Magnetometry

In plain words

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

Going deeper

A SQUID counts the magnetic flux from a whole sample – ideal for bulk crystals, blind to a single flake. A nitrogen-vacancy centre at the tip of a diamond probe senses the stray field nanometres above a flake and images its domains. For thin films the hard part is attributing the signal: substrate, glue and specks of iron can outweigh a monolayer.

Measuring a moment

A SQUID – a superconducting quantum interference device – is a ring of superconductor interrupted by one or two , so sensitive to the magnetic flux threading it that it can count single flux quanta. Moving a sample through pick-up coils connected to it measures the sample’s magnetic moment; a vibrating-sample magnetometer does the same with an ordinary coil and a vibrating sample. Plotting the moment against field gives loops, and against temperature the Curie or – the standard first characterisation of every bulk magnetic crystal, from CrI₃ to Fe₃GeTe₂.

Too small to measure that way

A flake a few micrometres across has a moment many orders of magnitude below what a SQUID can resolve, and the substrate, the glue and any speck of iron from tweezers or tape contribute far more. Even a film covering a whole substrate gives a signal comparable to these backgrounds. That is how reports of strong room-temperature ferromagnetism in monolayer VSe₂ arose from bulk magnetometry, while later X-ray magnetic , which picks out the magnetism of vanadium alone, found none. For thin films, bulk magnetometry is a starting point that needs confirmation from an element-specific or local probe.

Nanoscale sensors

Local probes reach single layers. A nitrogen-vacancy centre in diamond – a nitrogen atom next to a missing carbon – has a spin whose resonance frequency shifts with the magnetic field and can be read out with light. Placed at the tip of a scanning probe, it measures the stray field a few tens of nanometres above a flake, quantitatively and at room or low temperature, and has imaged the magnetisation and domains of single and few-layer CrI₃. Magnetic force microscopy and scanning SQUIDs built on the tip of a pipette complement it, alongside the optical and circular-dichroism methods most used for 2D magnets.

For specialists

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 against field and temperature, from which ordering temperatures, saturation moments and 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 ( effect, ) 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.

Where this comes from

Magnetometry with nitrogen-vacancy defects in diamond Rondin et al. · Reports on Progress in Physics 77, 056503 (2014)
Strong room-temperature ferromagnetism in VSe₂ monolayers on van der Waals substrates Bonilla et al. · Nature Nanotechnology 13, 289 (2018) cited by 1,713
Evidence of spin frustration in a vanadium diselenide monolayer magnet Wong et al. · Advanced Materials 31, 1901185 (2019) cited by 153
Probing magnetism in 2D materials at the nanoscale with single-spin microscopy Thiel et al. · Science 364, 973 (2019)

Sensor

A device that turns something in its surroundings – a gas, a magnetic field, a pressure, a molecule in blood – into an electrical signal. 2D materials make unusually sensitive sensors because every atom is on the surface: a few molecules landing on a single layer change how well it conducts. Graphene also makes very good magnetic-field sensors. The hard part is not sensitivity but selectivity – responding to one thing and ignoring everything else – and staying stable for years.

Transducers in which a stimulus changes an electrical property of a 2D layer: chemiresistive and field-effect gas and humidity sensors, in which adsorbates transfer charge and shift the conductance (graphene registered single NO₂ molecules in 2007); Hall sensors, in which graphene’s low carrier density and high mobility give a large, temperature-stable Hall voltage; biosensors with receptors on a graphene or MoS₂ channel that bind target molecules; and strain, pressure and light sensors. Sensitivity comes from the all-surface geometry and the low density of states; the limits are selectivity, drift and hysteresis from humidity and contamination, recovery time, device-to-device variation and calibration, addressed by functionalisation, encapsulation and arrays read by pattern recognition.

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

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

Josephson effect

A current that flows between two superconductors through a thin barrier with no voltage at all, carried by pairs of electrons tunnelling across – slipping through a barrier that everyday physics says they cannot pass. How large that current is, and how it reacts to a magnetic field, is one of the sharpest ways to find out what kind of superconductor you are holding.

Phase-coherent tunnelling of Cooper pairs across a weak link, giving a supercurrent I = I_c·sin Δφ and, under a voltage, an oscillation at 2eV/h. In van der Waals stacks the weak link can be a graphene channel, a semiconducting monolayer or a twisted interface, and the current–phase relation, the Fraunhofer pattern and the temperature dependence of the critical current report on ballistic transport, edge modes and pairing symmetry.

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

Hall effect

Send a current along a strip in a magnetic field and the moving charges are pushed towards one edge, so a small voltage appears across the strip. Its size tells how many charge carriers there are, and its sign whether they are electrons or holes, which makes it the standard way to count them. In a magnetic material a sideways voltage appears even without an outside field – the anomalous Hall effect, a handy way to see whether a tiny flake is magnetic.

The transverse voltage that the Lorentz force produces when a current flows in a perpendicular magnetic field. For one type of carrier in a 2D sheet the Hall resistance is B/ne, independent of thickness, so its slope gives the sheet density n and its sign the carrier type; combined with the sheet resistance it gives the Hall mobility. Two carrier types make the Hall resistance non-linear in B and call for a two-band fit. In magnetic conductors an extra term that follows the magnetisation – the anomalous Hall effect – comes from the Berry curvature of the bands (intrinsic) or from skew and side-jump scattering (extrinsic); quantised, it becomes the quantum anomalous Hall effect.

Full explanation

Magnetoresistance

A change in electrical resistance when a magnetic field is applied. It is how the read head of a hard disk senses its bits, and in some layered magnets the change is enormous – a stack can go from barely conducting to conducting – which is how the magnetic state of a few atomic layers is read out electrically.

The field dependence of resistivity. Ordinary orbital magnetoresistance is positive and usually small, though enormous in compensated semimetals such as WTe₂; giant and tunnelling magnetoresistance come from spin-dependent transport across magnetic layers; colossal magnetoresistance from a field-driven change of electronic state. In van der Waals stacks a few layers of CrI₃ act as a spin filter whose resistance changes by orders of magnitude as adjacent layers align, which is how layer-by-layer magnetic order became measurable in transport.

Full explanation