Magnetic moment

Everyday term

In plain words

The strength and direction of the tiny magnet an atom or an electron carries. Every electron is a small magnet through its , and its motion around an atom can add more. In most atoms the electrons pair up and their magnets cancel; atoms with unpaired electrons – chromium, manganese, iron, nickel, the rare earths – keep a moment. How these moments line up decides whether a material is a , an antiferromagnet or no magnet at all.

As the site uses it

Below roughly 80–100 K the electrons freeze into a charge order with a 2×2 pattern that appears to pick a handedness and, by some measurements, to break time-reversal symmetry without any magnetic moments.

CsV₃Sb₅, KV₃Sb₅ · Kagome metals AV₃Sb₅

The best-studied candidate for a Kitaev quantum spin liquid: a state in which magnetic moments never settle into an ordered pattern, even at absolute zero, and which theory predicts should carry exotic excitations called Majorana fermions.

α-RuCl₃ · Ruthenium trichloride and Kitaev magnets

Going deeper

An electron’s moment comes from its spin and its orbital motion. Paired electrons cancel, so the moment of an ion comes from its unpaired electrons – about one Bohr magneton each in a 3d ion. How the moments of neighbouring atoms line up makes a ferromagnet, an antiferromagnet or a ferrimagnet.

Where moments come from

An electron carries a magnetic moment of almost exactly one Bohr magneton through its spin, and circling in an it can carry an orbital moment as well. In a filled shell the electrons pair up, spin against spin and orbit against orbit, and nothing is left over. Partly filled shells are what make atoms magnetic: the 3d shell of chromium, manganese, iron, cobalt and nickel, and the 4f shell of the rare earths.

In a crystal, the atoms around a 3d ion usually lock its orbital motion in place, so its moment comes almost entirely from spin: about one Bohr magneton for each unpaired electron, three for Cr³⁺ with its three d electrons, five for Mn²⁺ with five. Heavier 4d and 5d ions, such as ruthenium in α-RuCl₃, combine spin and orbital motion through strong , which is why their magnetism depends so strongly on direction.

Local and itinerant

In magnetic the moments sit on the atoms and stay there: CrI₃, CrSBr, the MPS₃ family and MnBi₂Te₄ are lattices of local moments coupled by exchange. finds how large the moments are in the ordered state and where they point – in MnBi₂Te₄, 4.04 Bohr magnetons per manganese, ferromagnetic within each layer and opposite from one layer to the next below 24 K (Yan and colleagues, 2019), somewhat less than the five of a free Mn²⁺ ion.

In metals the moments belong partly to the conduction electrons and need not come in whole numbers. Flux-grown Fe₃GeTe₂ orders with 1.11 Bohr magnetons per iron, pointing out of the layers, and as iron is lost from the lattice its , and magnetisation all fall: crystals grown by order near 220 K, flux-grown ones near 150 K (May and colleagues, 2016).

Three numbers for one moment

Three values are often quoted, and they differ. The saturation moment comes from in a field strong enough to align everything. The effective moment comes from the Curie–Weiss behaviour of the susceptibility above the ordering temperature and includes the quantum fluctuations of the spin, so it is larger: about 3.9 Bohr magnetons for Cr³⁺, against 3 at saturation. The ordered moment, from neutron diffraction, is what the moments actually do in the ordered state, and fluctuations – strongest in low dimensions – can shrink it.

In a none of these can be weighed with an ordinary magnetometer, so moments are inferred from , from the fields at which layers flip, or from , which also separates spin from orbital moments, element by element.

For specialists

The magnetic dipole of an atom, ion or electron, measured in Bohr magnetons (μB ≈ 9.27 × 10⁻²⁴ J/T). In insulating magnets it is a local moment set mainly by the spins of unpaired d or f electrons – about one Bohr magneton per unpaired electron for 3d ions, whose orbital moment the crystal field largely quenches: 3 μB for Cr³⁺, 5 μB for Mn²⁺. Ordered moments from neutron diffraction often come out below these values, 4.04 μB per manganese in MnBi₂Te₄. In metallic magnets the moment belongs partly to itinerant electrons and need not be near a whole number, as with 1.11 μB per iron in Fe₃GeTe₂.

Where this comes from

Crystal growth and magnetic structure of MnBi₂Te₄ Yan et al. · Physical Review Materials 3, 064202 (2019)
Magnetic structure and phase stability of the van der Waals bonded ferromagnet Fe_3−xGeTe₂ May et al. · Physical Review B 93, 014411 (2016)

In the news

The newest items in the site’s news feed that use the term, one from each source.

Preprintnot yet peer reviewed 11 Oct 2026 arXiv

Field Response of the Orbital Moment Probed by Integrated Magnetic Circular Dichroism

Magnetic (MCD) is an optical probe of orbital breaking. Although frequency integrated MCD is related to the self-rotation contribution to orbital magnetization at zero field, its magnetic response generally differs from the thermodynamic orbital susceptibility. Here, we define…

TheoryTwisted graphene Graphene

Preprintnot yet peer reviewed 6 Oct 2026 arXiv

Interfacial Charge Transfer and Morphology Govern Magnetism in Ultrathin VOx/MoSe2 Heterostructures

Engineering magnetism in two-dimensional through interfacial interactions offers an attractive alternative to substitutional and provides opportunities for integrating magnetic and optoelectronic functionality within the same . Here, we investigate ultrathin VOx films deposited on…

TheoryExperimentMoSe₂

Preprintnot yet peer reviewed 30 Sep 2026 arXiv

First-Principles Study of Two-Dimensional CeN: Interplay between Structural Stability, Electronic Structure, and Magnetism

In this work, the structural stability, and the electronic and magnetic properties of a novel CeN monolayer derived from the (111) surface of bulk rock salt CeN are investigated using calculations. Dimensional reduction produces substantial changes in the local atomic environment, decreasing the Ce-N…

Theory

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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

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

Orbitals and hybridisation

The shapes an electron’s cloud can take around an atom. Electrons do not circle the nucleus like planets; each sits in an orbital, a region with a definite energy and shape – a sphere (s), a dumbbell (p) or a clover-like shape (d). When atoms bond, their orbitals overlap and can blend into new ones pointing at the neighbours, which is hybridisation: in graphene each carbon mixes one s and two p orbitals into three bonds in the plane (sp²), leaving one p orbital standing up out of the sheet. Which orbitals hold the outermost electrons decides much of what a material does. Electrons in an orbital still carry a kind of circling motion, angular momentum, and the magnetism that comes from it rather than from their spin is called orbital magnetism.

Single-electron states of an atom labelled by angular momentum – s, p, d, f – whose overlap between neighbours forms bonds and bands. Hybridisation mixes orbitals on one atom, as in graphene’s sp² carbon, with three in-plane σ bonds 1.42 Å long and a half-filled π band from the out-of-plane p orbital, where the Dirac cones lie; or between atoms, as in the p–d hybridisation of transition-metal compounds. In 2H TMDCs a hybridisation gap splits a d band off from the rest, and whether it is half-filled or full separates metallic NbSe₂ and TaS₂ from semiconducting MoS₂. “Orbital” also names the electron’s motion: orbital magnetism comes from circulating electrons rather than from spin.

Full explanation

Metal, semimetal and insulator

The three basic ways a solid treats electricity, set by how its electrons fill the energies open to them. In a metal they fill a band of energies only partly, so the smallest push sets them moving, and it conducts at any temperature. In an insulator they fill a band completely and a wide gap separates it from the next, so nothing can move. A semimetal sits in between: two bands just touch or overlap a little, leaving a small number of mobile electrons and holes. NbSe₂ is a metal, graphene a semimetal, hBN an insulator.

A classification by where the Fermi level falls in the band structure. In a metal it crosses a partly filled band, leaving a Fermi surface, a carrier density of order one per atom (about 10²² cm⁻³) and a resistivity that falls on cooling. In a band insulator it lies in a gap of several electronvolts; a semiconductor is an insulator whose gap is small enough to be doped or gated. A semimetal has a slight overlap between conduction and valence bands (graphite, bismuth, bulk WTe₂) or bands that touch at isolated points (graphene), giving low and nearly equal densities of electrons and holes. Interactions can open gaps that band theory does not predict: Mott insulators from half-filled bands, excitonic insulators from semimetals.

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

Magnetometry

Measuring how magnetic a sample is, or how readily a magnetic field magnetises it – its magnetic susceptibility. For a crystal you can hold, this is routine: it is moved through a coil or past a superconducting sensor called a SQUID, which picks up its tiny magnetic field. A flake one atom thick is a different matter: its magnetism is far too weak for such instruments and is swamped by the substrate it sits on. So 2D magnets are usually studied with light, with currents, or with single-spin sensors in diamond that hover nanometres above the flake.

Measurement of magnetic moment or stray field. SQUID and vibrating-sample magnetometry of bulk crystals, with sensitivities around 10⁻⁸ emu (10⁻¹¹ A·m²), give magnetisation and magnetic susceptibility (magnetisation per unit field) against field and temperature, from which ordering temperatures, saturation moments and anisotropy follow; torque and Hall magnetometry and magnetic force microscopy extend this to small samples. Monolayer flakes lie far below SQUID sensitivity and are swamped by substrate diamagnetism and magnetic contamination, so their magnetism is read optically (MOKE, RMCD), electrically (anomalous Hall effect, tunnelling magnetoresistance) or with scanning nitrogen-vacancy magnetometry, which images stray fields quantitatively at the nanoscale. Claims of room-temperature ferromagnetism in thin films based on bulk magnetometry, as for monolayer VSe₂, need element-specific (XMCD) or local confirmation.

Full explanation

X-ray absorption spectroscopy (XAS)

Shining X-rays of tunable energy on a sample and watching how strongly it absorbs as the energy sweeps past the binding energy of one element’s inner electrons. Each element absorbs at its own energies, so the method looks at one element at a time – the iron in a catalyst, the vanadium in a magnet – and the exact shape of the absorption edge tells its oxidation state and surroundings. The bright, tunable X-rays it needs come from synchrotrons: large rings in which electrons circling close to the speed of light give off intense light, used also for photoemission and diffraction.

Absorption of tunable X-rays at a core-level edge of one element: the near-edge region (XANES) reflects oxidation state, empty states and local symmetry; the extended region (EXAFS) gives bond lengths and coordination; circularly polarised X-rays give X-ray magnetic circular dichroism (XMCD), element-specific spin and orbital moments. It uses synchrotron radiation and works operando. Operando XAS located Fe³⁺ in unusually short-bonded octahedral sites as the active centres of (Ni,Fe)OOH water-oxidation catalysts; XAS and XMCD on monolayer VSe₂ found vanadium 3d¹ and correlated spins without long-range order, against bulk-magnetometry reports of room-temperature ferromagnetism.

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

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

Density functional theory (DFT)

The workhorse calculation of materials physics. Rather than following every electron, it works with the electron density and a recipe for how electrons avoid one another – which makes a whole crystal cheap enough to compute, and makes the accuracy depend entirely on that recipe.

Ground-state electronic structure from the density, exact in principle by Hohenberg–Kohn and made practical by the Kohn–Sham equations with an approximate exchange–correlation functional. Two dimensions need care: a vacuum gap wide enough that periodic images stop interacting or a truncated Coulomb interaction, a dispersion correction for interlayer binding, and the knowledge that semi-local functionals underestimate gaps – hybrid functionals narrow that error at far higher cost, and quantitative gaps and optical spectra need GW and Bethe–Salpeter on top.

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