Multiferroic

Everyday term

In plain words

A material that is magnetic and electrically polarised at the same time, so a magnetic field can shift its charge and an electric field can turn its magnetism. The combination is rare, because the two kinds of order usually want incompatible atoms.

Going deeper

A multiferroic carries magnetic and electric order at once. In the type-II case the two are not merely coexisting: the spin arrangement itself breaks inversion symmetry and produces the polarisation, which is why reversing the spiral reverses the charge.

Two orders that get in each other’s way

The reason multiferroics are rare is chemical. The classic way to make a oxide is to give a transition metal an empty d shell, so it can shift off-centre toward its oxygen neighbours. Magnetism needs the opposite: a partly filled d shell carrying a moment. One ion cannot easily do both.

The workarounds are all indirect. A lone pair of electrons on a heavy ion such as bismuth can drive the displacement while the magnetic ion is left alone, which is how BiFeO₃ manages both at room temperature. Geometric distortions, charge ordering, and improper mechanisms where polarisation appears as a by-product of some other structural instability all appear in the catalogue. In each of these type-I cases the two orders have separate causes – and, as a direct consequence, they barely influence one another.

Type II: letting the magnetism do the work

The alternative is to make the responsible for the polarisation. A spiral or cycloidal arrangement can lack a centre of inversion all by itself, and through spin–orbit effects – the inverse or spin-current mechanism – the electrons redistribute slightly, leaving a net electric dipole tied to the of the spiral.

This is what makes type-II multiferroics interesting: the coupling is not an add-on but the origin, so a magnetic field that changes the spiral changes the polarisation, and an electric field can select the handedness. The price is that the polarisation is small, typically a hundred times less than in a conventional ferroelectric, and that it only exists where the spiral does – which is usually well below room temperature.

Down to a single layer

Whether any of this survives in two dimensions is being tested on NiI₂. Its nickel layers order into a proper-screw spin helix with a definite handedness, and that handedness couples to the charge to give a polar, chirality-selected state. Circular measurements pick up the magneto-chiral ground state and its electromagnon modes; birefringence and show a state that breaks both three-fold rotation and inversion; and the whole set of signatures follows down to the .

The caveat is that this evidence is optical. Second-harmonic generation and birefringence establish symmetry and a polar state; they are not a measurement of a switchable polarisation with electrodes, which in a single layer of an iodide is a hard experiment. A 2023 reply argued that these optical signatures alone do not establish a single-layer multiferroic. , and stacking in few-layer samples also shift the transition, so the layer-number dependence is part of the physics rather than a detail.

For specialists

A material carrying more than one ferroic order – usually ferroelectric together with (anti)ferromagnetic – plus magnetoelectric coupling between them. Type-I multiferroics have independent origins and weak coupling; in type-II the polarisation is produced by the magnetic order itself, typically a spiral, and the coupling is strong. NiI₂ has been reported to keep a type-II order, with spiral magnetism and polarisation appearing together, down to the single layer – although the optical evidence is disputed.

Where this comes from

The renaissance of magnetoelectric multiferroics Spaldin and Fiebig · Science 309, 391 (2005) cited by 2,877
Evidence for a single-layer van der Waals multiferroic Song et al. · Nature 602, 601 (2022) cited by 404
Dilemma in optical identification of single-layer multiferroics Jiang et al. · Nature 619, E40 (2023) cited by 53

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

Skyrmion and the Dzyaloshinskii–Moriya interaction

A skyrmion is a tiny whirl in the magnetisation of a material: the magnetic direction turns smoothly from pointing down at its centre to pointing up at its rim. It behaves like a particle – a small current can move it, and it is hard to destroy, because undoing the whirl would mean flipping a whole region at once – which makes skyrmions candidates for dense, low-power magnetic memory. Most are held together by the Dzyaloshinskii–Moriya interaction, a twisting force between neighbouring magnetic atoms that appears only where a mirror symmetry is missing.

A particle-like spin texture whose magnetisation wraps the unit sphere once, giving it an integer topological charge. Bloch-type skyrmions form in bulk chiral magnets (MnSi, 2009) and Néel-type ones at interfaces and in polar crystals. They are stabilised by the antisymmetric Dzyaloshinskii–Moriya interaction – proportional to the cross product of neighbouring spins, arising from spin–orbit coupling where inversion symmetry is broken – competing with exchange, anisotropy and the applied field; dipolar-stabilised skyrmion bubbles form without it. Among 2D magnets, Fe₃GeTe₂ hosts bubbles and, in WTe₂/Fe₃GeTe₂ heterostructures, interface-induced Néel skyrmions. Their emergent magnetic field can add a topological contribution to the Hall effect, and their current-driven motion by spin–orbit torques underlies racetrack-memory proposals.

Full explanation

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

Linear and circular dichroism

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 flake this way reveals hidden directions in it – its crystal axes, its magnetic order, which valley its electrons sit in – without touching it.

Polarisation-dependent absorption: linear dichroism between orthogonal linear polarisations, from in-plane anisotropy of the lattice or of an order that breaks rotational symmetry; circular dichroism between left and right circular polarisations, from broken mirror or time-reversal symmetry. 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 TMDCs 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.

Full explanation

Second-harmonic generation (SHG)

Shine intense light on a crystal and a little of it comes back at exactly twice the frequency – half the wavelength, which is how a green laser pointer turns invisible infrared into green light. It happens only if the crystal has no centre of symmetry, which makes it a quick, contactless test of symmetry, layer number and crystal orientation.

A second-order nonlinear response, forbidden in centrosymmetric media, so in 2H TMDCs it appears for odd layer numbers and vanishes for even ones. The polarisation dependence gives crystal orientation, and so the twist angle in a stack; the intensity follows layer number and strain; and it detects broken inversion symmetry in ferroelectric and magnetic layers where no other quick probe exists.

Full explanation

Substrate

The base a thin film or flake sits on – often a polished slice of silicon, glass or sapphire. For a crystal one atom thick, the substrate is not just a table: its bumps, stray charges and vibrations reach right into the sheet and change how it conducts and glows. That is why the same material can behave differently on two substrates, and why the flattest, cleanest one – boron nitride – gives the best results.

The material beneath a 2D layer. It acts on the layer through surface roughness, charged impurities, surface optical phonons, dielectric screening, strain and charge transfer, and during growth it sets orientation through epitaxy. Replacing SiO₂ with hexagonal boron nitride, which is atomically flat and nearly free of dangling bonds and charge traps, improved the mobility and charge homogeneity of graphene by close to an order of magnitude.

Full explanation

Dielectric screening

The way a material weakens the pull between two charges inside it: its own electrons shift slightly and partly cancel the field between them. A sheet one atom thick has almost nothing around it to do this, so charges in it attract each other far more strongly than in a thick crystal – which is why light makes tightly bound pairs in 2D materials, and why whatever a sheet rests on changes its properties.

The reduction of the Coulomb interaction by the polarisation of bound electrons and ions and, in metals and doped layers, by free carriers, described by a dielectric function ε(q, ω). In a monolayer the field lines between distant charges run through the surroundings, so ε(q) approaches 1 as q → 0 and the screening is non-local and set by the environment. Exciton binding energies reach hundreds of meV, and a change of substrate or encapsulation shifts the quasiparticle gap by 100 meV or more while the optical gap barely moves.

Full explanation