Linear and circular dichroism

In plain words

When a material absorbs light differently depending on how the light is polarised. In linear dichroism the difference is between light vibrating along one direction of the crystal and across it, as in a polarising filter; in circular dichroism, between light whose vibration turns one way and the other. Shining polarised light on a this way reveals hidden directions in it – its crystal axes, its , which its electrons sit in – without touching it.

Going deeper

Light can be polarised along a line or turning in a circle. A crystal with chains or another preferred direction absorbs light along them more than across them (linear dichroism), which shows its axes and its order. A material whose valleys or magnetisation prefer one handedness absorbs one circular polarisation more than the other (circular dichroism).

Two pairs of polarisations

Light is a wave whose electric field vibrates across its direction of travel. If the vibration stays along one line, the light is linearly polarised; if it turns, tracing a circle, it is circularly polarised, either left- or . A material that treats two directions in its plane differently absorbs the two linear polarisations differently – linear dichroism – and one that differs from its mirror image, or carries a magnetisation, absorbs the two circular ones differently: circular dichroism.

The effect is measured by comparing absorption, transmission or reflection for the two polarisations of a pair, often by switching rapidly between them and picking out the small difference. Under a microscope it maps the crystal axes and domains of a flake in seconds.

Linear dichroism: hidden directions

Crystals with a low-symmetry lattice absorb more strongly along one axis. Black phosphorus is the classic case: its puckered layers absorb light polarised along the armchair direction far more than along the zigzag direction, so a rotating polariser finds the orientation of a flake directly, and made from it sense polarisation. Chain-like crystals such as TiS₃ and in-plane such as In₂Se₃ behave the same way.

Order that breaks rotational symmetry shows up even in a hexagonal lattice. In the antiferromagnet FePS₃ the line up in zigzag chains, and below the the absorption acquires a strong linear dichroism; following it with temperature and thickness tracks the magnetic order in flakes far too small for .

Circular dichroism: valleys and magnets

In MoS₂ and its relatives the two valleys of the , K and K′, absorb opposite circular polarisations: light of one handedness excites electrons only in one valley, light of the other only in the other. This valley-selective circular dichroism, predicted and observed in 2012, lets light write and read valley information, the basis of valleytronics.

In a magnet the two circular polarisations are absorbed differently in proportion to the magnetisation. Reflective magnetic circular dichroism, a sister of the , is a standard way to record loops of single magnetic layers such as CrI₃. At X-ray energies tuned to the absorption edge of one element it measures that element’s spin and orbital moments separately, which makes it a strict test of whether a claimed 2D magnet is magnetic at all.

For specialists

Polarisation-dependent absorption: linear dichroism between orthogonal linear polarisations, from in-plane of the lattice or of an order that breaks rotational symmetry; circular dichroism between left and right circular polarisations, from broken mirror or . In black phosphorus, ReS₂ and the transition metal trichalcogenides linear dichroism follows the crystal axes; in FePS₃ it appears with zigzag antiferromagnetic order and tracks it with temperature. In monolayer valley-selective circular dichroism at K and K′ underlies optical valley polarisation, and magnetic circular dichroism – reflective in the visible, XMCD at X-ray absorption edges – measures magnetisation, with sum rules separating spin and orbital moments.

Where this comes from

Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics Xia et al. · Nature Communications 5, 4458 (2014)
Valley-selective circular dichroism of monolayer molybdenum disulphide Cao et al. · Nature Communications 3, 887 (2012)
Control of valley polarization in monolayer MoS₂ by optical helicity Mak et al. · Nature Nanotechnology 7, 494 (2012) cited by 4,072
Observation of giant optical linear dichroism in a zigzag antiferromagnet FePS₃ Zhang et al. · Nano Letters 21, 6938 (2021)

Chirality

The property of an object that cannot be turned into its own mirror image, like a left and a right hand or a corkscrew that turns one way. Molecules can be chiral, and so can crystals: in tellurium the atoms form screw-shaped chains that wind either to the left or to the right. Electrons, spins and vibrations can take on a handedness too, and chiral materials can treat left- and right-turning light, or spins pointing one way or the other, differently.

The absence of improper symmetry operations (mirror planes, inversion, rotoreflections), so that an object and its mirror image are distinct enantiomorphs. Chiral crystals belong to the 65 Sohncke space groups, such as trigonal tellurium (P3₁21 or P3₂21), whose helical chains give natural optical activity, current-induced magnetisation and radial spin textures through spin–orbit coupling. Chirality also describes Weyl fermions, whose chirality sets the chiral anomaly and the chiral magnetic effect; edge modes that propagate one way; spin spirals and skyrmions with a fixed sense of rotation from the Dzyaloshinskii–Moriya interaction; phonons carrying angular momentum in the valleys of TMDCs; and proposed chiral orders such as loop currents in kagome metals and Mn₃Si₂Te₆. Barron’s distinction between true and false chirality decides which physical effects a given handedness allows.

Full explanation

Ferroelectricity

A material that holds an electric polarisation – one side slightly positive, the other slightly negative – with no voltage applied, and that can be flipped by a field and stay flipped. That memory of the last field applied is what makes it useful for storing data.

A spontaneous, switchable electric polarisation produced by a structural distortion that breaks inversion symmetry. In 2D the usual obstacle – depolarising fields destroying the polarisation as a film thins – is sidestepped in three ways: in-plane polarisation, layered compounds whose dipoles survive to the monolayer such as CuInP₂S₆ and In₂Se₃, and sliding ferroelectricity, where the polarisation belongs to the interface between layers rather than to the layers themselves.

Full explanation

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

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

Band structure

The map of the energies an electron may have in a crystal. The allowed energies come in ranges called bands, with forbidden gaps between them – like the decks of a multi-storey car park, where a car can stand on a deck but never between two. Whether a material conducts, gives off light or lets its electrons move easily can all be read from it, and in a layered material the map changes with the number of layers.

The electron energies E(k) of a periodic crystal as functions of crystal momentum, one branch per band, usually plotted along high-symmetry lines of the Brillouin zone. Band edges, slopes and curvatures give the gap, group velocities and effective masses; crossings and inversions give the topology. In layered crystals interlayer hybridisation makes it depend on thickness: the valence-band maximum of MoS₂ moves from Γ in the bulk to K in the monolayer, turning an indirect gap into a direct one.

Full explanation

Time-reversal symmetry

The idea that the laws governing electrons would look just as valid if you ran a film of them backwards. Reversing time flips every motion and every spin, so a material with no magnetism of its own usually keeps this symmetry, while a magnet – or a magnetic field – breaks it. Which case applies decides a lot: some protected edge currents need the symmetry, and others need it broken.

The antiunitary operation t → −t, which reverses momenta and spins; for spin-½ electrons T² = −1, giving Kramers degeneracy of every state at time-reversal-invariant momenta. It is broken by magnetic order or applied fields. Its presence protects the helical edge states of quantum spin Hall insulators and makes Berry curvature odd in k, so valley Hall but not anomalous Hall effects survive; its breaking allows Chern insulators, the anomalous Hall effect and Kerr rotation, the standard probes of spontaneous breaking in correlated phases.

Full explanation