Nuclear magnetic resonance (NMR)

In plain words

Listening to atomic nuclei in a magnetic field. Many nuclei – hydrogen, carbon-13, nitrogen-15, fluorine, phosphorus – are tiny magnets that turn about the field at a precise radio frequency, and that frequency shifts slightly with the chemical surroundings of each nucleus and with the magnetism near it. Hospital MRI scanners use the same physics. For layered materials, NMR tells which chemical groups sit on a sheet and in what proportions, and how the around a nucleus behave.

Going deeper

Nuclear spins turn about a magnetic field and absorb radio waves at a frequency set by their surroundings, so each chemical site gives its own line and the line areas count the atoms. A nonmagnetic nucleus among magnetic atoms feels their spins, which makes NMR a probe of magnetism from inside the crystal.

Nuclei as probes

Nuclei with spin behave like tiny bar magnets. In a strong magnetic field they turn about the field direction at a frequency set by the field and the kind of nucleus – hundreds of megahertz for hydrogen in a laboratory magnet – and absorb radio waves at exactly that frequency. The electrons around a nucleus screen the field slightly, so the resonance shifts by a few parts per million with the chemical environment: a hydrogen in one group resonates at a different frequency from a hydrogen in another.

In a solid the lines are broadened by interactions that depend on how each crystallite is oriented; spinning the sample rapidly about an axis tilted 54.7° from the field averages much of that away and gives lines sharp enough to tell sites apart.

What is in the sheet, and on it

Diffraction sees order; NMR sees every atom of a given kind, ordered or not, and counts them. Carbon nitride made from melamine is a case in point: its structure had long been argued over, and ¹³C and ¹⁵N solid-state NMR, together with and calculations, showed it to be melon – chains of heptazine units linked by NH bridges and carrying NH₂ groups (Lotsch and colleagues, 2007).

For , the surface terminations decide , conductivity and how the sheets behave in water. ¹H and ¹⁹F NMR of Ti₃C₂T_x found –F and –OH terminations intimately mixed, with significantly fewer –OH than –F and –O, and proportions that depend strongly on how the MXene was made (Hope and colleagues, 2016).

Spins seen from the nucleus

In a magnet a nucleus feels the field of the electron spins around it, so its resonance shifts with their local magnetisation, and its relaxation reveals how they fluctuate. In the layered Ni₂P₂S₆ the phosphorus nuclei sit among the nickel atoms. Their shift stops following the bulk susceptibility close to the broad maximum it shows above the – the mark of quasi-two-dimensional spin correlations – and the coupling they feel fits exchange running through the sulfur atoms (Dioguardi and colleagues, 2020).

NMR needs many nuclei, so it works on bulk crystals and powders rather than single : like , it measures the parent crystal of a 2D magnet.

For specialists

Resonant radio-frequency absorption by nuclear spins in a magnetic field; chemical or Knight shifts and couplings report local bonding, while relaxation rates probe dynamics. Solid-state NMR, with the sample spun fast to sharpen its lines, resolves structure in powders that diffraction cannot fully solve – ¹³C and ¹⁵N spectra confirmed the heptazine building blocks of melon – and ¹H/¹⁹F NMR quantifies MXene terminations (–F, –O, –OH), whose proportions depend on synthesis. In magnets the shift of a nonmagnetic nucleus follows the local spin susceptibility: in Ni₂P₂S₆ the ³¹P shift departs from the bulk susceptibility near its broad maximum, tying that maximum to quasi-two-dimensional spin correlations.

Where this comes from

Unmasking melon by a complementary approach employing electron diffraction, solid-state NMR spectroscopy, and theoretical calculations – structural characterization of a carbon nitride polymer Lotsch et al. · Chemistry – A European Journal 13, 4969 (2007) cited by 959
NMR reveals the surface functionalisation of Ti₃C₂ MXene Hope et al. · Physical Chemistry Chemical Physics 18, 5099 (2016)
Quasi-two-dimensional magnetic correlations in Ni₂P₂S₆ probed by ³¹P NMR Dioguardi et al. · Physical Review B 102, 064429 (2020) cited by 18

Spin

A built-in property of every electron that makes it a tiny magnet. Measure it along any direction and you only ever find one of two answers, ‘up’ or ‘down’. Despite the name, nothing is actually spinning – the word stuck from an early picture – but the magnetism is real: countless electron spins lined up are what make a fridge magnet stick. Spintronics tries to carry information in spin rather than in charge.

The intrinsic angular momentum of the electron, ħ/2, with a magnetic moment of almost exactly one Bohr magneton; a measurement along any axis yields one of two values. In solids spin couples to orbital motion through spin–orbit coupling and to other spins through exchange; in 2D materials it sets magnetic order, spin–valley locking and how long a spin survives as a carrier of information.

Full explanation

Electron diffraction

Sending a beam of electrons through or onto a crystal and recording the pattern of spots it scatters into. Electrons behave as waves far shorter than the distance between atoms, so a regular lattice sends them out in sharp directions, and the pattern is a map of the lattice. Because electrons interact strongly with matter, even a single layer of atoms gives a clear pattern – something X-rays, which pass almost straight through, cannot do.

Diffraction of electrons, whose wavelength at transmission-microscope energies is a few picometres, by the periodic potential of a crystal; the spot pattern samples its reciprocal lattice. Strong scattering makes it work on single layers: selected-area diffraction in a TEM gives the orientation, twist angle and lattice constant of a flake; low-energy electron diffraction (LEED), at tens to hundreds of electronvolts, sees only the top layers of an epitaxial film in ultrahigh vacuum and reveals its superstructure; convergent-beam diffraction tests point-group symmetry, including whether there is a centre of inversion; and ultrafast electron diffraction follows the lattice after a laser pulse, picosecond by picosecond.

Full explanation

Ferromagnet and antiferromagnet

In a ferromagnet the tiny magnets of the atoms all point the same way, as in a fridge magnet. In an antiferromagnet neighbours point in opposite directions and cancel out; if the opposing magnets differ in size they cancel only in part, and the material is a ferrimagnet. Ferromagnets and antiferromagnets have both been found in sheets only one layer thick.

Magnetically ordered states with parallel (ferromagnetic) or antiparallel (antiferromagnetic) alignment of neighbouring moments; antiparallel moments of unequal size make a ferrimagnet. Long-range order in 2D requires magnetic anisotropy to evade the Mermin–Wagner theorem; CrI₃ monolayers are Ising-like ferromagnets that couple antiferromagnetically between layers, and the MPS₃ compounds are antiferromagnets.

Full explanation

Neutron scattering

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 spins 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.

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 ordering temperature (Shull, 1949); polarised neutrons separate magnetic from nuclear scattering. Inelastic scattering on triple-axis and time-of-flight spectrometers maps phonon and magnon dispersions, 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 2D materials are measured in bulk form; monolayers are out of reach, and bulk results are transferred to thin layers with care.

Full explanation