SQUID-on-Lever Probes: NanoSQUID Sensing

• SQUID-on-Lever probes are nanoscale scanning sensors that integrate a miniaturized SQUID at the tip of a cantilever or lever, combining magnetic sensing with precise distance control.
• Advanced fabrication methods—including self-aligned apex deposition, focused-ion-beam patterning, and wafer-scale lithography—achieve loop diameters down to 10 nm and versatile device architectures.
• Experimental implementations demonstrate high flux and thermal sensitivity, enabling imaging of nanoscale vortices, currents, and spin textures, with robust operation in fields up to 1–2.5 T.

Searching arXiv for recent and foundational papers on SQUID-on-lever / SQUID-on-cantilever / SQUID-on-tip probes. Searching for "SQUID-on-lever scanning probe" on arXiv. SQUID-on-lever probes are scanning superconducting quantum interference device sensors in which a nanoSQUID is integrated at, or very near, the free end of a compliant mechanical element such as a cantilever or lever, so that magnetic sensing and nanoscale distance control are co-localized. In the published literature, the term spans true SQUID-on-cantilever implementations and closely related SQUID-on-tip architectures that place the loop at the apex of a sharp scanned support; conceptually, both realize a “SQUID-on-probe” geometry in which the loop is miniaturized, brought within nanometers to tens of nanometers of the sample, and operated as part of a scanning microscope (Wyss et al., 2021, Finkler et al., 2010). The field has evolved from self-aligned aluminum SQUID-on-tip devices with effective areas down to $0.034\ \mu\mathrm{m}^2$, flux sensitivity $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$, and operation up to $0.6\ \mathrm{T}$ (Finkler et al., 2010), to cantilever-integrated niobium devices with magnetic, thermal, and topographic contrast (Wyss et al., 2021), wafer-scale wireframe SQUID-on-cantilever platforms (Roskamp et al., 16 Jan 2026), sputtered Nb and MoGe SQUID-on-tip probes directly transferable to lever integration (Romagnoli et al., 2023), and advanced SQUID-on-lever probes with sub-100-nm spatial resolution and integrated control functionality (Weber et al., 3 Aug 2025).

1. Historical emergence and device concept

The modern lineage of SQUID-on-lever probes begins with the demonstration of a complete dc nanoSQUID fabricated directly on the apex of a sharp quartz tip and used as the sensing element of a scanning SQUID microscope (Finkler et al., 2010). In that implementation, a hollow quartz tube of 1 mm outer diameter was mechanically pulled to a sharp tip with apex diameter controllable between $\sim 100$ and $400\ \mathrm{nm}$, and a self-aligned three-step evaporation process produced a loop at the very apex with two weak links acting as Josephson junctions. The essential conceptual advance was to place the full SQUID loop at the scanned apex itself, so that the minimum sensor–sample separation was limited primarily by tip–surface interactions and the feedback scheme rather than by the lateral footprint of a planar chip (Finkler et al., 2010).

This geometry is directly continuous with later SQUID-on-cantilever realizations. A true nanometer-scale SQUID-on-cantilever scanning probe was demonstrated by patterning a niobium nanoSQUID at the apex of a commercial non-contact AFM cantilever, yielding an effective diameter of $365\ \mathrm{nm}$, field sensitivity of $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$, and thermal sensitivity of $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$, while operating in magnetic fields up to $1.0\ \mathrm{T}$ (Wyss et al., 2021). A later wafer-scale realization placed nanoscale SQUIDs at the apex of wireframe tips on self-aligned superconducting cantilever probes, with effective diameters ranging from several micrometers down to $100\ \mathrm{nm}$ and operation up to $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$0 (Roskamp et al., 16 Jan 2026). More recent planar silicon cantilever probes integrated nanometer-scale niobium SQUIDs with inner-loop sizes down to $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$1, flux sensitivity of $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$2, and spatial resolution better than $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$3 at $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$4 (Weber et al., 3 Aug 2025).

A parallel thread is the development of vector-sensitive and multifunctional apex SQUIDs. The three-junction Pb SQUID-on-tip introduced a double-loop, three-junction geometry with tunable sensitivity to both in-plane and out-of-plane magnetic fields and demonstrated spin sensitivity better than $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$5 (Anahory et al., 2014). Tapping-mode SQUID-on-tip microscopy with proximity Josephson junctions combined AFM with nanoSQUID sensing, minimized nanoSQUID–sample distance, provided in-plane magnetic sensitivity, and used frequency multiplexing to image currents, magnetism, dissipation, and topography without lasers (Rog et al., 29 Aug 2025). This suggests that the distinction between “lever,” “cantilever,” and “tip” architectures is partly geometric and partly technological; the unifying principle is the integration of a nanoSQUID with a scanned mechanical probe.

2. Probe architectures and fabrication strategies

Three fabrication paradigms dominate the literature: self-aligned apex deposition on pulled quartz supports, focused-ion-beam patterning on preformed cantilevers, and wafer-scale molding or lithography followed by nanoscale post-definition.

The earliest self-aligned apex process used three thermal evaporation steps of aluminum on a pulled quartz tip: 25 nm at $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$6, 25 nm at $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$7, and 17 nm at $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$8, thereby defining two leads and an apex ring without lithography or FIB (Finkler et al., 2010). The ring overlapped the leads at two thicker superconducting regions, while two thinner sections of the ring acted as Dayem-bridge-like weak links with effective width about $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$9 (Finkler et al., 2010). Later work extended this non-lithographic strategy by using grooved quartz capillaries and integrated shunts near the apex. Specifically designed grooved quartz capillaries enabled effective diameters down to $0.6\ \mathrm{T}$0, and integration of a Cr/Au shunt $0.6\ \mathrm{T}$1 located $0.6\ \mathrm{T}$2 from the apex produced non-hysteretic, high-performance In and Sn SQUID-on-tip devices (Anahory et al., 2020).

A second route begins from a prefabricated cantilever or lever and defines the SQUID by FIB milling in a deposited superconducting film. In a niobium SQUID-on-cantilever scanning probe, a commercial non-contact AFM cantilever was milled into a triangular plateau, coated on the front side with 5 nm Ti, 50 nm Nb, 2 nm Pt, and 10 nm Au, and then sculpted by Ga$0.6\ \mathrm{T}$3 FIB into two superconducting leads, a loop with two Dayem bridges, and a nearby protruding AFM tip (Wyss et al., 2021). A related planar silicon cantilever process employed wafer-scale optical lithography to define three Nb leads terminating at a triangular apex region, after which Ne- or He-FIB milling produced loops with hole diameters down to $0.6\ \mathrm{T}$4, modulation lines, or a third Josephson junction (Weber et al., 3 Aug 2025). This architecture preserves the cantilever mechanics of AFM while placing the SQUID directly at the apex.

A third strategy realizes self-aligned 3D cantilever probes at wafer scale. In the wireframe SQUID-on-cantilever platform, low-stress Si-rich nitride was deposited on Si (100), anisotropic KOH etching formed sharp or truncated inverted pyramids, and corner lithography left nanowires in the ribs and, for sharp pyramids, a nanodot at the apex (Roskamp et al., 16 Jan 2026). A TEOS/SiRN/TEOS stack then defined the cantilever and an undercut required for shadow-effect deposition. Magnetron sputtering of Ti: 5 nm, Nb: 60 nm, Pd: 2 nm, and Au: 20 nm coated the nanowires and wiring while preserving electrical isolation by shadowing across the undercut (Roskamp et al., 16 Jan 2026). FIB milling at the apex then defined either constrictions in an open-loop wireframe or an entire nanoSQUID on a sharp wireframe tip (Roskamp et al., 16 Jan 2026).

Conventional magnetron sputtering has also been adapted to apex nanoSQUID fabrication on quartz supports in a way explicitly described as transferable to SQUID-on-lever design (Romagnoli et al., 2023). Commercial quartz capillaries with four longitudinal grooves, outer diameter 1 mm and inner diameter 0.4 mm, were pulled to apex diameters $0.6\ \mathrm{T}$5, coated with a Ti/Au strip 350 $0.6\ \mathrm{T}$6m from the apex to form a shunt of $0.6\ \mathrm{T}$7, and then directionally sputtered at $0.6\ \mathrm{T}$8, $0.6\ \mathrm{T}$9, and $\sim 100$0 to form leads and an apex loop (Romagnoli et al., 2023). Nb devices used a 3 nm Ti base layer, 25–30 nm Nb per step, and a 3 nm Ti cap; MoGe devices used 35–40 nm per step (Romagnoli et al., 2023). This simplified sputtering route yielded effective diameters from 50 to $\sim 100$1 and operating fields up to $\sim 100$2 (Romagnoli et al., 2023).

Implementation	Core fabrication route	Representative dimensions / materials
Self-aligned SOT	Three-step Al evaporation on pulled quartz tip	Effective loop diameter 208 nm; weak-link width about 30 nm; Al (Finkler et al., 2010)
Sputtered apex SQUID	Directional magnetron sputtering on grooved quartz capillary	Effective diameters 48 nm (Nb) and 74 nm (MoGe) (Romagnoli et al., 2023)
SQUID-on-cantilever	Nb-coated AFM cantilever patterned by FIB	Effective diameter 365 nm; Ti/Nb/Pt/Au stack (Wyss et al., 2021)
Wireframe SQUID-on-cantilever	Corner lithography + Nb sputtering + FIB	Effective diameters from several $\sim 100$3m down to 100 nm (Roskamp et al., 16 Jan 2026)
Advanced planar SoL	Wafer-scale lithography + Ne/He-FIB on Si cantilever	Inner-loop sizes down to 10 nm; Nb (Weber et al., 3 Aug 2025)

A plausible implication is that the field has progressively traded artisanal apex fabrication for wafer-compatible methods while attempting to preserve the defining advantages of apex placement, small loop area, and short sensor–sample spacing.

3. SQUID physics, junction types, and readout schemes

Most SQUID-on-lever probes are dc SQUIDs based on Dayem-bridge or constriction junctions. In the early apex aluminum device, the two thinner sections of the apex ring acted as weak links and the measured interference pattern was fitted with the standard asymmetric SQUID model of Tesche–Clarke, yielding junction critical currents $\sim 100$4 and $\sim 100$5 with $\sim 100$6, $\sim 100$7, and screening parameter $\sim 100$8 (Finkler et al., 2010). The extracted loop inductance was $\sim 100$9, whereas the geometric inductance was $400\ \mathrm{nm}$0, so kinetic inductance dominated (Finkler et al., 2010). In that device, the kinetic inductance was described by

$400\ \mathrm{nm}$1

with estimated cross section $400\ \mathrm{nm}$2 and $400\ \mathrm{nm}$3 (Finkler et al., 2010).

The importance of kinetic inductance persists in later devices. In sputtered Nb and MoGe SQUID-on-tip probes, $400\ \mathrm{nm}$4 was estimated from the modulation depth to be $400\ \mathrm{nm}$5 and $400\ \mathrm{nm}$6, the latter producing reduced modulation depth because of large kinetic inductance (Romagnoli et al., 2023). In the wireframe SQUID-on-cantilever, the inductance parameter extracted from the measured critical-current modulation was $400\ \mathrm{nm}$7, corresponding to $400\ \mathrm{nm}$8, again dominated by kinetic inductance of the constriction bridges (Roskamp et al., 16 Jan 2026).

Readout schemes vary with junction damping and architecture. The aluminum apex SQUID was operated in a voltage-bias configuration through a small series resistor $400\ \mathrm{nm}$9, with the SQUID current read by a SQUID series array amplifier in feedback mode; the resulting I–V characteristics were non-hysteretic and showed negative differential resistance consistent with the Aslamazov–Larkin model when the bias circuitry was included (Finkler et al., 2010). Sputtered Nb and MoGe apex devices at 4.2 K used a voltage source $365\ \mathrm{nm}$0 in series with $365\ \mathrm{nm}$1, while the SQUID was shunted by $365\ \mathrm{nm}$2 and further stabilized by the Ti/Au strip at $365\ \mathrm{nm}$3 for Nb or $365\ \mathrm{nm}$4 for MoGe (Romagnoli et al., 2023). The Stewart–McCumber parameter,

$365\ \mathrm{nm}$5

was $365\ \mathrm{nm}$6 for Nb and $365\ \mathrm{nm}$7 for MoGe, corresponding to slightly overdamped, non-hysteretic I–V curves (Romagnoli et al., 2023).

SQUID-on-cantilever probes patterned in niobium used a similar semi-voltage-biased philosophy. The AFM-cantilever device employed $365\ \mathrm{nm}$8, $365\ \mathrm{nm}$9, parasitic series resistance $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$0, and a Pt shunt $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$1 bridging the two leads outside the loop, producing a reproducible, nearly single-valued $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$2 relation (Wyss et al., 2021). The advanced planar SoL likewise used a semi-voltage-biased circuit with a large $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$3, shunt $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$4, parasitic $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$5, and SSAA current readout, explicitly to avoid problems from I–V hysteresis (Weber et al., 3 Aug 2025).

Not all probes use constriction junctions. Tapping-mode SQUID-on-tip microscopy introduced niobium–copper SNS proximity Josephson junctions, defined by leaving a $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$6 long Cu nanobridge between Nb electrodes (Rog et al., 29 Aug 2025). The design emphasized a substantial $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$7 product, non-hysteretic I–V curves at all temperatures, a single-valued current–phase relation at all temperatures, and a transfer function $9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$8 of a few mV/$9.5\ \mathrm{nT}/\sqrt{\mathrm{Hz}}$9, at least an order of magnitude larger than typical nanoSQUIDs (Rog et al., 29 Aug 2025). This allowed direct four-wire readout at room temperature without cryogenic amplification (Rog et al., 29 Aug 2025).

Vector and multifunctional control have motivated nonstandard loop topologies. The three-junction Pb SQUID-on-tip implemented two side loops and three Dayem-bridge junctions, giving two loop fluxes $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$0 and $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$1 and corresponding $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$2 and $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$3 modes (Anahory et al., 2014). The relation between applied in-plane and out-of-plane fields and these flux coordinates was written as

$620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$4

which underlies working-point selection for $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$5- or $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$6-dominant sensitivity (Anahory et al., 2014). The advanced planar SoL pursued a different control strategy: a 2-JJ version with a modulation line, and a 3-JJ version in which a control current shifts the interference pattern by phase bias rather than by direct flux injection (Weber et al., 3 Aug 2025).

4. Mechanical integration and scanning operation

The defining feature of SQUID-on-lever probes is mechanical co-integration of the sensor with a scanned resonator. Several distinct mechanical solutions have emerged.

The original apex SQUID microscope glued the SOT to one tine of a quartz tuning fork and operated at 300 mK, using either frequency shift or amplitude reduction as the feedback signal, analogous to tuning-fork AFM and near-field optical microscopy (Finkler et al., 2010). The oscillation amplitude of the tip was typically $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$7, so it did not limit magnetic spatial resolution, and the SOT could be scanned a few nm above the surface (Finkler et al., 2010). A later detailed description of this architecture specified a 32,768 Hz quartz tuning fork, shear-force feedback, and tip–sample separations of a few nm, with spatial resolution about 200 nm and direct imaging of vortices and local AC magnetic response (Finkler et al., 2012).

In a true SQUID-on-cantilever implementation, the resonator is a compliant AFM lever. The niobium SQUID-on-cantilever probe was built on a Nanosensors ATEC-NC non-contact AFM cantilever of length $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$8, width $620\ \mathrm{nK}/\sqrt{\mathrm{Hz}}$9, thickness $1.0\ \mathrm{T}$0, resonance frequency $1.0\ \mathrm{T}$1, and spring constant $1.0\ \mathrm{T}$2 (Wyss et al., 2021). Its flexural motion was driven by a piezoelectric disc and detected by a fiber-optic interferometer; as the probe approached the sample, force-induced changes in the effective spring constant shifted the resonance frequency, and a phase-locked loop tracked $1.0\ \mathrm{T}$3 continuously (Wyss et al., 2021). In constant-frequency mode, the vertical scanner was adjusted to maintain a fixed $1.0\ \mathrm{T}$4, stabilizing the tip–sample distance to within a few nm (Wyss et al., 2021). A protruding tip about 175 nm high next to the SQUID loop served purely for topography and prevented the SQUID itself from physically contacting the sample (Wyss et al., 2021).

The advanced planar SoL also used cantilever mechanics, but with much smaller planar silicon levers fabricated from SOI. These had length $1.0\ \mathrm{T}$5, width $1.0\ \mathrm{T}$6, thickness $1.0\ \mathrm{T}$7, spring constant $1.0\ \mathrm{T}$8, and resonance at 4.2 K in vacuum of 577 kHz with $1.0\ \mathrm{T}$9 (Weber et al., 3 Aug 2025). The cantilever was driven at its fundamental resonance with oscillation amplitude $100\ \mathrm{nm}$0, displacement was measured by fiber interferometry, and tip–sample interaction shifted the resonance frequency already at $100\ \mathrm{nm}$1 separation, enabling gentle non-contact approach (Weber et al., 3 Aug 2025). For enhanced magnetic contrast, the sample could also be oscillated in the $100\ \mathrm{nm}$2 direction at $100\ \mathrm{nm}$3 with $100\ \mathrm{nm}$4, producing

$100\ \mathrm{nm}$5

which was detected by lock-in amplification as a field-derivative image (Weber et al., 3 Aug 2025).

The wireframe SQUID-on-cantilever platform emphasized AFM compatibility at the fabrication level. A superconducting probe on a $100\ \mathrm{nm}$6 SiRN cantilever was operated in a room-temperature commercial AFM in tapping mode on highly oriented pyrolytic graphite, and no degradation was observed (Roskamp et al., 16 Jan 2026). Mechanical parameters such as spring constant and resonance frequency were not explicitly given, but the dimensions suggest standard AFM-like operation (Roskamp et al., 16 Jan 2026).

A further convergence of AFM and apex SQUID concepts is found in tapping-mode SQUID-on-tip microscopy. Here a nanoSQUID was fabricated at the apex of a small SiN cantilever mechanically coupled to an Akiyama-type quartz tuning fork (Rog et al., 29 Aug 2025). The first cantilever bending mode, around tens of kHz, was used for AFM; the topographic feedback was determined by the repulsive part of the tip–sample interaction potential, and the quartz tuning fork provided self-sensing and self-actuation without optical beams (Rog et al., 29 Aug 2025). This allowed continuous scanning for seven weeks in tapping mode without probe or sample degradation (Rog et al., 29 Aug 2025). A plausible implication is that the distinction between “SQUID-on-tip” and “SQUID-on-lever” is increasingly blurred at the level of microscope mechanics, with hybrid architectures adopting whichever resonator and distance-control method best minimize stand-off and maximize stability.

5. Sensitivity, spatial resolution, and operating-field range

The central performance metrics for SQUID-on-lever probes are flux noise, field noise, spin sensitivity, spatial resolution, and operating magnetic field range. These quantities vary widely with loop size, material, weak-link type, stand-off distance, and readout electronics.

Early aluminum apex SQUIDs reported a white flux noise level

$100\ \mathrm{nm}$7

corresponding, for $100\ \mathrm{nm}$8, to field sensitivity

$100\ \mathrm{nm}$9

with white noise extending from tens of Hz to at least $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$00 (Finkler et al., 2010). For a spin located on the axis of a circular loop, the sensitivity expression used was

$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$01

yielding $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$02 for on-axis spins under the loop and $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$03 near the perimeter where the relevant scale is the weak-link width $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$04; for the smallest 130 nm device, sensitivity $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$05 was projected (Finkler et al., 2010).

Grooved-quartz In and Sn SQUID-on-tip probes pushed these figures dramatically. With effective diameter $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$06, a flux noise of $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$07 and spin noise of $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$08 were reported, with operation at sub-Kelvin temperatures and in high magnetic fields of over $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$09 (Anahory et al., 2020). The relation

$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$10

was used for spin sensitivity at the loop center (Anahory et al., 2020). Sputtered Nb apex devices likewise achieved very low noise for transferred lever integration, with a 48 nm device showing minimum white field noise $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$11, low-field flux noise $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$12, and spin sensitivity $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$13 at low field or $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$14 near $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$15 (Romagnoli et al., 2023).

True cantilever-based devices initially traded some nanoscale performance for mechanical robustness and multifunctionality. The 365 nm niobium SQUID-on-cantilever achieved white flux noise

$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$16

and field sensitivity

$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$17

at 4.2 K and $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$18, together with thermal sensitivity

$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$19

and operation in fields up to $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$20 (Wyss et al., 2021). The corresponding thermal response at $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$21 was

$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$22

(Wyss et al., 2021).

The wireframe SQUID-on-cantilever platform emphasized geometry and scalability more than ultimate noise, reporting a lowest measured white flux noise floor

$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$23

without feedback loop and without cryogenic pre-amplifier, and interference persisting in the smallest 114 nm device up to fields $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$24, with small jumps near $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$25 attributed to vortex entry (Roskamp et al., 16 Jan 2026). By contrast, the advanced planar SoL achieved both nanometer-scale resolution and competitive noise: best white noise

$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$26

at 12 kHz, with operation up to about $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$27 at 4.2 K (Weber et al., 3 Aug 2025). Analysis of the point spread function by skyrmion imaging yielded a FWHM of 87 nm, and magnetic modulations with period $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$28 were resolved (Weber et al., 3 Aug 2025).

Spatial resolution is not set by loop size alone. The susceptibility literature on planar scanning SQUIDs made explicit that spatial resolution is determined by both the size of the field-sensitive area and its spacing from the sample surface (Kirtley et al., 2016). For sub-micron planarized susceptometers with 0.2 $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$29m pickup loops, realistic response widths were still $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$30 because the effective height and shielding geometry broadened the point spread function (Kirtley et al., 2016). By contrast, apex and lever geometries in which the loop resides at the mechanical tip can reduce the stand-off to tens of nanometers or a few nanometers and thereby realize much closer correspondence between spatial resolution and loop dimension (Finkler et al., 2010, Weber et al., 3 Aug 2025).

Operating field range is also architecture-dependent. Aluminum apex SQUIDs operated in fields as high as $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$31 because all dimensions were nanoscale and the leads along the quartz tube were aligned parallel to the applied field (Finkler et al., 2010). Sputtered Nb apex devices extended this to $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$32, attributed in part to Ti-induced NbTi alloying and field alignment along the tip axis (Romagnoli et al., 2023). The 39 nm In SOT functioned in fields of over $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$33 (Anahory et al., 2020). Vector-sensitive Pb three-junction apex SQUIDs demonstrated working points at fields in the tens of mT range and white field noise of $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$34 for in-plane and $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$35 for out-of-plane sensitivity (Anahory et al., 2014). The planar SoL and wireframe cantilever devices demonstrated up to about $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$36 and $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$37, respectively (Weber et al., 3 Aug 2025, Roskamp et al., 16 Jan 2026). This suggests that high-field robustness depends not only on material choice but also on whether the loop and leads present large perpendicular superconducting areas prone to vortex entry.

6. Applications, limitations, and future directions

SQUID-on-lever probes have been developed primarily for nanoscale magnetic imaging, but the literature shows a broader instrument class that can image currents, vortices, susceptibilities, dissipation, and topography in a single platform.

Current mapping is a recurrent demonstration. The aluminum apex SQUID imaged the self-field of a current-carrying Al serpentine structure, specifically a 200 nm-thick Al serpentine carrying 2 mA at 510 Hz, with field profiles matching theoretical calculations very well (Finkler et al., 2010). The niobium SQUID-on-cantilever imaged a 750 nm wide, 300 nm thick saw-tooth Au wire, measuring both $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$38 above the wire for $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$39 at $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$40 and an image proportional to $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$41 by cantilever actuation at $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$42 with amplitude 15 nm and $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$43 (Wyss et al., 2021). Tapping-mode SQUID-on-tip microscopy pushed current sensitivity further by resolving nanoscale currents as small as 100 nA in a niobium serpentine at sub-$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$44m spatial resolution, using averaging of 35 repeated scans at the lowest current (Rog et al., 29 Aug 2025).

Vortex imaging remains a canonical application. The SOT microscope imaged vortex lattices and local AC magnetic response in superconductors (Finkler et al., 2012). The niobium SQUID-on-cantilever imaged vortices and screening patterns in artificial spin systems and conductors (Wyss et al., 2021). Tapping-mode SQUID-on-tip microscopy used gradiometric imaging in which the sample was oscillated out of plane with 35 nm rms amplitude, allowing direct imaging of Pearl-vortex currents in a 60 nm thick Nb film and visualization of geometry-dependent vortex nucleation in triangle, circle, and square microstructures (Rog et al., 29 Aug 2025).

Nanomagnetism and spin textures are major current targets. The three-junction Pb apex SQUID independently measured $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$45 and $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$46 components of local fields, making $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$47 preferable for current mapping and $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$48 preferable for vortex detection, with in-plane spin sensitivity $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$49 at 10 nm distance (Anahory et al., 2014). The advanced planar SoL imaged skyrmions at the surface of bulk Cu$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$50OSeO$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$51, extracted an 87 nm PSF from a single skyrmion, and resolved helical magnetization with period $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$52 (Weber et al., 3 Aug 2025). A larger 150 nm In SOT at 300 mK imaged the stray field of a single Fe$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$53O$1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$54 nanocube and inferred a transition of the easy magnetization axis from the $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$55 direction at room temperature to an in-plane orientation at low temperature, plausibly associated with the Verwey phase transition (Anahory et al., 2020).

Thermal and multifunctional imaging have become distinctive advantages of lever-based or hybrid probes. The niobium SQUID-on-cantilever measured local temperature oscillations induced by Joule heating, using exchange gas to thermally link the sensor and sample and demodulating at the second harmonic $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$56, thereby achieving $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$57 thermal sensitivity (Wyss et al., 2021). Tapping-mode SQUID-on-tip microscopy likewise separated static magnetism, AC current response, dissipation, and topography by frequency multiplexing, without external radiation or cryogenic amplification (Rog et al., 29 Aug 2025).

Limitations recur across architectures. Self-aligned apex fabrication depends sensitively on tip geometry and film uniformity, making loop reproducibility at $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$58 and below nontrivial (Finkler et al., 2010). Quartz tips are mechanically fragile (Finkler et al., 2010). 1/f noise remains an issue below tens of Hz or up to $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$59, depending on device and readout (Finkler et al., 2010, Anahory et al., 2014). Hysteresis and self-heating can complicate Dayem-bridge operation, as seen explicitly in Pb $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$60-SQUIDs, where hysteretic I–V curves arise from self-heating and disappear only near a hysteresis crossover temperature below $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$61 (Paul et al., 2016). In cantilever devices, a separate sharp protrusion can protect the SQUID but imposes a finite offset between the mechanical contact point and the loop, increasing minimum stand-off (Wyss et al., 2021). Modulation currents in integrated control lines can perturb sensitive samples through stray fields, motivating low-current phase-bias schemes such as the three-junction SoL (Weber et al., 3 Aug 2025).

Future directions are explicit in the literature. Different superconductors, including Nb, NbN, Pb, and others, are expected to extend $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$62, $1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}}$63, or both (Finkler et al., 2010). Smaller loop diameters below 100 nm are repeatedly identified as a route to improved spin coupling and spatial resolution, provided kinetic inductance and noise remain controlled (Finkler et al., 2010, Roskamp et al., 16 Jan 2026). Wafer-scale fabrication and self-aligned templates suggest standardization and batch production (Roskamp et al., 16 Jan 2026, Weber et al., 3 Aug 2025). Integrated on-tip circuitry—modulation lines, field coils, a third junction, or susceptometry channels—appears increasingly feasible in lever architectures and much less so in conventional hand-fabricated apex tips (Weber et al., 3 Aug 2025, Roskamp et al., 16 Jan 2026). A plausible implication is that future SQUID-on-lever probes will continue to merge the apex proximity of SQUID-on-tip devices with the reproducibility, functionality, and systems integration of planar microfabrication.