# Magnetic Microscopy in Rock Magnetism — lecture notes These notes are a plain-language companion to the reveal.js lecture. Each instrument section is paired with the interactive illustration used in the slides. The magnetic maps in the shared microscope lab are synthetic teaching data. For stray-field instruments, the map is calculated from the magnetic dipole equation for five buried grains with different three-dimensional moments, then evaluated at the sensor height. By the end of the lecture, students should be able to describe an instrument as a chain rather than as a black box: **magnetic source → physical interaction → sensor response → electronics → recorded dataset → interpretation**. That chain is the central idea of these notes. ## The common measurement problem A rock contains many magnetic grains. Each grain has a magnetization, but an instrument rarely measures that magnetization directly. Instead, the magnetization produces a magnetic field or changes the behavior of electrons, light, a mechanical probe, or a quantum sensor. The instrument turns that change into a voltage, intensity, phase, frequency, or position. The same four questions apply to every instrument: 1. What part of the sample creates the signal? 2. What physical interaction carries that information to the sensor? 3. What number or image does the detector actually record? 4. What assumptions are needed to turn the recorded signal into a magnetic interpretation? ## The quantities that are easy to mix up **Magnetization, M**, is magnetic moment per unit volume. It describes the source inside the material. A uniformly magnetized grain can be thought of as many atomic moments whose vector sum is not zero. **Magnetic field, H**, describes the applied field and the field associated with free currents. **Magnetic induction, B**, is the field that enters the Lorentz force and is sensed by most field probes. In SI units, **B = μ₀(H + M)** inside magnetic material. Outside the specimen, where **M = 0**, the distinction is simpler: **B = μ₀H**. **Magnetic flux, Φ**, is the surface integral of the field through a loop: **Φ = ∫B · dA**. A pickup coil or SQUID loop does not sample a mathematical point. It measures field integrated over its finite area, with a weighting that depends on loop geometry and standoff. **Magnetic moment, m**, is the volume integral of magnetization. A bulk magnetometer usually reports this net vector. Two specimens can have the same net moment while containing very different domain patterns, which is why microscopy adds information. **A useful classroom distinction:** magnetization is the source, field is what leaves the source, flux is field collected through an area, and voltage is often the electrical signal produced from that flux. ## How a magnetic signal becomes a number Most instruments perform one of four conversions: 1. **Motion to voltage.** A changing flux produces an induced voltage. VSMs and induction coils use this route. 2. **Field to force or charge motion.** MFM converts a force gradient into cantilever phase or frequency. Hall probes convert sideways carrier motion into voltage. 3. **Field to phase or energy.** Electron holography, Josephson devices, and NV centers use a phase or energy shift. 4. **Magnetization to optical or X-ray contrast.** Kerr, Faraday, XMCD, and SEMPA use polarization-dependent interactions. The detector normally records a proxy, not magnetization itself. Calibration relates the proxy to a physical observable. Inversion goes one step farther and estimates the source that produced the observable. Calibration is usually constrained; inversion is often non-unique. ### Lorentz force A moving charge is pushed sideways by a magnetic field: **F = q(v × B)** when the electric-field term is absent. This is the basis of electron-beam deflection in Lorentz TEM and the transverse voltage in a Hall sensor. ### Magnetic phase An electron is a wave as well as a particle. Electric potential and magnetic vector potential change the phase accumulated by that wave. Electron holography measures phase by interference. Ptychography reconstructs phase from many overlapping diffraction patterns. ### Zeeman splitting A magnetic field changes the energy spacing between spin states. In an NV center, this changes the microwave frequencies that reduce the red fluorescence. Measuring the resonance-frequency shift gives the magnetic-field projection along the NV axis. ### Josephson effect The Josephson effect is easier to explain if we begin with the superconductors rather than the barrier. Below its critical temperature, a conventional superconductor contains many paired electrons called **Cooper pairs**. The pairs behave collectively and can be described by one macroscopic wavefunction, **Ψ = |Ψ|eᶦθ**, where **θ** is a quantum phase. The phase is not a clock reading or a geometric angle. It records where the collective superconducting wave lies in its cycle. A **Josephson junction** is a weak link between two superconductors. The link may be a very thin insulator, a normal metal, or a narrow constriction. Although ordinary single electrons would see a barrier, the superconducting states remain weakly coupled and Cooper pairs tunnel coherently across it. Two relations summarize the junction: - **DC Josephson relation: Iₛ = I꜀ sin φ.** A supercurrent can cross the junction with zero time-averaged voltage. Its magnitude depends on the phase difference **φ = θ₂ − θ₁**. The critical current **I꜀** is the largest zero-voltage supercurrent the junction can carry. - **AC Josephson relation: V = (Φ₀/2π)dφ/dt**, where **Φ₀ = h/2e ≈ 2.07 × 10⁻¹⁵ Wb** is the magnetic-flux quantum. A voltage makes the phase difference advance in time. The current then oscillates at a frequency exactly related to that voltage. The words “DC” and “AC” name two consequences of the same phase physics. They do not mean that a DC SQUID uses only the DC Josephson effect. A working DC SQUID uses both the current–phase relation and the voltage–phase relation. ### Flux quantization connects phase to magnetic flux The superconducting wavefunction must return to the same value after going once around a closed loop. Its accumulated phase change therefore has to be an integer multiple of **2π**. In a sufficiently thick superconducting loop this requirement leads, more precisely, to **fluxoid quantization**. In the simple teaching limit we say that the loop keeps track of flux in units of **Φ₀**. This does not mean a SQUID can report only whole flux quanta. The periodic response provides a ruler. Electronics can interpolate extremely small fractions of one period, just as an analog voltmeter can read a fraction of the spacing between printed marks. ### How a DC SQUID works, step by step A DC SQUID is a superconducting loop interrupted by **two Josephson junctions**, one in each arm. 1. **Current divides between two coherent paths.** A bias current enters the loop and splits through the two junctions. 2. **Applied flux changes the allowed phase difference.** For a symmetric, low-inductance teaching model, the junction phases obey approximately **φ₁ − φ₂ = 2πΦ/Φ₀**. 3. **The two supercurrents interfere.** At integer values of **Φ/Φ₀**, the two paths add constructively and the loop can carry a larger zero-voltage current. Near half-integer values they oppose one another and the effective critical current is smaller. The ideal modulation is approximately **I꜀,SQUID = 2I꜀|cos(πΦ/Φ₀)|**. 4. **A current bias converts that change into voltage.** The SQUID is biased slightly above part of its flux-dependent critical-current curve. When the allowed supercurrent is smaller, more of the bias is carried by the resistive channel and the measured voltage is larger. The result is a periodic **V(Φ)** curve. 5. **Feedback makes the periodic sensor linear.** A flux-locked loop chooses a steep part of **V(Φ)** as an operating point. If specimen flux moves the output away from that point, the electronics send a current through a feedback coil to cancel the change. The required feedback current is proportional to the incoming flux. The final recorded quantity is therefore usually not the raw wavy SQUID voltage. It is the calibrated feedback signal needed to hold the SQUID at a fixed phase-sensitive operating point. ### A succinct explanation for students > A SQUID splits superconducting current through two Josephson junctions. Magnetic flux changes the relative quantum phase of the two paths, so they interfere differently and change the SQUID voltage. A feedback coil cancels that change; the cancellation current is our linear measure of the original flux. ### Common SQUID misconceptions - The SQUID is fundamentally a **flux-to-voltage transducer**, not a point magnetic-field sensor. - The two junctions are weak links, but the device still retains coherent superconducting phase around the loop. - “Quantum interference” refers to interference of the macroscopic superconducting phase, not to individual electrons taking visible trajectories around the loop. - The flux-locked loop does not make the sensor more quantum. It makes a periodic quantum response linear, stable, and easier to calibrate. - A rock magnetometer and a scanning SQUID can use the same SQUID physics while having very different pickup-coil geometries and spatial resolutions. ### Force, polarization, and absorption MFM measures a magnetic force gradient with an oscillating cantilever. Bitter fluid accumulates where the stray-field gradient attracts its particles. Kerr and Faraday microscopes measure a small change in light polarization. XMCD measures the difference in X-ray absorption for opposite circular polarizations. ## Bulk instruments before microscopy Bulk instruments report the net behavior of the specimen. They establish the magnetic state and sensitivity needed before asking where the signal occurs. ### Vibrating sample magnetometer [Open the VSM pickup-coil illustration](assets/interactive/bulk/vsm_pickup_animation.html) - **Basic idea:** Moving a magnetic specimen changes the flux through nearby pickup coils. - **Operation:** The specimen vibrates at a known frequency while the applied field is stepped or swept. - **Collected data:** The induced AC voltage is calibrated into total magnetic moment, producing hysteresis, backfield, or FORC measurements. - **Remember:** The measurement is sensitive to centering and geometry, and it does not identify which grains carry the moment. The useful point is that the VSM does not measure a static field directly. The specimen's moment is made to move, so the flux through the pickup coils changes at the vibration frequency. Faraday's law converts that change into an AC voltage. A lock-in amplifier listens only at the known vibration frequency and phase, rejecting much of the unrelated electrical and environmental noise. Field is the controlled input; calibrated moment is the output. ### SQUID rock magnetometer [Open the SQUID rock-magnetometer illustration](assets/interactive/bulk/squid_magnetometer_animation.html) - **Basic idea:** Superconducting pickup coils couple the very weak flux from a remanent specimen into a SQUID. - **Operation:** The specimen moves through axial and transverse pickup geometries with known spatial response functions. - **Collected data:** The flux-locked-loop feedback voltage is fitted to obtain the three components of the bulk magnetic moment. - **Remember:** The instrument is extremely sensitive, but it still combines all magnetic sources in the specimen. #### From specimen moment to the reported vector The specimen normally does not pass through the microscopic SQUID loop itself. It moves through a much larger superconducting pickup-coil system. A superconducting input circuit transfers the pickup-coil flux to an input coil coupled inductively to the SQUID washer or loop. This transformer-like arrangement lets the cold SQUID sense a specimen several centimetres away while preserving low noise. The pickup coils are often wound as gradiometers. Oppositely wound sections reject nearly uniform environmental field but respond strongly when the localized specimen moves through them. The response versus specimen position has a known positive-and-negative shape. Software fits that response, rather than reading one peak voltage, to estimate the moment component aligned with that pickup geometry. Orthogonal coil sets recover the three-component moment vector. The complete chain is: **specimen moment → position-dependent flux in pickup coils → current in superconducting input circuit → flux in DC SQUID → flux-locked-loop feedback voltage → fitted moment component**. Because the fit assumes a particular source position and often a dipole-like specimen response, specimen centering, tray background, sample length, and strong magnetic gradients can bias the result. Exceptional flux sensitivity does not remove geometric systematic errors. ### AC susceptibility bridge [Open the susceptibility-bridge illustration](assets/interactive/bulk/susceptibility_bridge_animation.html) - **Basic idea:** A small oscillating field produces an oscillating magnetization, **M(t) = χH(t)**. - **Operation:** A balanced pair of pickup coils cancels the drive field; placing the specimen in one coil unbalances the bridge. - **Collected data:** Lock-in detection gives the in-phase and out-of-phase susceptibility at the drive frequency. - **Remember:** This measures the reversible low-field response, not remanence. Frequency dependence may reveal magnetic relaxation. Write the response as **χ = χ′ − iχ″**. The in-phase component **χ′** describes magnetization that follows the drive and stores magnetic energy reversibly. The out-of-phase component **χ″** describes a lag and therefore dissipation. A temperature- or frequency-dependent peak can occur when the measurement period becomes comparable to a magnetic relaxation time. The bridge cancels the much larger direct coupling from the drive coil so the small specimen response is detectable. ## Electron and coherent-diffraction microscopes ### Lorentz TEM [Open the Lorentz TEM illustration](assets/interactive/lorentz-tem-domain-deflection.html) - **Basic idea:** In-plane magnetic induction deflects transmitted electrons sideways. - **Operation:** In Fresnel mode, the image is intentionally defocused so electrons accumulate or spread near magnetic domain walls. - **Collected data:** A wide-field intensity image, often recorded through a field or temperature sequence. - **Remember:** Bright and dark lines are contrast produced by deflection and defocus; they are not a direct magnetization map. For an electron moving mainly along the beam direction, in-plane induction gives a transverse Lorentz force. Oppositely magnetized domains deflect electrons in different directions. At exact focus, that small angular change may be difficult to see; defocusing gives the rays distance to converge or diverge into bright and dark lines. Reverse the defocus and the contrast reverses, which is a useful diagnostic. Thickness, electrostatic potential, diffraction, and specimen tilt still influence the image. ### Off-axis electron holography [Open the electron-holography illustration](assets/interactive/instrument-lab.html?instrument=holography) - **Basic idea:** The electron wave that crossed the specimen interferes with a reference wave that crossed vacuum. - **Operation:** An electrostatic biprism overlaps the two waves and produces interference fringes. - **Collected data:** The fringe pattern is Fourier reconstructed into electron-wave amplitude and phase. After the electrostatic contribution is removed, spatial derivatives of magnetic phase give the projected in-plane induction. - **Remember:** The illustration uses Gaussian magnetic-phase functions whose derivatives form two divergence-free, circulating induction fields. The arrows are calculated from the phase gradient, so the vortex swirls are physically linked to the displayed phase rather than drawn independently. Reversal or specimen flipping is still needed experimentally. The biprism acts like an electron-wave beam splitter operated in reverse: it overlaps an object wave with a reference wave. Fringe position records phase difference and fringe contrast records coherence and amplitude. The reconstructed phase contains both electrostatic and magnetic contributions. A specimen flip, magnetization reversal, or carefully matched reference is used to separate them. The magnetic phase is a projection through thickness, so a single hologram does not reveal an arbitrary three-dimensional magnetization distribution. ### DPC and 4D-STEM [Open the DPC/4D-STEM illustration](assets/interactive/instrument-lab.html?instrument=dpc-stem) - **Basic idea:** A local electric or magnetic field shifts the transmitted diffraction pattern. - **Operation:** A focused electron probe rasters over the specimen while a pixelated detector saves a diffraction pattern at every position. - **Collected data:** A four-dimensional array, **I(x, y, kx, ky)**. Center-of-mass shifts provide a simple projected-field signal. - **Remember:** Structural diffraction, scan distortion, and specimen thickness can imitate or complicate magnetic shifts. The detector measures where momentum goes. If the entire bright-field disk shifts, its center of mass gives the average transverse momentum transfer to the beam. That transfer can come from electric field, magnetic induction, or diffraction from the crystal. Segmented DPC detectors compress the signal during acquisition; pixelated 4D-STEM detectors retain the full pattern and allow different estimators afterward, at the cost of much larger data volume and dose. ### Magnetic ptychography [Open the ptychography illustration](assets/interactive/instrument-lab.html?instrument=ptychography) - **Basic idea:** Strong overlap between neighboring coherent probes gives enough redundancy to recover complex amplitude and phase. Magnetic sensitivity comes from XMCD or another magnetic interaction, not from overlap alone. - **Operation:** In the Harrison et al. giant-magnetofossil experiment, pre-edge soft-X-ray phase-XMCD ptychographic projections were collected with left and right circular polarization about two perpendicular rotation axes. - **Collected data:** The experiment used 73 and 71 limited-angle projections. A support-constrained vector-tomography algorithm reconstructed all three components of magnetization with a maximum spatial resolution of roughly 50 nm. - **Remember:** The simplified 3D illustration follows the reported result: a spearhead-shaped grain containing a single vortex, a curved core, and a core-polarity reversal at a Bloch point. Limited tilt produces a missing wedge and can stretch the reconstruction along the beam direction. Ptychography is a computational microscope. Each diffraction pattern by itself has lost the phase of the scattered wave, but overlapping probe positions repeatedly illuminate the same material. The reconstruction searches for a complex object and probe that explain all patterns consistently. Magnetic contrast is obtained by comparing polarization-dependent reconstructions. Tomography then adds a second inverse problem: combine limited-angle projections to recover a three-dimensional vector field, with regularization and support constraints supplying information the experiment did not directly measure. ## Stray-field and scanning-probe microscopes ### Scanning SQUID microscope [Open the scanning-SQUID illustration](assets/interactive/instrument-lab.html?instrument=scanning-squid) - **Basic idea:** A small superconducting loop measures magnetic flux above the specimen. - **Operation:** The loop is rastered at a controlled height while the SQUID is held linear by feedback. - **Collected data:** Flux on a rectangular grid. Converting it to field requires the pickup-loop response and sensor height. - **Remember:** The loop area and standoff blur the true field, but the flux sensitivity can be exceptional. The pickup loop integrates **B · dA** over its area at every scan position. The image is therefore a convolution of the specimen's stray field with the loop's spatial response. A smaller loop improves spatial resolution but intercepts less flux; a larger loop often improves coupling to extended sources but blurs fine structure. Standoff adds another, often stronger, low-pass filter. Some scanning probes place the pickup loop and SQUID on the same chip. Others couple a pickup structure to a separate SQUID. In either case, the flux-locked loop measures the feedback required to null the incoming flux. To report **Bz**, moment, or magnetization rather than flux, one must model the pickup-loop area, height, orientation, shielding, and source geometry. ### Scanning Hall probe [Open the Hall-probe illustration](assets/interactive/instrument-lab.html?instrument=hall) - **Basic idea:** A perpendicular magnetic field pushes charge carriers sideways across a biased Hall cross. - **Operation:** The Hall cross rasters above the specimen while current and height remain controlled. - **Collected data:** Hall voltage calibrated into the local field component normal to the sensor. - **Remember:** The finite Hall cross averages the field, and offset voltage must be removed carefully. Drive a current along one direction of the cross. A perpendicular field bends carrier motion sideways until an electric field balances the magnetic force. The transverse Hall voltage is proportional to current and field, with a coefficient set by carrier density and device geometry. Reversing current or field helps separate true Hall voltage, which changes sign, from contact misalignment and thermoelectric offsets, which may not. ### Magnetic force microscopy [Open the MFM illustration](assets/interactive/instrument-lab.html?instrument=mfm) - **Basic idea:** A magnetized tip feels a force from the specimen's stray field. - **Operation:** The cantilever oscillates near resonance, often following surface topography first and then repeating the line at a lift height. - **Collected data:** Phase or resonance-frequency shift, approximately related to a vertical magnetic-force gradient. The animation uses a greyscale, tip-dependent response over a patterned film to emphasize that the result is not a calibrated **Bz** or field-intensity map. - **Remember:** Topography and electrostatics can leak into the image, and a strong tip can move soft magnetic structures. Treat the tip and specimen as a coupled magnetic system. The local force is approximately the gradient of the tip–sample interaction energy. In dynamic MFM, the force gradient changes the cantilever's effective spring constant, shifting its resonance frequency and phase. The image depends on the unknown tip moment distribution as well as the sample field, so MFM contrast is not a universal map of **Bz** or magnetization. Lift mode reduces topographic coupling but also increases standoff and removes short-wavelength magnetic information. ### Single-NV scanning magnetometry [Open the single-NV illustration](assets/interactive/instrument-lab.html?instrument=single-nv) - **Basic idea:** One NV center near the end of an AFM probe is a nanoscale spin-resonance field sensor. - **Operation:** A green laser excites the NV, microwaves address its spin transition, and the tip rasters close to the specimen. - **Collected data:** An ODMR resonance or selected-frequency signal at every pixel, giving the quantitative projection **BNV = B · nNV** along the tilted NV axis—not MFM's tip-dependent force-gradient contrast. - **Remember:** Close standoff gives high spatial resolution, but point-by-point spectroscopy makes large maps slow. The NV center's ground state has spin sublevels whose separation changes with magnetic field. Green illumination pumps the NV into a bright spin state; resonant microwaves transfer population into a state with lower fluorescence. The dip in fluorescence is called optically detected magnetic resonance, or ODMR. To first order, the resonance splitting measures the projection of field along the NV axis. Hyperfine structure, strain, temperature, microwave power, and off-axis field can alter the spectrum and must be included when precision matters. ## Wide-field optical microscopes ### Quantum diamond microscope [Open the wide-field QDM illustration](assets/interactive/qdm_animation.html) - **Basic idea:** A shallow layer containing many NV centers measures the magnetic field at all camera pixels in parallel. - **Operation:** Green light illuminates the diamond while microwave frequency is swept and a camera records red fluorescence. - **Collected data:** An image stack over microwave frequency. Fitting the ODMR spectrum at each pixel produces a magnetic-field map. - **Remember:** Optical resolution, NV-layer thickness, resonance linewidth, field of view, and sensitivity trade against one another. The QDM repeats the same ODMR physics as a single NV but uses an ensemble in every camera pixel. A frequency sweep produces a small spectrum at every pixel; fitting resonance positions makes a field map. Multiple NV crystallographic orientations can provide several field projections and, under suitable conditions, vector reconstruction. The ensemble provides parallel acquisition and more photons, while averaging over depth and optical point-spread reduces the spatial detail available from an individual shallow NV. ### Kerr microscopy [Open the Kerr-microscopy illustration](assets/interactive/instrument-lab.html?instrument=moke) - **Basic idea:** Reflection from a magnetized surface slightly rotates or elliptically distorts polarized light. - **Operation:** A polarizer prepares the illumination and an analyzer converts the small polarization change into camera intensity. - **Collected data:** Wide-field, often reference-subtracted images that can be recorded rapidly during field cycling. - **Remember:** Contrast is surface weighted and can be confused by reflectivity, polishing texture, or illumination changes. Magnetization changes the complex refractive index differently for different light polarizations. On reflection, this produces a small rotation and ellipticity. The analyzer is placed near extinction so a small polarization change becomes a measurable intensity change. Longitudinal, transverse, and polar Kerr geometries select different magnetization components through the illumination and detection geometry. Difference images are powerful for domain motion but can hide stationary domains and amplify drift. ### Magneto-optic indicator-film microscopy [Open the indicator-film illustration](assets/interactive/instrument-lab.html?instrument=moif) - **Basic idea:** Stray field rotates polarization in a Faraday-active indicator film placed close to the specimen. - **Operation:** Polarized light passes through the film, reflects, and returns through an analyzer to the camera. - **Collected data:** A wide-field intensity map calibrated to field through the film response. - **Remember:** The specimen–film gap and film thickness blur small features, and the indicator has its own nonlinear response. Here the specimen field is not read optically from the specimen itself. It first magnetizes or perturbs a separate indicator film. Faraday rotation accumulated through that film is then converted to intensity by crossed polarizers. The indicator therefore has its own saturation, hysteresis, domain structure, and calibration curve. What looks like a direct field map is the specimen field filtered by the specimen–film gap and by the magnetic and optical response of the indicator. ### Bitter ferrofluid imaging [Open the Bitter-fluid illustration](assets/interactive/instrument-lab.html?instrument=bitter) - **Basic idea:** A dilute colloid of superparamagnetic magnetite particles moves toward regions with a large stray-field gradient. - **Operation:** Place a thin, uniform ferrofluid layer on a carefully polished magnetic surface, cover it if the protocol calls for a coverslip, allow the particles to redistribute, and observe them with an optical microscope. - **Collected data:** A reflected- or transmitted-light image of particle density. Dark decorated bands commonly show where domain walls intersect the surface. - **Remember:** This is a surface-decoration image. It identifies strong gradient lines but does not directly give magnetization direction or calibrated field magnitude. Scratches, relief, stale fluid, and particle agglomeration can imitate magnetic contrast. The magnetic energy of a particle decreases where the field is stronger, so a field gradient produces a force. Brownian motion and fluid flow oppose unlimited accumulation. The observed pattern is therefore a kinetic and thermodynamic redistribution of particles, not a photograph of field lines. Controls with a demagnetized specimen, a changed field direction, or a freshly polished surface help distinguish magnetic decoration from surface contamination. ## Element-specific and surface-spin microscopes ### XMCD-PEEM and XMCD-STXM [Open the XMCD illustration](assets/interactive/instrument-lab.html?instrument=xmcd) - **Basic idea:** Near an element's X-ray absorption edge, absorption depends on the relative direction of photon helicity and magnetization. - **Operation:** Images are recorded with opposite circular polarization. PEEM detects emitted electrons; STXM detects transmitted X-rays. - **Collected data:** Registered image pairs are combined into an XMCD asymmetry map. Changing photon energy adds chemical and valence sensitivity. - **Remember:** PEEM is highly surface sensitive, STXM needs a thin specimen, and both normally require a synchrotron. At a selected absorption edge, circularly polarized X-rays couple differently to magnetic moments parallel and antiparallel to the beam. Recording both helicities and forming a normalized difference suppresses much of the nonmagnetic absorption. The signal measures the magnetization projection along the X-ray propagation direction and is element specific because the photon energy selects an electronic transition. Vector information requires changing specimen or beam orientation; oxidation and valence information require an energy scan rather than a single image pair. ### SEMPA [Open the SEMPA illustration](assets/interactive/instrument-lab.html?instrument=sempa) - **Basic idea:** Secondary electrons emitted by a focused electron beam carry the spin polarization of the topmost magnetic surface. - **Operation:** The electron beam rasters while spin detectors compare scattering into opposite channels. - **Collected data:** Two in-plane spin-asymmetry images can be combined into a surface magnetization-vector map. - **Remember:** The technique is extremely surface sensitive and normally requires an atomically clean surface in ultrahigh vacuum. The primary beam creates low-energy secondary electrons whose spin polarization reflects the magnetization of the topmost atomic layers. Spin-polarizing detectors use spin-dependent scattering from a target to turn that polarization into count asymmetries. Opposed detector channels suppress ordinary intensity variations, and two detector axes provide two in-plane magnetization components. Surface oxidation can dominate or destroy the signal even when the bulk remains strongly magnetic. ## Interpreting any magnetic map Standoff, active sensor area, and specimen thickness act as spatial filters. In a stray-field measurement, fine structure decays rapidly with distance. A visually sharp image is not proof that all source details were preserved. Before interpreting a magnetic image, record the sensor height, orientation, calibration, scan direction, applied field, temperature, specimen preparation, and every processing step. Change one of those conditions as a control. A height series, field reversal, tip change, specimen rotation, or repeat scan can reveal whether striking contrast is truly magnetic. Finally, magnetic inversion is usually non-unique. More than one internal magnetization distribution can produce nearly the same external field. Mineral maps, grain boundaries, known source geometry, micromagnetic calculations, and measurements from more than one direction supply the extra information needed for a defensible interpretation.