutrons carry no charge, so they pass deep into a sample, but they carry a tiny magnetic moment, so they feel the magnetic moments of atoms. That makes them the standard tool for finding how the in a magnet are arranged and – from the energy the neutrons lose – how the spins wave and wobble. The catch is that neutrons come only from research reactors and large accelerators, and the samples have to be large crystals.
Going deeper
Neutrons carry no charge but have a magnetic moment, so they penetrate deep and scatter off the spins of a magnet. New diffraction peaks below the ordering temperature reveal how the spins are arranged, and the energy neutrons lose maps the spin waves, from which exchange constants follow.
Why neutrons
Neutrons from a research reactor or a spallation source have wavelengths comparable to the spacing of atoms and energies comparable to the vibrations and of a crystal, so a single probe measures both structure and dynamics. Having no charge, they pass through centimetres of material and scatter from the nuclei themselves – which makes them sensitive to light elements such as hydrogen and lithium and able to tell isotopes apart. And their magnetic moment lets them scatter from the magnetic moments of atoms, which X-rays see only weakly. Clifford Shull and Bertram Brockhouse shared the 1994 Nobel Prize for developing neutron diffraction and spectroscopy.
Spin arrangements and spin waves
When a magnet orders, the periodic arrangement of its spins adds new diffraction peaks, or changes existing ones, from which the arrangement can be worked out – the method Shull used in 1949 to prove that exist. For layered magnets this is how the stacking of magnetic layers is determined, such as the antiferromagnetic stacking of the ferromagnetic layers in CrPS4.
Measuring the energy the neutrons lose maps spin waves across the whole Brillouin zone, and fitting them gives the and that models need. In CrI3 such measurements found gaps in the magnon spectrum discussed as ; in α-RuCl3 a broad continuum of scattering made it a leading candidate for a Kitaev .
Limits for 2D materials
Neutron beams are weak, and neutrons interact weakly, so experiments need grams of material – a large or hundreds of small ones aligned by hand – and days of beam time at a handful of facilities such as the Institut Laue-Langevin, ISIS, the Oak Ridge sources and J-PARC. A is far beyond reach. Neutron results on bulk crystals are therefore the reference against which thin layers are compared, using scattering, and transport, with care where thinning changes the stacking or the anisotropy. Boron-10, which absorbs neutrons strongly, also makes isotope-enriched hBN interesting as a neutron detector.
For specialists
Elastic and inelastic scattering of thermal and cold neutrons from nuclei and, through the neutron’s magnetic moment, from unpaired electrons. Diffraction gives the nuclear structure, with sensitivity to light elements and isotopes, and the magnetic structure from magnetic Bragg peaks below the (Shull, 1949); polarised neutrons separate magnetic from nuclear scattering. Inelastic scattering on triple-axis and time-of-flight spectrometers maps and magnon , exchange constants and continua – the magnon gaps of CrI3, the scattering continuum of α-RuCl3. Weak fluxes require gram-scale samples or many co-aligned crystals, so are measured in bulk form; monolayers are out of reach, and bulk results are to thin layers with care.