---
title: 'SQUID-on-Lever Probes: NanoSQUID Sensing'
url: https://www.emergentmind.com/topics/squid-on-lever-probes
type: topic
---

# SQUID-on-Lever Probes: NanoSQUID Sensing

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 [2109.06774][1002.2921]. 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 \(0.6\ \mathrm{T}\) [1002.2921], to cantilever-integrated niobium devices with magnetic, thermal, and topographic contrast [2109.06774], wafer-scale wireframe SQUID-on-cantilever platforms [2601.11331], sputtered Nb and MoGe SQUID-on-tip probes directly transferable to lever integration [2303.06989], and advanced SQUID-on-lever probes with sub-100-nm spatial resolution and integrated control functionality [2508.01927].

## 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 [1002.2921]. 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 [1002.2921].

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 \(1.0\ \mathrm{T}\) [2109.06774]. 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 \(1\ \mathrm{T}\) [2601.11331]. More recent planar silicon cantilever probes integrated nanometer-scale niobium SQUIDs with inner-loop sizes down to \(10\ \mathrm{nm}\), flux sensitivity of \(0.3~\mu\Phi_0/\sqrt{\rm{Hz}}\), and spatial resolution better than \(100\ \mathrm{nm}\) at \(4.2\ \mathrm{K}\) [2508.01927].

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 \(5\ \mu_B/\mathrm{Hz}^{1/2}\) [1410.1609]. 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 [2508.21575]. 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 \(-100^\circ\), 25 nm at \(+100^\circ\), and 17 nm at \(0^\circ\), thereby defining two leads and an apex ring without lithography or FIB [1002.2921]. 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 \(30\ \mathrm{nm}\) [1002.2921]. 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 \(39\ \mathrm{nm}\), and integration of a Cr/Au shunt \((\sim 5\ \mathrm{nm} / \sim 10\ \mathrm{nm})\) located \(\sim 360\text{–}400\ \mu\mathrm{m}\) from the apex produced non-hysteretic, high-performance In and Sn SQUID-on-tip devices [2001.03342].

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\(^+\) FIB into two superconducting leads, a loop with two Dayem bridges, and a nearby protruding AFM tip [2109.06774]. 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 \(10\text{–}15\ \mathrm{nm}\), modulation lines, or a third Josephson junction [2508.01927]. 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 [2601.11331]. 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 [2601.11331]. FIB milling at the apex then defined either constrictions in an open-loop wireframe or an entire nanoSQUID on a sharp wireframe tip [2601.11331].

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 [2303.06989]. Commercial quartz capillaries with four longitudinal grooves, outer diameter 1 mm and inner diameter 0.4 mm, were pulled to apex diameters \(<100\ \mathrm{nm}\), coated with a Ti/Au strip 350 \(\mu\)m from the apex to form a shunt of \(R_{\text{sh}} = 4\text{–}10\ \Omega\), and then directionally sputtered at \(+120^\circ\), \(-120^\circ\), and \(0^\circ\) to form leads and an apex loop [2303.06989]. 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 [2303.06989]. This simplified sputtering route yielded effective diameters from 50 to \(80\ \mathrm{nm}\) and operating fields up to \(2.5\ \mathrm{T}\) [2303.06989].

| 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 [1002.2921] |
| Sputtered apex SQUID | Directional magnetron sputtering on grooved quartz capillary | Effective diameters 48 nm (Nb) and 74 nm (MoGe) [2303.06989] |
| SQUID-on-cantilever | Nb-coated AFM cantilever patterned by FIB | Effective diameter 365 nm; Ti/Nb/Pt/Au stack [2109.06774] |
| Wireframe SQUID-on-cantilever | Corner lithography + Nb sputtering + FIB | Effective diameters from several \(\mu\)m down to 100 nm [2601.11331] |
| Advanced planar SoL | Wafer-scale lithography + Ne/He-FIB on Si cantilever | Inner-loop sizes down to 10 nm; Nb [2508.01927] |

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 \((1-\alpha)I_0 = 0.8\ \mu\mathrm{A}\) and \((1+\alpha)I_0 = 2.4\ \mu\mathrm{A}\) with \(I_0 = 1.6\ \mu\mathrm{A}\), \(\alpha = 0.5\), and screening parameter \(\beta = 2LI_0/\Phi_0 = 0.85\) [1002.2921]. The extracted loop inductance was \(L = 549\ \mathrm{pH}\), whereas the geometric inductance was \(L_g \approx 0.26\ \mathrm{pH}\), so kinetic inductance dominated [1002.2921]. In that device, the kinetic inductance was described by
\[
L_k = \frac{2\pi \mu_0 \lambda_L^2 R}{a},
\]
with estimated cross section \(a = 510\ \mathrm{nm}^2\) and \(\lambda_L \approx 0.58\ \mu\mathrm{m}\) [1002.2921].

The importance of kinetic inductance persists in later devices. In sputtered Nb and MoGe SQUID-on-tip probes, \(\beta_L = 2LI_c/\Phi_0\) was estimated from the modulation depth to be \(\beta_L^{\text{Nb}} \approx 0.66\) and \(\beta_L^{\text{MoGe}} \approx 2.75\), the latter producing reduced modulation depth because of large kinetic inductance [2303.06989]. In the wireframe SQUID-on-cantilever, the inductance parameter extracted from the measured critical-current modulation was \(\beta_L = 0.53\), corresponding to \(L \approx 20\ \mathrm{pH}\), again dominated by kinetic inductance of the constriction bridges [2601.11331].

Readout schemes vary with junction damping and architecture. The aluminum apex SQUID was operated in a voltage-bias configuration through a small series resistor \(R_b \sim 2\ \Omega\), 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 [1002.2921]. Sputtered Nb and MoGe apex devices at 4.2 K used a voltage source \(V_b\) in series with \(R_b = 6.1\ \mathrm{k}\Omega\), while the SQUID was shunted by \(R_s = 3\ \Omega\) and further stabilized by the Ti/Au strip at \(R_{\text{sh}} = 5\ \Omega\) for Nb or \(7\ \Omega\) for MoGe [2303.06989]. The Stewart–McCumber parameter,
\[
\beta_c = \frac{2\pi I_c R^2 C}{\Phi_0},
\]
was \(\approx 0.93\) for Nb and \(\approx 0.87\) for MoGe, corresponding to slightly overdamped, non-hysteretic I–V curves [2303.06989].

SQUID-on-cantilever probes patterned in niobium used a similar semi-voltage-biased philosophy. The AFM-cantilever device employed \(R_b = 6.1~\mathrm{k}\Omega\), \(R_s = 3~\Omega\), parasitic series resistance \(R_p = 2~\Omega\), and a Pt shunt \(R_{sh} = 4~\Omega\) bridging the two leads outside the loop, producing a reproducible, nearly single-valued \(I_{\text{SQUID}}(V_b)\) relation [2109.06774]. The advanced planar SoL likewise used a semi-voltage-biased circuit with a large \(R_b\), shunt \(R_s \sim 1\ \Omega\), parasitic \(R_p \approx 0.3\ \Omega\), and SSAA current readout, explicitly to avoid problems from I–V hysteresis [2508.01927].

Not all probes use constriction junctions. Tapping-mode SQUID-on-tip microscopy introduced niobium–copper SNS proximity Josephson junctions, defined by leaving a \(\sim 20\ \mathrm{nm}\) long Cu nanobridge between Nb electrodes [2508.21575]. The design emphasized a substantial \(I_cR_N\) product, non-hysteretic I–V curves at all temperatures, a single-valued current–phase relation at all temperatures, and a transfer function \(V_\Phi\) of a few mV/\(\Phi_0\), at least an order of magnitude larger than typical nanoSQUIDs [2508.21575]. This allowed direct four-wire readout at room temperature without cryogenic amplification [2508.21575].

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 \(\Phi_L\) and \(\Phi_R\) and corresponding \(\Phi^+ = \Phi_L + \Phi_R\) and \(\Phi^- = \Phi_L - \Phi_R\) modes [1410.1609]. The relation between applied in-plane and out-of-plane fields and these flux coordinates was written as
\[
\begin{pmatrix} \Phi^+ \\ \Phi^- \end{pmatrix}
=
\begin{pmatrix}
A_L\cos\alpha_L + A_R\cos\alpha_R & A_L\sin\alpha_L - A_R\sin\alpha_R \\
A_L\cos\alpha_L - A_R\cos\alpha_R & A_L\sin\alpha_L + A_R\sin\alpha_R
\end{pmatrix}
\begin{pmatrix} \mu_0 H_z \\ \mu_0 H_x \end{pmatrix},
\]
which underlies working-point selection for \(B_z\)- or \(B_x\)-dominant sensitivity [1410.1609]. 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 [2508.01927].

## 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 [1002.2921]. The oscillation amplitude of the tip was typically \(<1\ \mathrm{nm}\), so it did not limit magnetic spatial resolution, and the SOT could be scanned a few nm above the surface [1002.2921]. 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 [1206.2853].

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 \(160~\mu\mathrm{m}\), width \(45~\mu\mathrm{m}\), thickness \(4.6~\mu\mathrm{m}\), resonance frequency \(f_0 \approx 335~\mathrm{kHz}\), and spring constant \(k \approx 45~\mathrm{N/m}\) [2109.06774]. 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 \(f_0\) continuously [2109.06774]. In constant-frequency mode, the vertical scanner was adjusted to maintain a fixed \(\Delta f\), stabilizing the tip–sample distance to within a few nm [2109.06774]. 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 [2109.06774].

The advanced planar SoL also used cantilever mechanics, but with much smaller planar silicon levers fabricated from SOI. These had length \(\sim 60\,\mu\mathrm{m}\), width \(\sim 40\,\mu\mathrm{m}\), thickness \(\sim 2\,\mu\mathrm{m}\), spring constant \(\sim 45~\mathrm{N/m}\), and resonance at 4.2 K in vacuum of 577 kHz with \(Q\sim 15{,}000\) [2508.01927]. The cantilever was driven at its fundamental resonance with oscillation amplitude \(\sim 10\ \mathrm{nm}\), displacement was measured by fiber interferometry, and tip–sample interaction shifted the resonance frequency already at \(>500\ \mathrm{nm}\) separation, enabling gentle non-contact approach [2508.01927]. For enhanced magnetic contrast, the sample could also be oscillated in the \(z\) direction at \(f_{\text{mod}} = 177\ \mathrm{Hz}\) with \(\Delta z \approx 1.5\,\mathrm{nm}\), producing
\[
B_{\text{ac}} \approx \Delta z \,\frac{dB_z}{dz},
\]
which was detected by lock-in amplification as a field-derivative image [2508.01927].

The wireframe SQUID-on-cantilever platform emphasized AFM compatibility at the fabrication level. A superconducting probe on a \(150\ \mu\mathrm{m} \times 30\ \mu\mathrm{m}\) SiRN cantilever was operated in a room-temperature commercial AFM in tapping mode on highly oriented pyrolytic graphite, and no degradation was observed [2601.11331]. Mechanical parameters such as spring constant and resonance frequency were not explicitly given, but the dimensions suggest standard AFM-like operation [2601.11331].

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 [2508.21575]. 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 [2508.21575]. This allowed continuous scanning for seven weeks in tapping mode without probe or sample degradation [2508.21575]. 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
\[
S_\Phi^{1/2} = 1.8\times 10^{-6}\ \Phi_0/\sqrt{\mathrm{Hz}},
\]
corresponding, for \(A_\text{eff} = 0.034\ \mu\mathrm{m}^2\), to field sensitivity
\[
S_B^{1/2} \approx 1.1\times 10^{-7}\ \mathrm{T}/\sqrt{\mathrm{Hz}},
\]
with white noise extending from tens of Hz to at least \(10^4\ \mathrm{Hz}\) [1002.2921]. For a spin located on the axis of a circular loop, the sensitivity expression used was
\[
S_n = \Phi_n \frac{R}{r_e}\left(1 + \frac{h^2}{R^2}\right)^{3/2},
\]
yielding \(S_n \approx 65\ \mu_B/\sqrt{\mathrm{Hz}}\) for on-axis spins under the loop and \(\approx 33\ \mu_B/\sqrt{\mathrm{Hz}}\) near the perimeter where the relevant scale is the weak-link width \(w \sim 30\ \mathrm{nm}\); for the smallest 130 nm device, sensitivity \(<20\ \mu_B/\sqrt{\mathrm{Hz}}\) was projected [1002.2921].

Grooved-quartz In and Sn SQUID-on-tip probes pushed these figures dramatically. With effective diameter \(d=39\ \mathrm{nm}\), a flux noise of \(42\ \mathrm{n}\Phi_0\ \mathrm{Hz}^{-1/2}\) and spin noise of \(0.29\ \mu_B\ \mathrm{Hz}^{-1/2}\) were reported, with operation at sub-Kelvin temperatures and in high magnetic fields of over \(2.5\ \mathrm{T}\) [2001.03342]. The relation
\[
S_{\mu}^{1/2} = S_\Phi^{1/2} \frac{r}{r_e}
\]
was used for spin sensitivity at the loop center [2001.03342]. Sputtered Nb apex devices likewise achieved very low noise for transferred lever integration, with a 48 nm device showing minimum white field noise \(S_B^{1/2} \approx 340\ \mathrm{nT}/\sqrt{\mathrm{Hz}}\), low-field flux noise \(S_\Phi^{1/2} \approx 300\ \mathrm{n}\Phi_0 / \sqrt{\mathrm{Hz}}\), and spin sensitivity \(S_n^{1/2} \approx 2.7\ \mu_B/\sqrt{\mathrm{Hz}}\) at low field or \(6.6\ \mu_B/\sqrt{\mathrm{Hz}}\) near \(2\text{–}2.5\ \mathrm{T}\) [2303.06989].

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
\[
S_\Phi^{1/2} \approx 0.48~\mu \Phi_0 / \sqrt{\mathrm{Hz}}
\]
and field sensitivity
\[
S_B^{1/2} \approx 9.5~\mathrm{nT}/\sqrt{\mathrm{Hz}}
\]
at 4.2 K and \(B_a = 0\), together with thermal sensitivity
\[
S_T^{1/2} \lesssim 620~\mathrm{nK}/\sqrt{\mathrm{Hz}},
\]
and operation in fields up to \(1.0\ \mathrm{T}\) [2109.06774]. The corresponding thermal response at \(V_b = 0.55~\mathrm{V}\) was
\[
\frac{d I_{\text{SQUID}}}{dT} = -24.2~\mu\mathrm{A/K}
\]
[2109.06774].

The wireframe SQUID-on-cantilever platform emphasized geometry and scalability more than ultimate noise, reporting a lowest measured white flux noise floor
\[
S_\Phi^{1/2} \approx 3.8\ \mu\Phi_0 / \sqrt{\mathrm{Hz}}
\]
without feedback loop and without cryogenic pre-amplifier, and interference persisting in the smallest 114 nm device up to fields \(\ge 1\ \mathrm{T}\), with small jumps near \(\pm 0.8\ \mathrm{T}\) attributed to vortex entry [2601.11331]. By contrast, the advanced planar SoL achieved both nanometer-scale resolution and competitive noise: best white noise
\[
S_\Phi^{1/2} \approx 0.3~\mu\Phi_0/\sqrt{\mathrm{Hz}}, \qquad
S_B^{1/2} \approx 120~\mathrm{nT}/\sqrt{\mathrm{Hz}}
\]
at 12 kHz, with operation up to about \(0.5\ \mathrm{T}\) at 4.2 K [2508.01927]. Analysis of the point spread function by skyrmion imaging yielded a FWHM of 87 nm, and magnetic modulations with period \(65\ \mathrm{nm}\) were resolved [2508.01927].

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 [1605.09483]. For sub-micron planarized susceptometers with 0.2 \(\mu\)m pickup loops, realistic response widths were still \(\sim 0.75\text{–}1.0\ \mu\mathrm{m}\) because the effective height and shielding geometry broadened the point spread function [1605.09483]. 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 [1002.2921][2508.01927].

Operating field range is also architecture-dependent. Aluminum apex SQUIDs operated in fields as high as \(0.6\ \mathrm{T}\) because all dimensions were nanoscale and the leads along the quartz tube were aligned parallel to the applied field [1002.2921]. Sputtered Nb apex devices extended this to \(>2.5\ \mathrm{T}\), attributed in part to Ti-induced NbTi alloying and field alignment along the tip axis [2303.06989]. The 39 nm In SOT functioned in fields of over \(2.5\ \mathrm{T}\) [2001.03342]. Vector-sensitive Pb three-junction apex SQUIDs demonstrated working points at fields in the tens of mT range and white field noise of \(70\ \mathrm{nT}/\sqrt{\mathrm{Hz}}\) for in-plane and \(20\ \mathrm{nT}/\sqrt{\mathrm{Hz}}\) for out-of-plane sensitivity [1410.1609]. The planar SoL and wireframe cantilever devices demonstrated up to about \(0.5\ \mathrm{T}\) and \(1\ \mathrm{T}\), respectively [2508.01927][2601.11331]. 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 [1002.2921]. The niobium SQUID-on-cantilever imaged a 750 nm wide, 300 nm thick saw-tooth Au wire, measuring both \(B_z^{\text{AC}}(x,y)\) above the wire for \(I_{\text{AC}} = 100~\mu\mathrm{A}\) at \(4.17~\mathrm{kHz}\) and an image proportional to \(dB_z/dz\) by cantilever actuation at \(f_0 = 282~\mathrm{kHz}\) with amplitude 15 nm and \(I_{\text{DC}} = 200~\mu\mathrm{A}\) [2109.06774]. 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-\(\mu\)m spatial resolution, using averaging of 35 repeated scans at the lowest current [2508.21575].

Vortex imaging remains a canonical application. The SOT microscope imaged vortex lattices and local AC magnetic response in superconductors [1206.2853]. The niobium SQUID-on-cantilever imaged vortices and screening patterns in artificial spin systems and conductors [2109.06774]. 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 [2508.21575].

Nanomagnetism and spin textures are major current targets. The three-junction Pb apex SQUID independently measured \(B_x\) and \(B_z\) components of local fields, making \(B_x\) preferable for current mapping and \(B_z\) preferable for vortex detection, with in-plane spin sensitivity \(\approx 4.9~\mu_B/\sqrt{\mathrm{Hz}}\) at 10 nm distance [1410.1609]. The advanced planar SoL imaged skyrmions at the surface of bulk Cu\(_2\)OSeO\(_3\), extracted an 87 nm PSF from a single skyrmion, and resolved helical magnetization with period \(65 \pm 5\,\mathrm{nm}\) [2508.01927]. A larger 150 nm In SOT at 300 mK imaged the stray field of a single Fe\(_3\)O\(_4\) nanocube and inferred a transition of the easy magnetization axis from the \((111)\) direction at room temperature to an in-plane orientation at low temperature, plausibly associated with the Verwey phase transition [2001.03342].

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 \(2 f_{\text{AC}}\), thereby achieving \(\sim 620~\mathrm{nK}/\sqrt{\mathrm{Hz}}\) thermal sensitivity [2109.06774]. 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 [2508.21575].

Limitations recur across architectures. Self-aligned apex fabrication depends sensitively on tip geometry and film uniformity, making loop reproducibility at \(\sim 100\ \mathrm{nm}\) and below nontrivial [1002.2921]. Quartz tips are mechanically fragile [1002.2921]. 1/f noise remains an issue below tens of Hz or up to \(\sim 1\ \mathrm{kHz}\), depending on device and readout [1002.2921][1410.1609]. Hysteresis and self-heating can complicate Dayem-bridge operation, as seen explicitly in Pb \(\mu\)-SQUIDs, where hysteretic I–V curves arise from self-heating and disappear only near a hysteresis crossover temperature below \(T_c\) [1612.09200]. 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 [2109.06774]. 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 [2508.01927].

Future directions are explicit in the literature. Different superconductors, including Nb, NbN, Pb, and others, are expected to extend \(T_c\), \(H_c\), or both [1002.2921]. 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 [1002.2921][2601.11331]. Wafer-scale fabrication and self-aligned templates suggest standardization and batch production [2601.11331][2508.01927]. 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 [2508.01927][2601.11331]. 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.

Source: https://www.emergentmind.com/topics/squid-on-lever-probes