Magnetic Sensors — Deep Reference

Magnetic sensing has grown from the single Hall-effect chip that replaced the reed switch on a 1970s dishwasher into a $10B+ component industry covering eight distinct transduction physics, six orders of magnitude in field sensitivity (from teslas to femtoteslas), and applications running from a USD 0.40 phone-magnetometer chip up to a USD 2M+ SQUID-based magnetoencephalography (MEG) array. This note works through the physics, vendor landscape, and design constraints of each technology family — Hall (silicon and III-V), AMR / GMR / TMR (magnetoresistive), fluxgate, SQUID, optically-pumped (OPM), magneto-optical, MEMS Lorentz-force, and search-coil — and then maps them onto the seven dominant application clusters (current sensing, position / angle, anti-tamper, biomagnetism, geophysics, NDE / crack detection, and consumer phone / wearable). Where the Tier-1 note electromagnetics-engineering gives the field theory and sensors-catalog gives the high-level survey, this note targets the engineer who has to pick between an Allegro ACS758 and a TDK CUR-4000 for a 200 A traction inverter, between a fluxgate and an OPM for a 10 pT-class magnetocardiogram, or between a 3-axis Hall and an AMR-based encoder IC for a brushless drone motor.

See also

• electromagnetics-engineering
• electric-motors
• power-electronics
• mems
• bioinstrumentation
• sensors-catalog
• magnetic-and-optical-materials
• sensors-pose-motion

0. Historical timeline

A condensed chronology helps place each technology:

• 1879 — Edwin Hall (Johns Hopkins) discovers the Hall effect in a gold-foil strip.
• 1928 — Felix Bloch publishes the quantum theory of electronic conduction in metals; AMR understood.
• 1936 — Hugh Aston and Aitken at GEC produce the first practical rotating-coil magnetometer.
• 1962 — Brian Josephson predicts the Josephson tunnelling effect; Anderson and Rowell confirm 1963.
• 1964 — Robert Jaklevic et al. (Ford Research Labs) build the first DC SQUID.
• 1966 — Karl Strnat (USAF Aerospace Research Lab) demonstrates SmCo${}_5$, enabling small high-performance magnetic-sensor magnets.
• 1971 — First commercial Hall-effect IC (Sprague UGS3019); replaces reed switches in industrial controls.
• 1975 — IBM commercialises permalloy AMR thin-film read heads.
• 1980 — Vacquier-style ring-core fluxgate fielded on Voyager 1/2.
• 1984 — Sagawa (Sumitomo) and Croat (GM) independently announce Nd${}_2$Fe${}_{14}$B.
• 1988 — Albert Fert and Peter Grünberg independently discover giant magnetoresistance.
• 1995 — Honeywell HMC1001 — first widely-adopted commercial AMR sensor.
• 1997 — IBM ships GMR-based hard-disk read heads at scale; areal density crosses 1 Gb/in${}^2$.
• 2003 — TMR with MgO barrier (Yuasa & Parkin) achieves $\Delta R/R>100\%$.
• 2007 — Fert and Grünberg awarded Nobel Prize in Physics for GMR.
• 2010 — Phone-grade 3-axis MEMS magnetometer (Asahi Kasei AK8963) ships in millions of Galaxy S handsets.
• 2013 — QuSpin demonstrates wearable miniature OPM cell; founds the OPM-MEG era.
• 2018 — Cerca Magnetics + UCL deliver first commercial wearable OPM-MEG system.
• 2022 — TDK CUR 4000 differential-Hall current sensor in volume production for 800 V SiC traction inverters.

1. Sensor families at a glance

Eight transduction principles cover essentially the entire magnetic-sensor market. The figures of merit that distinguish them are:

• Field range — full-scale field the device measures without folding, saturating, or losing linearity.
• Resolution / noise floor — minimum detectable field, almost always quoted as $\mathrm{nT}/\sqrt{\mathrm{Hz}}$ at 1 Hz and at 1 kHz.
• Bandwidth — DC to upper $-3\mathrm{dB}$ frequency.
• Operating temperature — full-spec range; magnetic sensors degrade quickly above their Curie or amorphous-crystallisation temperatures.
• Size and power — phone-grade three-axis MEMS magnetometers run on 1–10 µA at 1.8 V; SQUID front-ends draw watts plus cryogen.
• Vector vs scalar — does the sensor measure $|\mathbf{B}|$ (scalar, e.g. proton precession) or one or more components of $\mathbf{B}$ (vector, e.g. Hall, fluxgate, SQUID)?

Technology	Field range	Noise floor (1 Hz)	BW	Temp	Cost	Typical use
Silicon Hall	$\pm$10 µT–10 T	100 nT/$\sqrt{\mathrm{Hz}}$	DC–1 MHz	-40\,\ldots\,+150\,^\circ\mathrm{C}	$0.20–10	current, position, switch
III-V Hall (InSb, GaAs)	$\pm$10 µT–10 T	10 nT/$\sqrt{\mathrm{Hz}}$	DC–MHz	-40\,\ldots\,+125\,^\circ\mathrm{C}	$1–50	precision current, lab
AMR	$\pm$0.1 µT–8 mT	1 nT/$\sqrt{\mathrm{Hz}}$	DC–5 MHz	-40\,\ldots\,+150\,^\circ\mathrm{C}	$1–10	compass, position
GMR	$\pm$10 µT–10 mT	1 nT/$\sqrt{\mathrm{Hz}}$	DC–10 MHz	-40\,\ldots\,+150\,^\circ\mathrm{C}	$1–20	read heads, current, NDE
TMR	$\pm$1 µT–10 mT	0.1 nT/$\sqrt{\mathrm{Hz}}$	DC–10 MHz	-40\,\ldots\,+150\,^\circ\mathrm{C}	$2–20	high-resolution position, biomag-research
Fluxgate	$\pm$1 nT–1 mT	5–20 pT/$\sqrt{\mathrm{Hz}}$	DC–10 kHz	-40\,\ldots\,+85\,^\circ\mathrm{C}	$500–20 000	space, geomag, security
SQUID (LTS / HTS)	fT–mT	1–10 fT/$\sqrt{\mathrm{Hz}}$	DC–MHz	4.2 / 77 K	$50 000+	MEG, MCG, NDE, geomag
OPM (Rb / Cs vapor)	fT–nT	5–20 fT/$\sqrt{\mathrm{Hz}}$	DC–500 Hz	25–180 °C	$15–50 k	MEG, MCG, geomag
MEMS Lorentz	$\pm$0.1 µT–10 mT	100 nT/$\sqrt{\mathrm{Hz}}$	DC–1 kHz	-40\,\ldots\,+85\,^\circ\mathrm{C}	$0.50–3	phone, wearable
Search-coil	down to fT (above 1 Hz)	0.1 pT/$\sqrt{\mathrm{Hz}}$ at 1 kHz	0.01 Hz–1 MHz	-40\,\ldots\,+85\,^\circ\mathrm{C}	$50–10 000	geophysics, EMC

Two structural rules drop out of the table. First, the noise floor of a vector sensor scales roughly with the cube root of the field volume it integrates — small chips can never beat a 10 mm Bartington Mag-03 head on noise alone, and the head can never beat a 50 mm SQUID gradiometer. Second, every order of magnitude of noise-floor improvement past $\sim$1 pT requires either cryogens or atomic physics — magnetoresistive devices have a hard floor near $10^{-12}\mathrm{T}/\sqrt{\mathrm{Hz}}$ set by Johnson noise of the sense element.

2. Hall-effect sensors

2.1 Physics

A current $I$ flowing through a thin conductor (thickness $t$) in a transverse magnetic field $B_z$ deflects the carriers via the Lorentz force $\mathbf{F}=q\mathbf{v}\times \mathbf{B}$. A transverse Hall voltage develops at steady state:

$V_{\mathrm{H}}=\frac{I{B}_z}{nqt}=R_{\mathrm{H}}\frac{I{B}_z}{t}$

with $R_{\mathrm{H}}=1/(nq)$ the Hall coefficient. High mobility and low carrier density both raise $V_{\mathrm{H}}$; the standard CMOS-compatible material is doped silicon (n-well, ${\mu }_n\sim 1000{\mathrm{cm}}^2/\mathrm{V}\mathrm{s}$), while III-V InSb (${\mu }_n\sim 77000$) and GaAs (${\mu }_n\sim 8500$) give 5–30× more signal at the cost of process complexity and offset / temperature drift.

2.2 Single-axis vs 3D Hall

A planar CMOS Hall plate is intrinsically sensitive to the component of $\mathbf{B}$ perpendicular to the silicon surface ($B_z$). Two architectural tricks extend this to multi-axis sensing:

• Spinning-current cross technique (Melexis Triaxis, AMS / ams-Osram). Four Hall plates are placed in a cross; current is rotated through them at 100–500 kHz and the four signals demodulated to give in-plane $B_x$ and $B_y$ (via the planar-Hall effect) and out-of-plane $B_z$ (conventional Hall). Offset cancels in the rotation, knocking residual offset from 10 mT to $\sim$50 µT.
• Integrated magnetic concentrators (IMC). A patterned NiFe disk on top of the die bends a small fraction of the in-plane field into the vertical direction at the plate edges. Used by ams-Osram in the AS5x and TDK-Micronas in the HAL 39xy series. Gives the most compact 3D Hall sensors in production.

2.3 Offset-cancellation techniques

A planar silicon Hall plate has a raw offset of 5–20 mT — far larger than most practical sensing fields — and that offset drifts with temperature, mechanical stress (piezo-Hall effect), and lifetime. Four orthogonal techniques are stacked in modern parts to drop the residual offset to $\sim$50 µT and the temperature drift to $<$ 0.5 µT/°C:

1. Spinning-current / orthogonal switching. Rotate the bias-current direction through the plate at 100 kHz – 1 MHz; the geometric offset rotates with it, while the Hall signal remains in-phase. Demodulation extracts the Hall and averages the offset to zero. Standard since the late 1990s; first proposed by Bilotti et al. at Allegro.
2. Chopper-stabilised amplifier. Same trick at the amplifier stage; modulates the input, demodulates after gain, the amplifier 1/f noise and offset move to the chopping frequency and are filtered out.
3. Auto-zero / digital trim. EEPROM stores a per-die offset calibration written at wafer probe; the ASIC subtracts on every conversion.
4. Stress compensation. A nearby unsensitive resistor bridge measures package-induced stress and the ASIC applies a piezo-Hall compensation. Critical for QFN and DFN-packaged automotive parts that see 30–60 MPa of post-moulding compressive stress.

2.4 Production silicon Hall families

Three vendors define the market for current-sensing Hall ICs:

• Allegro MicroSystems — ACS7xx series of single-package isolated current sensors with on-die conductor and Hall plate over the conductor. ACS758 (50, 100, 150, 200 A bidirectional, 1.2 V/V at low ranges down to 13.3 mV/A at 200 A, 4.8 kV isolation), ACS780 (auto-grade replacement), ACS37800 (Sigma-Delta digital output, power-monitoring AFE), ACS37002 (smallest QFN, 30–180 A), ACS780xLR (LR = low-resistance primary, 100 µΩ for traction). The newest ACS40031 moves to a digital interface (I3C) and 1 µT/$\sqrt{\mathrm{Hz}}$ noise floor at 200 A full scale. Allegro is the volume leader in EV / hybrid traction current sensing at $\sim$$200M annual revenue from the segment.
• Melexis — MLX91206/MLX91209 SOIC current sensors (200 kHz BW), MLX90395 Triaxis 3D Hall (16-bit per axis, I2C, $\pm$50 mT), MLX90372/MLX90373 rotary position (360° absolute with SPI/PWM/SENT), MLX90425 stray-field-robust 3D position with differential pair. The MLX92232 dual-die hybrid combines a Hall plate and a magnetoresistive arm to give a single-package position sensor with both absolute and incremental output. Melexis is the dominant supplier for automotive accelerator-pedal and steering-angle sensors, with $\sim$60 % share of premium-OEM ASIL-D pedal modules.
• TDK / Micronas — HAL 3625/HAL 3935/HAL 39xy linear and rotary Hall ICs; CUR 4000 / CUR 423x Differential Magnetic Field current sensors using a pair of Hall plates straddling a U-shaped busbar conductor for high common-mode rejection of stray fields (a class IEC 61869-10 conformant Rogowski-coil alternative for traction inverters). The HAR 379x 3D series sits on the same silicon as Melexis Triaxis competitors. TDK acquired Micronas in 2016 to become a one-stop Hall + permanent-magnet supplier.
• Infineon Technologies — TLE493D-W2B6 3D Hall with low-power wake-up, TLI4970 monolithic current sensor with on-die shunt, TLE5009/5012B dual-die GMR-Hall rotary position with redundant signal paths for ASIL-D. Infineon also supplies the TLE4906/TLE4961 family of switching Hall outputs for automotive ABS.
• Diodes Incorporated — AH373x omnipolar Hall switches for consumer / industrial latching applications; under $0.20 in volume.
• AKM Semiconductor / Asahi Kasei — AK8975/AK8963/AK09918 phone magnetometers using a hybrid Hall-on-MEMS structure; the AK09918 ships in essentially every Pixel and Samsung Galaxy from 2018 onward.

2.4 Current-sensing architectures with Hall

Five distinct topologies, each with a vendor:

1. Open-loop on-package conductor (ACS758, ACS780). 1.2 mΩ primary, $\pm$50–200 A bidirectional, 4.8 kV galvanic isolation. Cheapest at the part level but locks the system to a single current rating.
2. Open-loop with external busbar (Allegro CT4xx, Melexis MLX91216). Open Hall plate sits in the gap of a slotted ferromagnetic core that concentrates flux from the conductor. Used in EV battery-pack pyrofuse current monitoring (Hyundai E-GMP, GM Ultium, VW MEB).
3. Closed-loop (zero-flux) compensated current sensor (LEM CAS / LF series, Vacuumschmelze T60404, Tamura L08P series). A secondary coil drives a current that cancels the primary’s flux in the core; a small Hall plate or fluxgate detects the zero crossing. 0.1–0.5 % accuracy, $\pm$0.05 % linearity, 100 kHz–1 MHz BW. Workhorse of motor-drive R&D benches.
4. Differential Hall with IMC (TDK CUR 4000, Melexis MLX91220/91221). Two Hall plates spaced across a U-shape conductor null external uniform fields. Class 1 accuracy to 1 kA without core. Standard for traction inverters from 2022 onwards.
5. Hall + Rogowski hybrid (LEM HOPS series, Vacuumschmelze IT-series). The Hall captures DC and low frequency, a Rogowski coil captures the high-frequency current; their outputs add. Used in 800 V SiC traction inverters at Tesla Model S Plaid, Lucid Air, Porsche Taycan.

2.5 3D position with Hall

The dominant brushless-DC and EV-traction motor commutation sensor is a 3D Hall encoder rather than an optical encoder, for ruggedness:

• ams-Osram AS5048/AS5147/AS5048P — 14-bit on-axis magnetic rotary encoder; sister chip AS5147U has dual SPI for ASIL-D safety.
• Allegro A1335/A1338 — contactless 12-bit absolute rotary encoder, SPI.
• TDK / Micronas HAR 3725 — 14-bit, with stray-field immunity.
• Renesas / IDT ZMID520x — inductive position sensor (PCB-coil); not strictly Hall but commonly cross-listed.

These chips sit beneath a small diametrically-magnetised disk (typical $\varnothing 6\mathrm{mm}$ NdFeB N40 with axial 1 mm length, $B_r\approx 30\mathrm{mT}$ at the chip surface) and decode the angle to $0.05^{\circ }$ resolution at 10 krpm.

3. Anisotropic magnetoresistance (AMR)

3.1 Physics

AMR is the dependence of a ferromagnetic thin-film resistance on the angle $\theta$ between the current direction and the magnetisation direction:

$\rho (\theta )={\rho }_{\perp }+({\rho }_{\parallel }-{\rho }_{\perp }){\cos }^2\theta$

The relative change $\Delta R/R$ is small — typically 1–3 % for permalloy (Ni${}_{80}$Fe${}_{20}$) at room temperature — but with a Wheatstone bridge of four matched serpentine resistors the output is a clean sine in field angle. AMR was the dominant hard-disk read-head technology from 1990 to about 1997 before being displaced by GMR.

3.2 Production families

• NXP / Sensitec KMA / KMI / KMT series — KMA199E (steering angle, $\pm$180°), KMI series with on-die magnet for incremental wheel-speed sensing (ABS). Sensitec also offers AFF755B (TMR successor) and AA745 (Bridge AMR).
• Honeywell HMC1001 / HMC1002 / HMC1043 / HMC5883L — the HMC1001 1-axis and HMC1043 3-axis AMR are the legacy electronic-compass parts. The HMC5883L (now discontinued) was the canonical phone-magnetometer in 2010–2014.
• Sensitec AFF — AFF755 angle sensor used in Bosch and Continental ESP / ABS systems.

AMR has been overtaken by TMR for angle sensing in the last five years but retains a cost edge below 1 mT full-scale and is the standard for rotary-position sensors that must read through an aluminum or stainless-steel housing wall.

3.3 Set/reset coils

A permalloy AMR sensor’s easy axis can drift after exposure to a transverse field $>$ a few mT — the magnetisation aligns into a perpendicular domain pattern and the device sensitivity drops or reverses. Every production AMR sensor includes an on-die “set/reset” coil that pulses a few amp-turns along the easy axis (typically 3 A for 2 µs) on every measurement, forcibly re-aligning the domains. The set/reset coil also enables chopper-style noise reduction: alternate measurements with set and reset polarities cancel temperature-drift offset, while the field-dependent term sums constructively. The Honeywell HMC1001 application note (1995) is the canonical reference for this technique.

4. Giant magnetoresistance (GMR)

4.1 Physics

GMR is the resistance change in a stack of alternating ferromagnetic (FeCo, NiFe) and non-magnetic (Cu, Ru) layers, with thickness chosen so that adjacent layers couple antiferromagnetically. An external field rotates the moments to parallel alignment, reducing scattering and dropping the resistance by 5–20 %. Albert Fert (Université Paris-Sud, France) and Peter Grünberg (Forschungszentrum Jülich, Germany) discovered it independently in 1988 and shared the 2007 Nobel Prize in Physics. By 1997 IBM had GMR-based hard-disk read heads in production; by 2005 essentially every drive shipped used GMR.

4.2 Production families

• Allegro GMR — A175x, A1457 differential current sensors; A175x targets contactless ABS / camshaft / crankshaft position. GMR coupons.
• NVE Corporation (Eden Prairie, MN) — IMS NVT series of GMR magnetic isolators (galvanic isolation alternative to optocouplers, with 50 Mb/s data rate and 5 kV V${}_{\mathrm{iso}}$), AAH002 / AA005 / AAL024 GMR sensors for $\pm$0.5–10 mT. NVE remains the principal merchant-market GMR specialist.
• Sensitec GLM / GFR / GF / CMS — high-precision GMR current sensors for power-quality monitoring.
• Infineon TLE49xx / TLE5009 series — GMR-based wheel-speed and crankshaft / camshaft sensors for automotive powertrain. Crashed AMR competitively after 2010.

GMR’s main niche in 2026 is high-bandwidth current sensing of switched currents in SiC and GaN power converters (BW > 5 MHz at 500 A), where Hall sensors run out of bandwidth and Rogowski coils miss the DC.

5. Tunnel magnetoresistance (TMR)

5.1 Physics

Replace the non-magnetic metal spacer of a GMR stack with a thin (1–2 nm) insulating MgO tunnel barrier and the magnetoresistance ratio jumps to 100–600 % at room temperature — the tunnel magnetoresistance effect. The 2004 Yuasa / Parkin demonstration of $\Delta R/R\approx 200\%$ in CoFeB / MgO / CoFeB junctions enabled both modern hard-disk read heads (replacing GMR around 2007) and the MTJ memory bit that underlies STT-MRAM (Everspin EMD3D-series, Avalanche AS308x).

5.2 Production families

• TDK / InvenSense / Crocus Technology — TMR009x current-sensor MTJ arrays; bandwidth to 5 MHz with 50 nT/$\sqrt{\mathrm{Hz}}$ noise. Crocus’s MLU (Magnetic Logic Unit) wraps each MTJ with a self-reference write pulse for true-DC operation.
• MultiDimension Technology MMT (Zhangjiagang, China) — TMR2305 / TMR9001 / TMR2503 series of 3-axis TMR sensors and current modules. World’s largest TMR pure-play, supplying the bulk of Chinese phone OEM magnetometer market.
• Allegro CT100 — TMR-based gear-tooth sensor for transmission and gearbox sensing.
• Coto Magnetic Solutions — discrete TMR sense elements supplied for OEM integration.
• Analog Devices ADL5920 / ADXMS300 — research-grade TMR vector magnetometer modules.

TMR noise at 1 Hz is dominated by 1/f magnetic noise of the free layer; at 1 kHz Johnson noise of the junction takes over. Practical floors in 2026 are $\sim$200 pT/$\sqrt{\mathrm{Hz}}$ for the best commercial TMR magnetometers — close to the fluxgate range and a factor of 10–30 below GMR.

6. Fluxgate magnetometers

6.1 Physics

A small high-permeability (${\mu }_r>10^5$) toroidal or rod core is excited by a primary winding into deep alternating saturation. A secondary “pick-up” winding around the same core sees an output whose even harmonics — most importantly the second — are proportional to the ambient DC field $B_{\mathrm{ext}}$. A synchronous detector at $2f_{\mathrm{drive}}$ recovers $B_{\mathrm{ext}}$ vector component with sub-nT resolution and excellent DC stability. Modern fluxgates are 10–20 pT/$\sqrt{\mathrm{Hz}}$ at 1 Hz, far better than any magnetoresistive technology.

6.2 Production families

• Bartington Instruments (Witney, UK) — Mag-03 (3-axis vector, $\pm$70 µT to $\pm$1000 µT, 6 pT/$\sqrt{\mathrm{Hz}}$, the geomag standard since 1996); Mag-13 (next-gen, $\pm$70 µT to $\pm$2 mT); Mag690 (single-axis, ruggedised); Mag648/649 (compact field-portable); HC1/HC2 Helmholtz coil system for fluxgate calibration. Bartington supplies the bulk of geophysical and security-fence fluxgates.
• Stefan Mayer Instruments (Dinslaken, Germany) — FL1, FL3-100, FL3-1000, FLC3-70; the FLC3 series is the AMR-replacement OEM module. Common in vehicle-detection (induction-loop replacement) and unexploded-ordnance (UXO) detection.
• Magson (Berlin, Germany) — laboratory-grade and spaceborne fluxgates. Magson units fly on Cluster II, ROSETTA, JUICE.
• Schonstedt — handheld UXO and pipe / cable locator instruments.
• NASA / GSFC / JPL custom — the fluxgates on Voyager 1/2, Galileo, MESSENGER, MAVEN, JUNO, Parker Solar Probe are all custom space-qualified ring-core designs with 30 ppm/°C stability and < 0.5 nT calibration uncertainty over years of mission.
• Texas Instruments DRV425 — the only mass-market silicon-integrated fluxgate IC (2016 onwards). Differential dual-fluxgate inside a thin-film NiFe core on-chip, with feedback loop for closed-loop operation. 47 µT range, 1.5 nT/$\sqrt{\mathrm{Hz}}$ at 1 Hz, 47 kHz BW. Bridged the price gap between Hall ($1) and benchtop fluxgate ($1000); appears in EV charge-port current sensors and DC residual-current devices.

6.3 Core geometries

Three geometries dominate:

• Ring-core / racetrack — A toroidal or oval permalloy core with a single-turn primary and a wound secondary. Drive current saturates the core symmetrically; second-harmonic detection extracts the field component along the secondary’s axis. Excellent symmetry → low harmonic spurs → very low offset.
• Single-rod (Vacquier) — Two rod-shaped cores with opposing primary windings inside a common secondary. The historical airborne-magnetic-anomaly detector of WWII U-boat hunting. Used in handheld locators (Schonstedt GA-72Cd).
• Race-track on silicon (TI DRV425) — Two thin-film NiFe rods deposited on the IC with on-die windings; symmetric pickup eliminates secondary-mode pickup. The first viable monolithic fluxgate.

6.3 Application domains

• Geomagnetic monitoring — INTERMAGNET observatory standard: a Bartington Mag-03 plus an Overhauser scalar magnetometer (GEM Systems GSM-19, Scintrex SuperGrad) for absolute baseline.
• Space science — fluxgates on essentially every interplanetary probe and Sun-Earth-line spacecraft; calibration via in-flight Helmholtz cages.
• Unexploded ordnance / archaeology / mineral exploration — Mag-13 array on a cart or drone.
• Perimeter security — buried fluxgates detect ferrous-mass vehicle intrusion.
• Power-electronics current sensors — closed-loop “zero-flux” fluxgate transducers (LEM IT 60-S/ITN 12-P, Vacuumschmelze T60404 family) reach 0.0001 % linearity for current-shunt calibration and laboratory metrology.

7. SQUID magnetometers

7.1 Physics

A superconducting quantum interference device is a superconducting ring interrupted by one (RF SQUID) or two (DC SQUID) Josephson junctions. The maximum supercurrent through the ring varies periodically with the magnetic flux $\Phi$ threading it, with period the flux quantum ${\Phi }_0=h/(2e)\approx 2.07\times 10^{-15}\mathrm{Wb}$. A feedback loop locks the ring to one fringe and the feedback signal reports field changes with resolution $\sim 10^{-6}{\Phi }_0/\sqrt{\mathrm{Hz}}$ — femtotesla in a 1 mm${}^2$ pickup loop.

Two material families:

• Low-T${}_{\mathrm{c}}$ (LTS) SQUIDs — Nb / Al-Ox / Nb junctions, operate in 4.2 K liquid-helium bath. Noise floor $\sim 1\mathrm{fT}/\sqrt{\mathrm{Hz}}$ at 10 Hz. Standard for medical MEG.
• High-T${}_{\mathrm{c}}$ (HTS) SQUIDs — YBa${}_2$Cu${}_3$O${}_7$ thin-film step-edge or bicrystal junctions, operate in liquid nitrogen at 77 K. Noise floor 20–100 fT/$\sqrt{\mathrm{Hz}}$. Used where the cryogenic cost of helium is prohibitive (NDE field instruments, geomagnetic surveys).

7.2 Production families

• Magnicon (Hamburg, Germany) — XXF-1 / XXF-2 SQUID electronics, single and multi-channel current sensors. Standard front-end for European MEG, biomagnetism research.
• STAR Cryoelectronics (Santa Fe, NM) — SQUID-based MEG, current sensors, NDE sensors.
• Tristan Technologies / Quantum Design — turnkey MPMS / MPMS3 / SQUID-VSM systems for materials characterisation ($10^{-8}\mathrm{emu}$ resolution).
• CTF / VSM MEG Systems / Elekta-MEGIN / Yokogawa AETHER — full-helmet MEG instruments with 275–306 channel arrays of LTS SQUID gradiometers, located in shielded rooms with mu-metal walls.
• Supracon AG (Jena, Germany) — HTS SQUID magnetometers and gradiometers for NDE and geomag.

7.3 Configurations

• Single-axis magnetometer — one pickup loop. Picks up field plus all ambient noise. Used inside a multi-layer mu-metal magnetically shielded room (MSR).
• First-order gradiometer — two parallel pickup loops in series-opposition, baseline 50 mm. Rejects uniform far-field noise; favours local-source signal that varies across the baseline.
• Second-order gradiometer — four loops, two opposing pairs. Used in unshielded urban environments where even first-order rejection is insufficient.
• Vector array — three orthogonal pickup loops per site, for 3D source localisation.

7.4 SQUID applications

• Magnetoencephalography (MEG) — 275-channel CTF MEG, 306-channel Elekta-MEGIN Neuromag-Triux, in clinical use for presurgical epilepsy localisation (~$15M install). Detects cortical-neuron magnetic fields of order 50–500 fT at the scalp.
• Magnetocardiography (MCG) — 36–64 channel arrays for cardiac arrhythmia mapping; competitive with surface ECG for arrhythmia substrate. Commercial: Cardiomag Imaging (US), Sumitomo Heavy Industries (Japan).
• Geomagnetic NDE / nondestructive evaluation — Supracon HTS SQUIDs for aluminum-aircraft riveted-joint crack inspection.
• Materials magnetometry — Quantum Design MPMS3 in essentially every condensed-matter laboratory.
• Geophysical exploration — buried-pipeline integrity, ore-body magnetisation imaging.

8. Optically-pumped magnetometers (OPM)

8.1 Physics

A vapour of alkali atoms (typically ${}^{87}\mathrm{Rb}$ or Cs) is optically pumped by a circularly-polarised laser at the D1 line ($\sim$795 nm for Rb, 894 nm for Cs). Pumping aligns the spins parallel to the laser; an external magnetic field causes Larmor precession at ${\omega }_L=\gamma B$, with the gyromagnetic ratio $\gamma /2\pi \approx 7Hz/nT$ for Rb. Probing the spin polarisation with a weak second laser or with the same pump beam gives a signal whose phase or amplitude tracks $B$. In the SERF regime (Spin Exchange Relaxation Free, $B<10\mathrm{nT}$, density $>10^{14}{\mathrm{cm}}^{-3}$, T > 150\,^\circ\mathrm{C}) the noise floor drops to 5–20 fT/$\sqrt{\mathrm{Hz}}$, rivalling SQUID without cryogens.

Two scalar OPM operating modes:

• $M_x$ / $M_z$ self-oscillating — the cell drives itself at the Larmor frequency. Output is a frequency proportional to $|\mathbf{B}|$, with extremely high stability ($<$ 1 pT over hours). Standard for total-field geomagnetic survey (Geometrics G-822A).
• SERF zero-field magnetometer — operates near zero field by active nulling. Vector sensitive to the three field components transverse to the pump beam. Standard for biomag.

Three additional OPM atomic species in production use:

• Potassium (${}^{39}$K) — narrower lines, lower magnetic dipole noise, higher sensitivity. GEM Systems GSMP-35 — the gold standard for airborne geomagnetic survey.
• Cesium (${}^{133}$Cs) — widely used in airborne magnetometers (Geometrics G-859, Scintrex CS-3). Robust, low light-power requirement.
• Helium-4 metastable (${}^4$He${}^{\ast }$) — Mag4Health portable, requires RF discharge but no heater. Operating at room temperature is a major operational advantage for wearable MEG.

8.2 Production families

• QuSpin (Louisville, CO) — QZFM Gen-2 / Gen-3, the standard wearable OPM cell for OPM-MEG systems. 5 fT/$\sqrt{\mathrm{Hz}}$, $\pm$5 nT dynamic range, 6 W heater, 150 g sensor. Powering all current commercial OPM-MEG (Cerca Magnetics, Mag4Health, FieldLine Medical).
• FieldLine Medical (Boulder, CO) — HEDscan OPM-MEG system; integrates QuSpin or proprietary cells.
• Mag4Health (Grenoble, France) — proprietary ${}^4$He metastable OPM, $\sim$50 fT/$\sqrt{\mathrm{Hz}}$ but with the advantage of operating at $\sim$25 °C (no heater) — wearable for clinical-pediatric MEG.
• Twinleaf (Plainsboro, NJ) — VMR and microSAM OPMs; CSR scalar OPM for total-field magnetometry.
• Geometrics G-822A / G-859 — Cs-vapour airborne magnetometers for geomag survey (the workhorse since the 1970s).

8.3 Why OPM is displacing SQUID for MEG

The QuSpin cells are individually 12.5 × 16.5 × 24.5 mm and operate at $\sim$150 °C inside their own oven. A 360-channel OPM-MEG helmet conforms to the subject’s scalp, sits closer than the 25 mm SQUID dewar standoff, and gains 4–6× signal — and the helmet moves with the head (the subject can sit, stand, or walk), unlike fixed-Dewar SQUID systems. The first commercial OPM-MEG installs (Cerca Magnetics 2020, Sandia/Sandia 2021, FieldLine 2022) now compete head-to-head with the legacy 306-channel Elekta-MEGIN systems on signal quality, at one-fourth the install cost (no liquid helium, no MSR-only constraint).

8.4 Search-coil (induction-coil) magnetometers

A wound coil with $N$ turns and area $A$ around a high-permeability core senses time-varying field via Faraday:

$V_{\mathrm{ind}}(t)=-NA\frac{dB(t)}{dt}$

Search coils have no DC sensitivity but offer extremely low noise above 1 Hz — better than fluxgate down to $\sim$0.1 pT/$\sqrt{\mathrm{Hz}}$ at 1 kHz for a 200 mm laboratory coil. Vendors:

• EMI Corp / Geometrics BF-4 / BF-10 / BF-25 — magnetotelluric sounding (deep-Earth conductivity mapping at 0.001–1000 Hz).
• Lemi (Lviv) — LEMI-118, LEMI-120 induction-coil magnetometers for magnetotelluric surveys.
• MFS-06 / MFS-07e (Metronix) — German market leader; standard for MT exploration.
• NMR / MRI gradient coil monitor — a dedicated search coil watches the gradient slew-rate against a SAR-imposed limit; see mri-magnets-and-coils-deep.

In space, fluxgate magnetometers handle DC to a few Hz and search coils handle 1 Hz to 10 kHz, mounted on the same boom. The Cluster II “STAFF” search coil + FGM fluxgate combo set the template now followed on JUICE, MMS, Solar Orbiter.

9. Magneto-optical and Kerr methods

The magneto-optical Kerr effect (MOKE) and the Faraday effect rotate the polarisation of light by an amount proportional to the magnetisation of (or magnetic field within) the sample. Used in:

• Kerr microscopy — imaging domain structure in thin magnetic films and recording media. Vendors: Evico Magnetics, Durham Magneto-Optics. Resolution $\sim$300 nm with violet light.
• Magneto-optical current sensors — a fiber-optic loop around a high-voltage conductor uses the Faraday effect in silica fiber or in Bi-doped iron garnet to give a true-DC primary-isolated current measurement up to 800 kA without electronics in the HV zone. Standard in HVDC converter stations (ABB MOCT, NR-Tech UPSC-FOCT).
• Verdet-effect magnetic-field probes — TbGa garnet rod for high-field laboratory measurements (10–100 T pulsed magnets).
• Magneto-optical imaging films — Bi-doped iron garnet thin films grown on GGG substrates (Matesy GmbH). Field-sensitive Faraday rotation visualised on the film surface gives 10 µm spatial resolution. Used to image flux-pinning patterns in superconductors, magnetic-recording-tape archaeology, and current-path mapping in PCBs and IC packages.

The Faraday-effect HVDC current sensor deserves special note: ABB MOCT and NR-Tech UPSC-FOCT each underpin every $\ge 500$ kV HVDC station built after 2010 (e.g. INELFE France-Spain, Belo Monte Brazil, Changji-Guquan UHVDC China). The all-optical primary needs no insulator other than a glass fiber; the converter electronics sit at ground potential. Calibration is by physical fiber turn-count rather than by a transformer ratio, giving an absolute primary measurement immune to long-term drift.

10. MEMS magnetometers (consumer / phone)

A modern smartphone, smartwatch, drone IMU, or AR/VR controller carries a three-axis magnetometer chip costing $0.30–$0.70 in volume. Two transduction principles dominate the chips:

• Lorentz-force MEMS (NXP MAG3110, ST LSM6/LIS3MDL family). A small silicon proof-mass with on-chip current-carrying springs deflects under the Lorentz force from the ambient field; the deflection is read capacitively. 100 nT/$\sqrt{\mathrm{Hz}}$, 1 mA, 100 Hz BW.
• AMR or TMR die-level (Yamaha YAS532, Asahi Kasei AK09918, Bosch BMM150, Memsic MMC5983MA). Lower-power, faster sample, but require front-end ASIC for offset cancellation.

10.1 Production families

• STMicroelectronics LIS3MDL / LSM303AGR / LSM6DSO32 / LSM9DS1 — 3-axis AMR magnetometer alone or integrated with accelerometer / gyro into 6 / 9-axis IMU. The LIS3MDL is the canonical hobby-drone compass IC.
• Bosch Sensortec BMM150 / BMM350 — 3-axis Hall + AMR hybrid, $\pm$1300 µT, 0.3 µT noise.
• Asahi Kasei AK09918 / AK09940A — Hall-based, in iPhone, Pixel, and most Android flagships from 2018 onwards.
• Memsic MMC5983MA / MMC5633NJL — AMR, $\pm$8 G dynamic range, $\pm$0.4 mGauss noise floor.
• TDK / InvenSense ICM-20948 — 9-axis IMU with embedded AK09916 magnetometer.
• Yamaha YAS532 / YAS537 — legacy AMR magnetometer for feature-phone and wearable.

These chips are calibrated in-factory to within $\pm$1 % gain and $\pm$100 µT offset and then trim themselves against soft-iron and hard-iron sources by the figure-eight calibration ritual familiar to anyone who has set up a hobby drone.

11. Application clusters

11.1 Current sensing

Five regimes by magnitude:

Range	Technology	Example part / system
< 1 A	shunt + opamp	IC fuel-gauges (TI BQ34, MAX17260)
1 – 100 A	Hall on-package	Allegro ACS758, Melexis MLX91216
100 – 1000 A (traction)	Differential Hall + bus	TDK CUR4000, LEM HOPS-1k0
1 – 100 kA (HVDC)	Magneto-optical / fluxgate	ABB MOCT, LEM IT-2000s
> 100 kA (pulsed)	Rogowski + Hall	Pearson Electronics CT, Rocoil-Pro

Choice criteria: bandwidth (Hall 100 kHz – 1 MHz; Rogowski 0.05 Hz – 30 MHz; MOCT DC – 100 kHz; fluxgate DC – 100 kHz), DC capability (Hall, MOCT, fluxgate yes; Rogowski no), and galvanic isolation (Hall on-package, MOCT, closed-loop fluxgate all 5–15 kV-rated).

11.2 Position / angle

The dominant non-contact rotary encoder in 2026 is a 3-axis Hall or TMR die under a 6–10 mm diametrically-magnetised disk magnet. Sub-arc-minute resolution is achieved by interpolation of the sine/cosine outputs (CORDIC or arctan in-die).

• EV traction: ams-Osram AS5147U, Allegro A1338 in BYD / Tesla / VW MEB.
• Industrial servo: TDK Micronas HAR 3725, Renesas IPS-2200 inductive.
• Robotics: AksIM-4 (Renishaw) optical for high precision; iC-Haus iC-PT for position-via-Hall.
• Steering angle: Melexis MLX90372 + KMA199E redundant pair for ASIL-D in Bosch ESP9.x.
• Accelerator pedal: Melexis MLX90253 + MLX90290 redundant.

11.3 Anti-tamper / proximity

Reed switches are dead in new designs. Replacement: Hall switch with omnipolar latch (Allegro A1101 / A1106 / A1234, Diodes AH373x). Power consumption $<$ 1 µA in sleep with a periodic-wake architecture. Used in laptop-lid detection, smartphone flip-cover, smart-lock latch, refrigerator door, and meter-tamper detection. Higher-security tamper switches use a 3-axis Hall (MLX90395) to detect any approach of a permanent magnet from any direction, defeating the canonical magnet-on-the-side bypass.

11.3.1 Worked example — magnetic-disk-magnet rotary encoder

A brushless DC motor uses an ams-Osram AS5147U 14-bit on-axis rotary encoder reading a diametrically-magnetised NdFeB disk magnet (6 mm $\varnothing \times$ 2.5 mm, N40 grade, $B_r=1.27\mathrm{T}$). The chip sits 1.5 mm beneath the magnet face along the rotation axis. Estimate the field at the die and the angular noise.

• Disk-magnet axial-face field for a thin uniform diametral magnet, central axial distance $z$, with disk radius $a=3\mathrm{mm}$ and thickness $L=2.5\mathrm{mm}$: $B_{\perp }(z)\approx \frac{B_r}{2}\left(\frac{L}{\sqrt{a^2+z^2}}-\text{small correction}\right)\approx 0.5\cdot 1.27\cdot \frac{2.5}{\sqrt{9+1.5^2}}\approx 0.5\mathrm{T}\cdot 0.76\approx 31\mathrm{mT}$ For the in-plane $B_x$ / $B_y$ components at $z=1.5\mathrm{mm}$ off-axis the diametral disk produces $\sim$25 mT peak each, well within the AS5147U’s $\pm$80 mT input range.
• The AS5147U specifies $\sim$0.07° INL (integral nonlinearity, RMS) at 7 krpm. Over $360^{\circ }/2^{14}=0.022^{\circ }$ per LSB the noise floor is well below 1 LSB; in practice the dominant error is magnet misalignment and disk-magnet eccentricity ($\sim$0.1°), not chip noise.
• At 6 krpm the electrical-angle update period is 100 µs/electrical cycle for a 4-pole-pair PMSM. AS5147U has 16-bit SPI output at 10 Mbps clocking — 1.7 µs per read — and 11.5 µs propagation delay. Total angle-loop latency 13.2 µs is comfortable for a 10 kHz current loop.

11.3.2 Linear position with magnetic stripe and Hall array

Linear position over 0.1–10 m is sensed by a magnetised stripe (alternating N/S poles every 1–5 mm) and a 2-element Hall pickup. The Hall pair’s quadrature output decodes pole-pitch + interpolated subdivision. Vendors:

• iC-Haus iC-PR / iC-MH — linear Hall arrays with 1024× interpolation, $\pm$10 µm accuracy.
• Renishaw LM10 / LM13 — magnetic linear scales with Hall readhead, $\pm$15 µm on 5 mm pole pitch.
• AMO LMK / LMS — sub-µm magnetic-scale systems for CNC linear axes up to 30 m.
• RLS LMA10 — incremental magnetic encoders for high-vibration industrial use.

Magnetic linear scales are now the standard alternative to glass optical scales for $>$ 1 m axes — cheaper, immune to coolant / chips, but with 10× larger jitter (which is acceptable for milling and lathing but not for nanopositioning, where the optical incumbents remain).

11.4 Biomagnetism — MCG, MEG

Cortical-neuron and cardiac fields at the body surface are 10 fT – 1 pT — five to nine orders of magnitude smaller than the geomagnetic field. Two strategies coexist:

• LTS SQUID full-helmet MEG in MSR: Elekta-MEGIN Triux Neo (306-channel, ~$3M install + $200k/yr He), CTF Omega (275-channel). Standard for tertiary-care presurgical epilepsy localisation.
• OPM-MEG wearable: Cerca Magnetics OPM-MEG with 64–360 QuSpin cells in a 3D-printed scaffold helmet, in a custom Active Shielding cage (Magnetic Shields Ltd MuRoom). Subject can move during recording. Now fielded at UCL (UK), Nottingham, NIST, Sandia, and Cerca-trained sites for paediatric MEG.

MCG (magnetocardiography) is dominated by 36–64-channel SQUID arrays (Cardiomag, BMDsys) plus emerging OPM-MCG (FieldLine). The advantage over surface ECG is the unique sensitivity to vortex currents and to the body-internal current source rather than the body-surface potential.

11.5 Geophysics

• INTERMAGNET observatories — Bartington Mag-03 fluxgate + Overhauser scalar (GEM GSM-19F).
• Airborne magnetic survey — Cs-vapour OPM (Geometrics G-822A) towed behind helicopter, sampling at 10 Hz at 60 m altitude, for mineral exploration. Pico-tesla differential resolution over 50–60 µT background.
• Marine magnetics — same Cs-vapour OPM in a towfish behind a research vessel; mapping seafloor magnetic anomalies (Vine-Matthews stripes, plate tectonics).
• Volcano / earthquake forerunner monitoring — INTERMAGNET-grade fluxgate at remote sites.

11.6 NDE — crack and corrosion detection

• Magnetic flux leakage (MFL) in oil-and-gas pipeline pigging — Hall-array or fluxgate detects local field perturbation from a wall-thickness anomaly. Vendors: Baker Hughes (PII), Rosen, NDT Global, Lin Scan. A typical inline-inspection (ILI) tool carries 100–400 sensors around a 24–48 in pipe diameter and runs the full length of a continental pipeline at $\sim$1 m/s with on-board data logging.
• Eddy-current testing (ECT) — coil-based, but ECT array-probes (Olympus OmniScan ECA, ETher NDE Smart-EC) now use GMR or TMR pickup for higher resolution. Aerospace fastener-hole inspection uses 32–128-element arrays at 100 kHz–10 MHz drive.
• SQUID NDE — HTS SQUID gradiometers (Supracon) for aluminum aerospace skin-crack mapping at LANL, DLR, JAXA. Used on Airbus A380 wing-skin lap-joints for sub-mm fatigue-crack detection.
• Barkhausen-noise sensing — search-coil + HF spectrum analyser detects the microscopic magnetic-domain jumps of a stressed ferromagnetic part under cyclic field; used in residual-stress mapping for rolling-mill rolls and bearings (Stresstech RollScan).
• GMR/TMR pencil probes for aircraft skin / fastener corrosion. Sensitec, NVE, and ETher NDE all offer probe-tip GMR or TMR coupons at 5–50 µm spatial resolution.

11.7 Geomag drone and UAV magnetics

A new class of magnetometer-equipped drones has emerged since 2018, combining fluxgate or OPM heads with RTK-GNSS for centimetre-grade positioning. Vendors include MagArrow (Geometrics, Cs OPM, 10 pT/$\sqrt{\mathrm{Hz}}$), QuestUAV, GEM Systems GSMP-35A (Potassium OPM, 0.3 pT/$\sqrt{\mathrm{Hz}}$). Applications: UXO clearance of decommissioned military training ranges, archaeological mapping, mining exploration where conventional ground crews cannot access.

11.7 Consumer / phone

The 3-axis chip in a phone is used for electronic compass (north heading), augmented-reality device-pose (combined with gyro and accelerometer in a Madgwick or Mahony fusion), and increasingly for indoor pedestrian navigation by detecting building-steel magnetic signatures. Apple, Samsung, Xiaomi, and Pixel all use Asahi Kasei AK09918-class chips. The same chip in a smartwatch (Apple Watch, Garmin) underpins fitness-tracking heading.

11.8 Consumer / phone deep-dive — sensor fusion

The 3-axis magnetometer alone gives heading only with the device held perfectly level; any tilt mixes the vertical geomagnetic component into the horizontal-plane readout. Tilt-compensation requires accelerometer fusion (the “two-vector” Triad algorithm, or the more robust Madgwick / Mahony attitude estimator):

${\hat{\mathbf{q}}}_{k+1}={\hat{\mathbf{q}}}_k+{\dot{\hat{\mathbf{q}}}}_k\Delta t,\dot{\hat{\mathbf{q}}}=\frac{1}{2}\hat{\mathbf{q}}\otimes \mathbf{\omega }-\beta \nabla J(\hat{\mathbf{q}},\mathbf{a},\mathbf{m})$

with cost $J$ measuring how well the predicted accelerometer and magnetometer readouts match the gravity and geomagnetic reference vectors. The Madgwick filter (Sebastian Madgwick, 2010) runs at 100 Hz on a Cortex-M0 in $<$ 50 µs and gives sub-degree heading in clean magnetic environments. In Apple Watch, Pixel Watch, and Garmin fenix devices, an extended Kalman filter (EKF) replaces Madgwick for sustained heading stability against magnetometer disturbances.

12. Design and integration pitfalls

• Stray-field rejection. A 200 A traction inverter in an EV traction inverter sees 1–10 mT of stray field at the current sensor from adjacent phases. A standard single-Hall current sensor reads $\sim$10 % error. Use a differential-Hall (TDK CUR 4000) or shielded closed-loop sensor (LEM IT-200) — both reject uniform external field by $>$ 60 dB.
• Soft-iron and hard-iron distortion in phone compasses. Hard-iron offset (permanent magnetisation of the device case) shifts the sphere centre; soft-iron distortion (induced magnetisation of nearby ferromagnetic alloys) ellipsoidally squashes the sphere. Standard calibration: Tilt-compensated 12-point ellipsoid fit (Renaudin & Combettes 2014, Crassidis-Markley 2007), executed once per power-up.
• Hysteresis in fluxgate cores. Even a permalloy core has remanence equivalent to 1–10 nT offset uncertainty after large-field exposure. Recovery requires a degauss cycle (10 kHz AC excitation decaying over 1 s) or — for space missions — flight-time in-orbit calibration manoeuvres.
• SQUID flux trapping. A poorly-shielded SQUID can trap external flux in its pickup loop on cooldown; lock-on becomes impossible until warming and re-cooling. Solution: cool in zero field inside a mu-metal can.
• Sample-rate aliasing. Phone magnetometers sampled at 100 Hz alias 50 / 60 Hz line-frequency fields into a heading drift; either sample faster, or filter to $\le$ 25 Hz.
• Sensor heating. A 200 A current sensor with 1 mΩ insertion resistance dissipates 40 W in its own die — Hall temperature drifts 100–150 °C above ambient. Use a thermally-compensated part (ACS37800-style with internal temp sensor) and account for the drift in gain.
• Power-spectrum 1/f noise. Magnetoresistive sensors have a $1/f$ corner around 100 Hz – 1 kHz that dominates DC + low-frequency noise. Designs that demand DC sensitivity (current, position) must add a chopper / flip-coil scheme that modulates the input above the corner — every production TMR current sensor includes this.
• Temperature coefficient of permanent magnets. Sensor magnets lose 0.1 %/°C of remanence; over -40\,\ldots\,+125\,^\circ\mathrm{C} that is 16 % gain shift. The encoder IC must self-calibrate to magnet strength, or — better — sense field direction only (angle is independent of magnet strength).
• PCB orientation matters. Hall plates on a chip respond to $B_z$ perpendicular to the silicon surface; AMR / GMR / TMR coupons respond to in-plane $B_x$ or $B_y$. Switching from a Hall to a magnetoresistive replacement on a board redesign without rotating the package by 90° is a classic launch-day defect.
• OPM dynamic-range limit. SERF-regime OPM cells lose sensitivity above $\sim$10 nT, so MEG/MCG installations must compensate the Earth’s $\sim$50 µT field with active coil cancellation (e.g. the Cerca Magnetics shielded room with active 3D Helmholtz nulling).

13. Worked example — current sensor selection for an 800 V SiC traction inverter

A new EV traction inverter draws up to 500 A peak phase current at 800 V DC bus from SiC half-bridges switching at 20–40 kHz. The control loop needs 10 µs current loop bandwidth, 0.5 % accuracy at peak, and ASIL-C diagnostic coverage.

• Bandwidth requirement. A 10 µs control loop wants $\sim$100 kHz sensor BW. Hall (Allegro ACS37610: 250 kHz) and differential-Hall (TDK CUR 4250: 200 kHz) both qualify; a closed-loop fluxgate (LEM HOPS 1000-SB: 800 kHz) qualifies with margin.
• Accuracy. 0.5 % at 500 A = 2.5 A absolute. Most Hall parts spec $\pm$2 % at room temperature, $\pm$4 % over automotive temp range — borderline. Closed-loop fluxgate gives $\pm$0.1 % — over-spec but lower drift, so cleaner ageing over 10 years.
• Galvanic isolation. 800 V working voltage. AEC-Q200 isolation requirement: 5 kV working, 10 kV impulse. ACS758 (4.8 kV) is marginal; ACS37800 (5.0 kV) qualifies; LEM HOPS family (5.0 kV reinforced) qualifies cleanly.
• Stray-field rejection. Three-phase busbars 30 mm apart at 500 A produce 3–5 mT stray field at the sensor. Differential-Hall (CUR 4250) or shielded closed-loop sensor rejects $>$ 60 dB; single-Hall fails.
• Diagnostics. ASIL-C requires either redundant sensors or an internal diagnostic feature (LFM — Lockstep Functional Monitoring). TDK CUR 4250 and Allegro ACS37800 both have on-die redundancy with diagnostic output.

Verdict: TDK CUR 4250 at ~$3.50 in volume meets all five criteria with margin and ships with ASIL-C qualification. The fluxgate alternative (LEM HOPS) gives better accuracy but doubles cost and complicates supply. Most 2024–2026 OEM EV inverter releases (VW MEB Gen-2, Hyundai E-GMP, Ford F-150 Lightning, GM Ultium) converged on the differential-Hall+busbar architecture.

14. Standards and qualifications

• IEC 61869 — Instrument transformer / sensor accuracy classes; -10 covers electronic current and voltage sensors with Hall, fluxgate, MOCT. Class 0.1 — laboratory; class 0.5 — billing-grade metering; class 1.0 — protective relaying.
• ISO 26262 — Functional safety in road vehicles. ASIL-B / C / D rated 3D Hall position sensors require redundant on-die channels (Melexis MLX90425, Allegro A1335-D). The standard defines safety-relevant failure-in-time (FIT) targets: < 100 FIT for ASIL-B, < 10 FIT for ASIL-D random hardware failures.
• AEC-Q100 — Automotive qualification for ICs. Grade 0 covers -40\,\ldots\,+150\,^\circ\mathrm{C} for the entire Hall / TMR sensor portfolio. Grade 1 covers -40\,\ldots\,+125\,^\circ\mathrm{C} — standard for body-electronics Hall switches.
• IEEE 1149.1 (JTAG) — used on most digital-output magnetic sensors for in-system calibration trim.
• IEC 60601-2-33 — MR scanner magnetic-field exposure (the test environment for MR-conditional sensor labels). Sensors labelled MR-Conditional must withstand 1.5 T (or 3 T) static field and the 100 T/s gradient slew without function loss.
• INTERMAGNET — observatory-grade fluxgate standard; defines noise and stability targets for global geomagnetic monitoring (definitive 1-minute data products with $\le$ 5 nT uncertainty).
• ASTM E1444 — Magnetic Particle Testing standard (the NDE workhorse for ferromagnetic part inspection, complementary to GMR / TMR probe-based methods).
• DOE 10 CFR 1046 — US Department of Energy security-rule for magnetic-anomaly perimeter detection (drives sensitivity floor for buried-fluxgate vehicle detection).
• ISO 16750 — Road vehicle environmental conditions for electrical and electronic equipment; sets vibration, thermal-shock, and humidity profiles for traction-inverter current sensors.

15. Magnetic shielding for sensitive measurements

Any pT- or fT-class measurement collapses without a shielded environment. The shielding factor of a closed enclosure of inner radius $a$, wall thickness $t$, and relative permeability ${\mu }_r$ for a low-frequency uniform field is approximately:

$S\approx 1+\frac{4{\mu }_{r}t}{3a}$

A 5 mm mu-metal box (${\mu }_r\sim 50000$ at $B<0.1\mathrm{mT}$) with 200 mm inner radius gives $S\approx 1660$ — three orders of magnitude attenuation of the Earth’s field, taking 50 µT down to 30 nT. Stacking three nested mu-metal layers with 25 mm air gaps gives $S\approx 10^6$ overall (independent layers’ factors multiply, since the field re-distributes between layers).

Vendors:

• Magnetic Shield Corporation (US) — MuMETAL stock, custom-formed shields, mu-metal mesh.
• Magnetic Shields Ltd (Tonbridge, UK) — MuRoom shielded rooms (4-layer mu-metal, internal field < 5 nT). The standard MEG / OPM-MEG enclosure worldwide; UCL, Nottingham, Cerca, NIH all use MuRoom variants.
• Vacuumschmelze (VAC) — MUMETALL, ULTRAVAC nanocrystalline cores, supplied to medical and aerospace.
• IMEDCO AG (Switzerland) — turn-key Faraday + MSR rooms for MRI / MEG / TMS suites.

Active shielding (Helmholtz coils + feedback fluxgate) buys another factor of 10–100 at low frequencies for the same physical envelope and is now standard in OPM-MEG rooms.

15.1 Active shielding

For OPM-MEG installs that cannot afford a full mu-metal shielded room, a hybrid solution combines a 2-layer mu-metal cage with active 3-axis Helmholtz coils inside. The active coils sense the residual field (sub-nT at the OPM sensor cell) and inject feedback current to null it out. Vendors: Cerca Magnetics (UK), FieldLine Medical (US), Magnicon GmbH (Germany). Active-shield bandwidth is typically DC–500 Hz, complementing the static shielding of the mu-metal layers. The combination achieves an internal background field $<$ 5 nT — adequate for biomag OPM, at $\sim$1/4 the cost of a full 4-layer mu-metal Magnetic Shielding Ltd MuRoom.

16. Outlook

The two most active frontiers in 2026:

• OPM commoditisation. QuSpin, FieldLine, and Mag4Health are driving OPM cell prices from $15 k to $3–5 k each over 2024–2028. A 128-channel OPM-MEG (now $\sim$$2M) drops to under $1M, making MEG affordable for general hospitals rather than only academic centres.
• TMR-everywhere. TMR sensors with $\Delta R/R\sim 200$–600 % are pushing AMR and GMR out of automotive, industrial, and consumer position-sensing. MultiDimension Technology, TDK, Allegro, and NVE all ship production TMR magnetic sensors at sub-$5 unit cost; phone IMU magnetometers are migrating from Hall / AMR to TMR with 3–10× resolution improvement.

A third trend — diamond NV-centre magnetometry — has matured from physics demos (LANL, Fraunhofer IAF, QZabre, Element Six) to laboratory-grade instruments at $\sim$1 pT/$\sqrt{\mathrm{Hz}}$ with $\sim$10 nm spatial resolution. Commercial NV magnetometers from QZabre and Quantum Brilliance compete with SQUID in cell-biology magnetic imaging and may replace MFL sensors for spatial NDE in another five years.

Further reading

• Ripka, P. (Ed.). (2021). Magnetic Sensors and Magnetometers (2nd ed.). Artech House. Canonical reference covering Hall, AMR, GMR, TMR, fluxgate, and SQUID; the practical bible.
• Tumanski, S. (2011). Handbook of Magnetic Measurements. CRC Press. Field-instrument focus; chapters on calibration, shielding, search-coil design.
• Fagaly, R. L. (2006). “Superconducting quantum interference device instruments and applications.” Review of Scientific Instruments 77, 101101. The standard SQUID review.
• Boto, E. et al. (2018). “Moving magnetoencephalography towards real-world applications with a wearable system.” Nature 555, 657–661. The OPM-MEG breakthrough paper from the UCL / Nottingham group.
• Edelstein, A. (2007). “Advances in magnetometry.” Journal of Physics: Condensed Matter 19, 165217. Survey of sensitivity floors across technologies.
• Caruso, M. J. (1997). AMR Sensor Application Notes. Honeywell / Sensitec. The standard introduction to permalloy AMR design.
• Allegro MicroSystems. Hall-Effect Sensor IC Applications Guide (2022). Direct vendor application catalog.
• Melexis. Magnetic Sensors Handbook (2024). Same.

Adjacent

• electromagnetics-engineering — Lorentz force, magnetic-circuit reluctance, B-H curves; the field theory under every transduction method here.
• mems — Lorentz-force MEMS magnetometer fabrication, capacitive readout, on-chip ovens.
• bioinstrumentation — ECG/EEG sister-modalities to MCG/MEG; biopotential vs biomagnetism trade-offs.
• electric-motors — primary application of 3D Hall and AMR / TMR angle sensors.
• power-electronics — primary application of Hall / Rogowski / fluxgate current sensors.
• magnetic-and-optical-materials — permalloy, mu-metal, MgO tunnel barriers, soft ferrite — the materials that make the sensors.
• sensors-pose-motion — IMU + magnetometer fusion (Madgwick / Mahony / EKF) for orientation estimation.
• sensors-perception — phone-magnetometer-based indoor navigation.