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The Barnett effect is the change of a body's magnetization caused by mechanical rotation. Turning the whole specimen can bias the internal angular momentum carrying its magnetic moments, even with zero applied magnetic field. It is the reciprocal physical question to the Einstein-de Haas effect: impose rotation and measure magnetization, rather than change magnetization and observe mechanical motion. The relation between the two becomes especially transparent when the same signed gyromagnetic ratio connects magnetic moment and internal angular momentum.

Samuel Jackson Barnett published Magnetization by Rotation on 1 October 1915 in Physical Review. The Barnett rotation magnetometry experiment below provides an inspected modern example. The important distinction is between an equivalent term in a Hamiltonian and the actual external magnetic field measured by a magnetometer: the first biases the material; its resulting magnetization produces the second.

Let the specimen rotate uniformly with angular velocity $\mathbf{\Omega }=\Omega \hat{\mathbf{z}}$. In its rotating reference frame, the internal Hamiltonian containsHere $J_z$ is the internal angular momentum operator about the rotation axis, and ${\mathcal{H}}_0$ contains the internal interactions and any imposed magnetic field expressed in that frame. It does not include the separately treated rigid body's rotational kinetic energy. For a sector with magnetic moment $m_z=\gamma J_z$, the rotational term has exactly the form of a magnetic dipole potential energy:This Barnett equivalent magnetic field has tesla units, with the angular convention for the signed gyromagnetic ratio: $\Omega$ is in radians per second, not revolutions per second. Its sign matters. For an electronic contribution with $\gamma <0$, positive $\Omega$ favors positive $J_z$ and negative $m_z$. A sector with $\gamma >0$ has the opposite magnetic sign. Equal $\Omega$ need not correspond to equal Barnett fields for sectors having different gyromagnetic ratios.

A short derivation fixes the sign independently of any material model. Put $U(t)=\exp (-\mathrm{i}\Omega t{J}_z/\hslash )$ and transform a laboratory quantum state by $|{\psi }_{\mathrm{rot}}⟩=U^{†}|{\psi }_{\mathrm{lab}}⟩$. The Schrödinger equation givesThe transformed laboratory term is denoted by ${\mathcal{H}}_0$; a laboratory perturbation not stationary in the rotating frame can make it time dependent. Establishing a steady thermal response also requires exchange of internal angular momentum with the rotating body, for example through spin-lattice relaxation. A mere relabeling of coordinates cannot polarize isolated, unrelaxed spins.

The Barnett field is a useful description of spin-rotation coupling, not a claim that empty laboratory space acquires a uniform magnetic flux density $\Omega /\gamma$. In particular, inserting it into the Lorentz force on an unrelated test electric charge is unjustified. A nearby magnetometer detects the specimen's actual stray magnetic field and backgrounds, rather than directly detecting this internal Hamiltonian parameter.

A stationary magnetometer recording time variation of the background magnetic field while a moving instrument measures spatial variation. Subtracting the synchronized base changes reduces temporal contamination.

In 1986, Johannes Georg Bednorz and Karl Alexander Müller precipitated mixed oxalates from aqueous barium, lanthanum and copper nitrates using oxalic acid. Heating at $900{}^{\circ }\mathrm{C}$ for five hours preceded pressing at $4\mathrm{kbar}$ and reheating for sintering. X-ray diffraction resolved three phases. Rectangular pieces carried gold electrodes and indium wires; four-terminal sensing in a continuous-flow cryostat measured electrical resistance versus temperature. Annealing atmosphere and measuring electric current density were varied; larger electric current densities suppressed the drop. An onset near $35\mathrm{K}$ differed from the much lower temperature where the drop approached three orders of magnitude.^[ref]

This was evidence for possible granular superconductivity, with phase identification unfinished. The paper deferred Meissner effect and heat capacity tests; its proof note corrected bulk lanthanum/barium ratios. A resistive onset did not establish a uniform bulk superconducting transition temperature.^[ref]

Their 1987 authored lecture describes later magnetometer checks on lead, followed by magnetic susceptibility measurements: samples with a resistive drop developed diamagnetism at somewhat lower temperatures. Combining magnetic, transport and X-ray diffraction results identified barium-substituted $\mathrm{L}{\mathrm{a}}_2\mathrm{Cu}{\mathrm{O}}_4$ as the superconducting phase. These later results strengthened the case beyond the initial mixed-phase transport evidence.^[ref]

Dmitry Budker develops optical methods for measuring weak magnetic fields. Resonant light interacts with an atomic vapor, preparing or probing atomic polarization whose evolution depends on the field. Measuring an optical signal therefore converts atomic magnetic response into a sensitive magnetometer. His coauthored review connects this method with geomagnetic sensing, detection of nuclear magnetic resonance and tests of fundamental symmetries.^[ref]

Instrument manufacturer and issuer of manuals for field magnetometers.

Magnetic shielding reduces an unwanted magnetic field in a specified region. Residual fields and fields generated inside the shield still need to be assessed in a magnetometer experiment.

A magnetic skin layer is the region penetrated by an oscillating magnetic field in a conducting material. With constant magnetic permeability $\mu$ and electrical conductivity $\sigma$, define the magnetic diffusivityHere $\eta$ has units ${\mathrm{m}}^2{\mathrm{s}}^{-1}$; it is not the electrical resistivity $1/\sigma$. Negligible material motion reduces the resistive induction equation to magnetic diffusion.

Take the conductor to occupy $y>0$ and use time dependence $e^{i\omega t}$ with $\omega >0$. For a tangential magnetic field, the one-dimensional equation isThe solution decaying into the conductor hasThus the skin depth $\delta$ is both the amplitude decay length and the distance for one radian of phase lag. Raising frequency by a factor of four halves $\delta$. ^[ref]

If the boundary amplitude varies slowly as $C(x)$, the solenoidal magnetic-field constraint additionally requires, to leading order,Indeed ${\partial }_x{\hat{B}}_x+{\partial }_y{\hat{B}}_y=0$. This normal component is smaller by the ratio of $\delta$ to the along-boundary variation length; a predominantly tangential field need not be exactly tangential.

A demonstration described by Hermann A. Haus and James R. Melcher drives a winding on a magnetic core passing through a slit in an aluminium block. A magnetometer probe samples the field through a measuring slit. Comparing 60 and 240 Hz tests the predicted factor-of-two change in penetration depth. ^[ref]

A magnetometer measures a magnetic field or a specimen's magnetic dipole moment. A vibrating-sample magnetometer determines the latter from the electromotive force induced in pickup coils by specimen motion.

Paleomagnetism reconstructs past magnetic fields from remanent magnetization in rocks and other materials. Cooling volcanic minerals can acquire thermoremanent magnetization; later heating, alteration or mineral growth can change the record.

An oriented field sample preserves the relation between the measured magnetic direction and its geological setting. Shielded laboratory magnetometers and stepwise heating or alternating-field treatment help separate components acquired at different times. Combined with independent ages and structural corrections, the results test continental reconstruction and past field reversals.^[ref]

Oceanic magnetic anomalies. Newly formed oceanic crust contains magnetic minerals. As it cools through their magnetic blocking temperatures, it acquires thermoremanent magnetization recording the ambient field polarity. Continuing seafloor spreading carries that record away from the ridge. Geomagnetic reversals therefore generate approximately paired marine magnetic stripes parallel to the ridge, with older crust farther from its axis. A magnetometer measures the superposed field above this magnetized material; subtracting a reference field reveals magnetic anomalies. The anomaly sign and shape depend on magnetization direction, latitude, source depth and geometry, so a positive measured anomaly is not universally identical to normal rock polarity.^[ref]

Matching a sequence of stripes to an independently dated reversal chronology gives plate ages and spreading histories. A stripe of width $w$ formed over interval $\Delta t$ implies half-spreading rate $v=w/\Delta t$ under steady symmetric spreading; full separation speed is $2v$. Unequal widths on opposite flanks can reflect asymmetric spreading or later deformation. Alteration, remagnetization and overlapping magnetic sources complicate inversion. The sequence correlation is stronger evidence than an isolated stripe or a field-strength peak.

Rayleigh-Bénard convection. Consider a horizontal fluid layer of thickness $d$, hotter below by $\Delta T>0$. The conductive state is motionless with a linear temperature gradient. A rising warm parcel is buoyant, but viscosity resists its motion and thermal diffusion erases its temperature anomaly. In the Boussinesq approximation, density variations are retained in buoyancy while the flow is otherwise incompressible. The competing effects are measured by the Rayleigh number and Prandtl number,For stress-free impermeable, fixed-temperature boundaries, linear stationary disturbances with horizontal wavenumber $q/d$ giveMinimizing gives $q_c=\pi /\sqrt{2}$ and the critical Rayleigh number for an isothermal layer, ${\mathrm{Ra}}_c=27{\pi }^4/4\simeq 657.5$. Two rigid no-slip, fixed-temperature boundaries instead give approximately $1708$; the critical value is not independent of boundary conditions.^[ref]

Above onset, buoyancy can sustain overturning rolls and heat transfer exceeds pure conduction, with Nusselt number $\mathrm{Nu}>1$. Nonlinear advection eventually limits the disturbance; larger driving can produce time-dependent or turbulent states. The ideal Boussinesq problem does not require hexagonal cells: planform selection depends on boundaries and non-Boussinesq effects. Convection driven by surface tension at a free surface is a distinct mechanism. An adverse temperature gradient supplies driving, but overcoming diffusion and viscosity requires a finite threshold.

The decisive change was from moving continents within a supposedly permanent ocean floor to moving coherent tectonic plates that include both continental and oceanic lithosphere. Several independent observations made that change testable.

Continental connections supplied the initial problem. In the early twentieth century, Alfred Wegener assembled matching continental margins, correlatable rock belts and mountain chains, shared fossil assemblages, and paleoclimate indicators into the case for continental drift. Reassembling Gondwana, for example, makes geographically separated glacial deposits and striation directions compatible with one ice-sheet system. Fits at the continental shelf edge are physically more meaningful than exact fits to modern coastlines, which have been modified by erosion and sea-level change. The evidence suggested relative movement, but did not justify the proposed forces: continents cannot readily plough independently through strong oceanic rock. A convincing mechanism and independent motion measurements were missing.

Oceanography changed the boundary conditions. Echo-sounding surveys revealed a connected spreading ridge system, axial valleys, subduction trenches and long fracture zones. Seismic refraction surveys established systematic differences between continental and oceanic crust. Thin oceanic sediment cover, high ridge heat flux and the lack of very old exposed oceanic basement made permanent, ancient ocean basins increasingly implausible. Harry Hammond Hess proposed creation of oceanic lithosphere at ridges and recycling at trenches: seafloor spreading without requiring an expanding Earth. Slow mantle convection supplied a physically plausible connection between surface transport and internal heat loss. The mechanism need not have been completely quantified before its kinematic predictions could be tested.^[ref]

Magnetic records supplied a clock and a speedometer. Dated continental lavas established a sequence of geomagnetic reversals. Marine magnetometers then found elongated, approximately paired marine magnetic stripes on either side of ridges. The 1963 interpretation by F. J. Vine and D. H. Matthews combined repeated reversals with seafloor spreading: cooling basalt locks in remanent magnetization, and continuous motion converts a time sequence into a spatial sequence. If a polarity interval lasts $\Delta t$ and occupies width $w$ on one ridge flank, its half-spreading rate is $w/\Delta t$. Matching several reversals tests the predicted sequence, rather than merely fitting a single stripe.^[ref] Different apparent polar wander paths for different continents also became mutually consistent after continental reconstruction, favoring relative continental motion over independent magnetic-pole histories.

Earthquakes identified creation, translation and consumption. Improved global seismology located shallow earthquakes along ridges and transforms, and dipping Wadati-Benioff zones beneath trenches. Their progressive focal depths identified cold, coherent slabs entering the mantle. Focal mechanisms showed extension at spreading boundaries, tangential slip at transforms and convergence at trenches. In 1965, John Tuzo Wilson's transform fault interpretation made a particularly discriminating prediction: active slip occurs between offset ridge segments, with a sense that can be opposite to that inferred by treating the entire lineament as an ordinary offset fault. The outer fracture zones are inherited traces, not continuing active plate boundaries. Agreement of focal mechanisms with the transform prediction linked magnetic and seismic evidence.

The late-1960s synthesis made these observations one quantitative theory. Relative motion of rigid tectonic plates on a sphere can be described by an Euler angular velocity vector, with $\mathbf{v}=\mathbf{\omega }\times \mathbf{r}$. Spreading rates, transform azimuths and slip directions must fit the same rotation, and relative angular velocities must close around plate circuits. The resulting framework accounted for global boundary geometry and earthquake mechanisms without moving continents separately from the seafloor. Deep-ocean drilling beginning in 1968 subsequently confirmed that basement and overlying sediments generally become older away from ridges; this was a powerful confirmation of an already emerging synthesis, not a prerequisite discovered decades earlier.^[ref]

Thus plate tectonics succeeded through agreement between geological reconstruction, magnetic chronology, ocean-floor structure, seismology and rigid-plate kinematics. Modern satellite geodesy verifies motions directly, but belongs to the later confirmation of the theory, not its original 1960s evidence.

In a weak applied field, magnetic susceptibility relates magnetization to magnetic field intensity, $M=\chi H$. Its sign, temperature dependence and nonlinear field dependence distinguish several mechanisms.

Diamagnetism is the orbital response opposing an applied magnetic field, with $\chi <0$. Closed-shell atoms and filled bands generally give a weak, nearly temperature-independent response. In a simple free electron metal, Landau diamagnetism contributes ${\chi }_L=-{\chi }_P/3$; the factor is specific to the isotropic parabolic-band model and is not universal in crystals.

Paramagnetism gives $\chi >0$. Localized magnetic moments align statistically with the field against thermal disorder. For independent moments of angular momentum $J$,which is the Curie law. Exchange interactions often lead approximately to the Curie–Weiss law, $\chi =C/(T-\Theta )$, sufficiently far above any ordering temperature. The sign of $\Theta$ suggests predominantly parallel or antiparallel exchange, though it is not a complete classification. Conduction electrons instead exhibit Pauli paramagnetism:for $g\simeq 2$ and a spin-summed density of states per unit volume. Only states close to the Fermi energy change occupation, making this response nearly temperature independent when $k_{B}T\ll E_F$.

Ferromagnetism has spontaneous parallel magnetic order below a Curie temperature. Exchange interaction, not simply classical dipole attraction, provides the dominant alignment mechanism. In the convention $H=-J_{\mathrm{ex}}{\sum }_{⟨ij⟩}{\mathbf{S}}_i\cdot {\mathbf{S}}_j$, positive $J_{\mathrm{ex}}$ favours alignment. Magnetic domains can make a ferromagnet's total magnetization vanish before an external field aligns its domains. Domain motion and anisotropy produce saturation, hysteresis, remanent magnetization and a reverse field measured by magnetic coercivity.

Antiferromagnetism has oppositely ordered sublattices below a Néel temperature; equal opposing moments give zero net magnetization while retaining a nonzero staggered order parameter. A susceptibility anomaly and magnetic neutron diffraction reveal this order even when bulk magnetization vanishes. Ferrimagnetism also has opposing sublattices but unequal contributions, giving a nonzero spontaneous net moment. Above their ordering temperatures both can become paramagnetic. Measurements with a magnetometer as a function of field and temperature, supplemented by magnetic diffraction, therefore distinguishes a compensated ordered material from an ordinary paramagnet.

Measure total magnetic field along the same south–north line with a calibrated magnetometer, recording position, time and sensor height. A simultaneous base-station magnetometer measures temporal variation so that diurnal changes can be removed from the moving survey. Avoid disturbed periods and magnetic contamination from vehicles, fences, power lines and equipment. Choose station spacing much smaller than the expected anomaly width, for example tens to hundreds of metres for a kilometre-scale target.

Subtract the epoch-appropriate International Geomagnetic Reference Field or another stated regional main-field model to obtain a total-field magnetic anomaly. Level overlapping traverses and remove offsets or drift where appropriate. Accurate terrain/sensor geometry is needed for comparison with a geological model, but there is no universal magnetic analogue of a constant-density Bouguer slab correction: the effect depends on the distribution and direction of magnetization. Measure magnetic susceptibility and remanent magnetization on representative greenstones, granite and host rock to test the assumed magnetic sources.

An absolute scalar magnetometer that infers $|\mathbf{B}|$ from the free Larmor precession frequency of polarized protons. It measures field strength rather than field direction.

Solar Orbiter is an ESA-led spacecraft with strong NASA participation, launched in February 2020 to connect observations of the Sun with measurements of the solar wind. Its heliocentric orbit and gravity assists allow observations from different distances and increasing solar latitudes, rather than restricting every view to the plane from which Earth sees the Sun.^[ref]

Its ten instruments divide into six for remote sensing and four for sampling the surrounding environment. The remote sensing instruments observe emitted or scattered light from the Sun and its surroundings. The local instruments measure plasma, energetic particles, electric fields, magnetic fields and waves. A magnetometer and particle analysers therefore answer different questions from an image: one measures conditions at the spacecraft, while the other helps locate the remote source.^[ref]

A scientific comparison can ask whether a feature observed near the Sun is associated with a later change in the velocity distribution or composition of locally sampled particles. Identifying the connection requires accounting for the material's travel time and the changing geometry; simultaneous timestamps alone do not establish a common origin. The mission's combined apparatus makes such tests possible. A 2024 analysis, for example, separated proton and alpha particle populations in its solar wind data rather than representing all ions by one mean speed.^[ref]

Space weather describes changing conditions in the Sun, solar wind, magnetosphere and upper atmosphere that affect space-based or terrestrial systems. Its effects depend on the physical disturbance. Solar flares can increase ionization and disrupt radio propagation, energetic particles can damage spacecraft electronics, and coronal mass ejections can trigger geomagnetic storms. These mechanisms need different observations and forecasts.^[ref]

A useful measurement chain starts with spacecraft upstream of Earth, often near the Sun-Earth inner Lagrange point. Magnetometers measure the interplanetary magnetic field, while plasma instruments estimate particle density, speed and temperature. NOAA combines these measurements with models to monitor approaching disturbances; the magnetic-field direction matters as well as the flow speed.^[ref]

At the ground, changing magnetic fields induce electric fields. Faraday's law of induction gives the loop relation $\mathcal{E}=-d{\Phi }_B/dt$. In an extended conducting system, the resulting current also depends on electrical resistance and the spatially varying fields. A large magnetic disturbance can therefore affect a power grid even though its conductors are far below the space plasma. Measurements and a physical coupling model connect the solar disturbance to the terrestrial effect.

Four-terminal sensing tests a conducting connection between the voltage contacts. A magnetometer instead tests the sample's magnetic response. These measurements provide complementary constraints: the first is sensitive to a continuous path, while the second also depends on screening geometry and preparation history.

For transport, define $V_{ab}$ between the inner contacts and use the reversed-electric current estimator from four-terminal sensing. Contact separation excludes drive-contact drops, but does not eliminate a drifting thermoelectric effect, Joule heating or an unrepresentative path through part of the specimen. Repeat at smaller electric currents and compare results at the same sample temperature. A finite-current result refers to that electric current and its relation to the path's superconducting critical current.

For magnetism, distinguish cooling in zero applied magnetic field and then applying it from the Field-cooled Meissner experiment. Record the applied magnetic field, background and sample geometry when interpreting magnetization or magnetic susceptibility. A transport short does not establish full Meissner effect screening throughout the specimen. Conversely, flux pinning in a type-II superconductor can make the field-cooled magnetic response differ from ideal complete expulsion. Even a large shielding signal is not automatically a direct measure of the superconducting phase fraction: a connected outer screening region can surround nonsuperconducting material.

Voyager 1 is a spacecraft launched on 5 September 1977 to investigate the outer Solar system. It flew past Jupiter in March 1979 and Saturn in November 1980, then continued outward on an extended mission to study the environment beyond the planets.^[ref]

On 25 August 2012 it crossed the heliopause, the boundary between the solar wind-dominated heliosphere and the surrounding interstellar medium. This boundary concerns the plasma environment; it is not a boundary beyond which the Sun's gravity vanishes. Its scientific instruments include detectors of charged particles, a magnetometer and a Voyager plasma-wave instrument. Together, measurements of particles, magnetic fields and plasma waves allow a moving probe to investigate a remote environment that cannot be sampled in a terrestrial laboratory.^[ref]