Superconducting Quantum Interference Device Microscopy Research Articles

Oscillating paramagnetic Meissner effect and Berezinskii-Kosterlitz-Thouless transition in underdoped Bi2Sr2CaCu2O8+δ.

Superconducting phase transitions in two dimensions lie beyond the description of the Ginzburg-Landau symmetry-breaking paradigm for three-dimensional superconductors. They are Berezinskii-Kosterlitz-Thouless (BKT) transitions of paired-electron condensate driven by the unbinding of topological excitations, i.e. vortices. The recently discovered monolayers of layered high-transition-temperature ([Formula: see text]) cuprate superconductor Bi2Sr2CaCu2O8+δ (Bi2212) meant that this 2D superconductor promised to be ideal for the study of unconventional superconductivity. But inhomogeneity posed challenges for distinguishing BKT physics from charge correlations in this material. Here, we utilize the phase sensitivity of scanning superconducting quantum interference device microscopy susceptometry to image the local magnetic response of underdoped Bi2212 from the monolayer to the bulk throughout its phase transition. The monolayer segregates into domains with independent phases at elevated temperatures below [Formula: see text]. Within a single domain, we find that the susceptibility oscillates with flux between diamagnetism and paramagnetism in a Fraunhofer-like pattern up to [Formula: see text]. The finite modulation period, as well as the broadening of the peaks when approaching [Formula: see text] from below, suggests well-defined vortices that are increasingly screened by the dissociation of vortex-antivortex plasma through a BKT transition. In the multilayers, the susceptibility oscillation differs in a small temperature regime below [Formula: see text], consistent with a dimensional crossover led by interlayer coupling. Serving as strong evidence for BKT transition in the bulk, we observe a sharp jump in phase stiffness and paramagnetism at small fields just below [Formula: see text]. These results unify the superconducting phase transitions from the monolayer to the bulk underdoped Bi2212, and can be collectively referred to as the BKT transition with interlayer coupling.

Estimating the Net Magnetic Moment of Geological Samples From Planar Field Maps Using Multipoles

AbstractRecent advances in magnetic microscopy have enabled studies of geological samples whose weak and spatially nonuniform magnetizations were previously inaccessible to standard magnetometry techniques. A quantity of central importance is the net magnetic moment, which reflects the mean direction and the intensity of the magnetization states of numerous ferromagnetic crystals within a certain volume. The planar arrangement of typical magnetic microscopy measurements, which originates from measuring the field immediately above the polished surface of a sample to maximize sensitivity and spatial resolution, makes estimating net moments considerably more challenging than with spherically distributed data. In particular, spatially extended and nonuniform magnetization distributions often cannot be adequately approximated by a single magnetic dipole. To address this limitation, we developed a multipole fitting technique that can accurately estimate net moment using spherical harmonic multipole expansions computed from planar data. Given that the optimal location for the origin of such expansions is unknown beforehand and generally unconstrained, regularization of this inverse problem is critical for obtaining accurate moment estimates from noisy experimental magnetic data. We characterized the performance of the technique using synthetic sources under different conditions (noiseless data, data corrupted with simulated white noise, and data corrupted with measured instrument noise). We then validated and demonstrated the technique using superconducting quantum interference device microscopy measurements of impact melt spherules from Lonar crater, India and dusty olivine chondrules from the CO chondrite meteorite Dominion Range 08006.

Direct Observation of Quantum Anomalous Vortex in Fe(Se,Te)

Vortices are topological defects of type-II superconductors in an external magnetic field. In a similar fashion to a quantum anomalous Hall insulator, quantum anomalous vortex (QAV) spontaneously nucleates due to orbital-and-spin exchange interaction between vortex core states and magnetic impurity moment, breaking time-reversal symmetry (TRS) of the vortex without an external field. Here, we used scanning superconducting quantum interference device microscopy (sSQUID) to search for its signatures in iron-chalcogenide superconductor Fe(Se,Te). Under zero magnetic field, we found a stochastic distribution of isolated anomalous vortices and antivortices with flux quanta $\Phi_0$. By applying a small local magnetic field under the coil of the nano-SQUID device, we observed hysteretic flipping of the vortices reminiscent of the switching of ferromagnetic domains, suggesting locally broken-TRS. We further showed vectorial rotation of a flux line linking a paired vortex-antivortex with the local field. These unique properties of the anomalous vortices satisfied the defining criteria of QAV. Our observation suggests a quantum vortex phase with spontaneous broken-TRS in a high-temperature superconductor.

Frustrated ferromagnetic transition in AB-stacked honeycomb bilayer

In two-dimensional (2D) ferromagnets, anisotropy is essential for the magnetic ordering as dictated by the Mermin-Wagner theorem. But when competing anisotropies are present, the phase transition becomes nontrivial. Here, utilizing highly sensitive susceptometry of scanning superconducting quantum interference device microscopy, we probe the spin correlations of ABC-stacked CrBr3 under zero magnetic field. We identify a plateau feature in susceptibility above the critical temperature (TC) in thick samples. It signifies a crossover regime induced by the competition between easy-plane intralayer exchange anisotropy versus uniaxial interlayer anisotropy. The evolution of the critical behavior from the bulk to 2D shows that the competition between the anisotropies is magnified in the reduced dimension. It leads to a strongly frustrated ferromagnetic transition in the bilayer with fluctuation on the order of TC, which is distinct from both the monolayer and the bulk. Our observation demonstrates unconventional 2D critical behavior on a honeycomb lattice.

SQUID maps magnetic fields of superconducting qubit circuits

Scanning superconducting quantum interference device microscopy could help optimize qubit circuits for advanced quantum computing.

Magnetic memory and spontaneous vortices in a van der Waals superconductor.

Doped Mott insulators exhibit some of the most intriguing quantum phases of matter, including quantum spin liquids, unconventional superconductors and non-Fermi liquid metals1-3. Such phases often arise when itinerant electrons are close to a Mott insulating state, and thus experience strong spatial correlations. Proximity between different layers of van der Waals heterostructures naturally realizes a platform for experimentally studying the relationship between localized, correlated electrons and itinerant electrons. Here we explore this relationship by studying the magnetic landscape of tantalum disulfide 4Hb-TaS2, which realizes an alternating stacking of a candidate spin liquid and a superconductor4. We report on a spontaneous vortex phase whose vortex density can be trained in the normal state. We show that time-reversal symmetry is broken in the normal state, indicating the presence of a magnetic phase independent of the superconductor. Notably, this phase does not generate ferromagnetic signals that are detectable using conventional techniques. We use scanning superconducting quantum interference device microscopy to show that it is incompatible with ferromagnetic ordering. The discovery of this unusual magnetic phase illustrates how combining superconductivity with a strongly correlated system can lead to unexpected physics.

Nanoscale magnetic field imaging for 2D materials

Nanometer-scale imaging of magnetization and current density is the key to deciphering the mechanisms behind a variety of new and poorly understood condensed matter phenomena. The recently discovered correlated states hosted in atomically layered materials such as twisted bilayer graphene or van der Waals heterostructures are noteworthy examples. Manifestations of these states range from superconductivity, to highly insulating states, to magnetism. Their fragility and susceptibility to spatial inhomogeneities limits their macroscopic manifestation and complicates conventional transport or magnetization measurements, which integrate over an entire sample. In contrast, techniques for imaging weak magnetic field patterns with high spatial resolution overcome inhomogeneity by measuring the local fields produced by magnetization and current density. Already, such imaging techniques have shown the vulnerability of correlated states in twisted bilayer graphene to twist-angle disorder and revealed the complex current flows in quantum Hall edge states. Here, we review the state-of-the-art techniques most amenable to the investigation of such systems, because they combine the highest magnetic field sensitivity with the highest spatial resolution and are minimally invasive: magnetic force microscopy, scanning superconducting quantum interference device microscopy, and scanning nitrogen-vacancy center microscopy. We compare the capabilities of these techniques, their required operating conditions, and assess their suitability to different types of source contrast, in particular magnetization and current density. Finally, we focus on the prospects for improving each technique and speculate on its potential impact, especially in the rapidly growing field of two-dimensional (2D) materials.

Single Particle Multipole Expansions From Micromagnetic Tomography.

Micromagnetic tomography aims at reconstructing large numbers of individual magnetizations of magnetic particles from combining high‐resolution magnetic scanning techniques with micro X‐ray computed tomography (microCT). Previous work demonstrated that dipole moments can be robustly inferred, and mathematical analysis showed that the potential field of each particle is uniquely determined. Here, we describe a mathematical procedure to recover higher orders of the magnetic potential of the individual magnetic particles in terms of their spherical harmonic expansions (SHE). We test this approach on data from scanning superconducting quantum interference device microscopy and microCT of a reference sample. For particles with high signal‐to‐noise ratio of the magnetic scan we demonstrate that SHE up to order n = 3 can be robustly recovered. This additional level of detail restricts the possible internal magnetization structures of the particles and provides valuable rock magnetic information with respect to their stability and reliability as paleomagnetic remanence carriers. Micromagnetic tomography therefore enables a new approach for detailed rock magnetic studies on large ensembles of individual particles.

Observation of robust edge superconductivity in Fe(Se,Te) under strong magnetic perturbation

The iron-chalcogenide high temperature superconductor Fe(Se,Te) (FST) has been reported to exhibit complex magnetic ordering and nontrivial band topology which may lead to novel superconducting phenomena. However, the recent studies have so far been largely concentrated on its band and spin structures while its mesoscopic electronic and magnetic response, crucial for future device applications, has not been explored experimentally. Here, we used scanning superconducting quantum interference device microscopy for its sensitivity to both local diamagnetic susceptibility and current distribution in order to image the superfluid density and supercurrent in FST. We found that in FST with 10% interstitial Fe, whose magnetic structure was heavily disrupted, bulk superconductivity was significantly suppressed whereas edge still preserved strong superconducting diamagnetism. The edge dominantly carried supercurrent despite of a very long magnetic penetration depth. The temperature dependences of the superfluid density and supercurrent distribution were distinctively different between the edge and the bulk. Our Heisenberg modeling showed that magnetic dopants stabilize anti-ferromagnetic spin correlation along the edge, which may contribute towards its robust superconductivity. Our observations hold implication for FST as potential platforms for topological quantum computation and superconducting spintronics.

Characterization of Scanning SQUID Probes Based on 3D Nano-Bridge Junctions in Magnetic Field**Supported by the National Key R &D Program of China (Grant Nos. 2017YFF0206105, 2016YFA0301002 and 2017YFA0303000), the Young Investigator Program of CAS (Grant No. 2016217), the Frontier Science Key Programs of the CAS (Grant No. QYZDYSSW-JSC033), and the Strategic Priority Research Program of CAS (Grant No. XDA18000000), the

We develop superconducting quantum interference device (SQUID) probes based on 3D nano-bridge junctions for the scanning SQUID microscopy. The use of these nano-bridge junctions enables imaging in the presence of a high magnetic field. Conventionally, a superconducting ground layer has been employed for better magnetic shielding. In our study, we prepare a number of scanning SQUID probes with and without a ground layer to evaluate their performance in external magnetic fields. The devices show the improved magnetic modulation up to 1.4 T. It is found that the ground layer reduces the inductance, and increases the modulation depth and symmetricity of the gradiometer design in the absence of the field. However, the layer is not compatible with the use of the scanning SQUID probe in the field because it decreases its working field range. Moreover, by adding the layer, the mutual inductance between the feedback coil and the SQUID also decreases linearly as a function of the field.

SQUID microscopy for mapping vector magnetic fields

We mounted a vector-scanning superconducting quantum interference device (SQUID) sensor on a commercial SQUID microscope and successfully improved the sensitivity and spatial resolution of the sensor. Our proposed vector 3D SQUID sensor used multilayered niobium (Nb)-based technology; we realized three SQUID sensors in the structure of a vector pickup coil system on a single chip. The vector pickup coil system was built with three pickup coils that were orthogonal to one another to obtain the X, Y, and Z components of a magnetic field vector. To improve both sensitivity and spatial resolution, we attempted to reduce the inner diameter by increasing the number of windings of the pickup coils using the multilayered Nb process. The design value for the dc SQUID sensors was either the critical current density Jc = 320 A cm−2 for two Josephson junctions (JJs) or the critical current Ic = 12.8 μA for the 2 μm × 2 μm JJs. To measure the current–voltage (I–V) and voltage–flux (V–Φ) characteristics of a sensor, we constructed a homemade measurement system. The fundamental characteristics of our SQUID sensors were in good agreement with the design parameters. We mounted our vector SQUID sensor on a commercial scanning SQUID microscope (SQM2000, Seiko Instrument Inc.) with a single flux-locked loop channel to test one of the three channels. We repeated the measurements three times to obtain the X, Y, and Z componential images of the magnetic field from a single vortex, and we synthesized the 3D mapping of the magnetic field vectors from a single vortex. We proved that our sensor mounted on a SQUID microscope was suitable for measuring the X, Y, and Z components of a vector magnetic field.

Finite-size effect of critical penetration of Pearl vortices in narrow superconducting flat rings

We revisit the critical penetration of Pearl vortices in narrow superconducting flat rings cooled in magnetic fields. Scanning superconducting quantum interference device microscopy measurements showed how a magnetic field penetrates and vortices are trapped in flat rings made of amorphous MoGe thin films. Counting the number of trapped vortices for each image, we found that the vortices are completely excluded from the ring annulus when the applied field H is below a threshold field Hp: Above this field, the vortices increase linearly with the field. The obtained values of Hp depend on the annulus width wring and follow the relation μ0Hp=(1.9±0.1)Φ0/wring2 with the superconducting flux quantum Φ0. This relationship provides an insight into the effect of the net-current circulating in the annular region and also leads to a precise control to trap or eliminate vortices in flat rings.

Scanning SQUID microscope with an in-situ magnetization/demagnetization field for geological samples

Magnetic properties of rocks are crucial for paleo-, rock-, environmental-magnetism, and magnetic material sciences. Conventional rock magnetometers deal with bulk properties of samples, whereas scanning microscope can map the distribution of remanent magnetization. In this study, a new scanning microscope based on a low-temperature DC superconducting quantum interference device (SQUID) equipped with an in-situ magnetization/demagnetization device was developed. To realize the combination of sensitive instrument as SQUID with high magnetizing/demagnetizing fields, the pick-up coil, the magnetization/demagnetization coils and the measurement mode of the system were optimized. The new microscope has a field sensitivity of 250 pT/√Hz at a coil-to-sample spacing of ∼350 µm, and high magnetization (0–1 T)/ demagnetization (0–300 mT, 400 Hz) functions. With this microscope, isothermal remanent magnetization (IRM) acquisition and the according alternating field (AF) demagnetization curves can be obtained for each point without transferring samples between different procedures, which could result in position deviation, waste of time, and other interferences. The newly-designed SQUID microscope, thus, can be used to investigate the rock magnetic properties of samples at a micro-area scale, and has a great potential to be an efficient tool in paleomagnetism, rock magnetism, and magnetic material studies.

Analysing magnetism using scanning SQUID microscopy.

Scanning superconducting quantum interference device microscopy (SSM) is a scanning probe technique that images local magnetic flux, which allows for mapping of magnetic fields with high field and spatial accuracy. Many studies involving SSM have been published in the last few decades, using SSM to make qualitative statements about magnetism. However, quantitative analysis using SSM has received less attention. In this work, we discuss several aspects of interpreting SSM images and methods to improve quantitative analysis. First, we analyse the spatial resolution and how it depends on several factors. Second, we discuss the analysis of SSM scans and the information obtained from the SSM data. Using simulations, we show how signals evolve as a function of changing scan height, SQUID loop size, magnetization strength, and orientation. We also investigated 2-dimensional autocorrelation analysis to extract information about the size, shape, and symmetry of magnetic features. Finally, we provide an outlook on possible future applications and improvements.

Current-induced nonuniform enhancement of sheet resistance in Ar+ -irradiated SrTiO3

The sheet resistance Rs of Ar+ irradiated SrTiO3 in patterns with a length scale of several microns increases significantly below 40 K in connection with driving currents exceeding a certain threshold. The initial lower Rs is recovered upon warming with accelerated recovery around 70 and 160 K. Scanning superconducting quantum interference device microscopy shows local irreversible changes in the spatial distribution of the current with a length scale of several microns. We attribute the observed nonuniform enhancement of Rs to the attraction of the charged single-oxygen and dioxygen vacancies by the crystallographic domain boundaries in SrTiO3. The boundaries, which are nearly ferroelectric below 40 K, are polarized by the local electrical field associated with the driven current and the clustered vacancies which suppress conductivity in their vicinity and yield a noticeable enhancement in the device resistance when the current path width is on the order of the boundary extension. The temperatures of accelerated conductivity recovery are associated with the energy barriers for the diffusion of the two types of vacancies.

Scanning SQUID microscopy of a ferromanganese crust from the northwestern Pacific: Submillimeter scale magnetostratigraphy as a new tool for age determination and mapping of environmental magnetic parameters

Ferromanganese crusts record long-term deep-sea environmental changes. Thus, providing their reliable high-resolution age models is important. We applied a magnetostratigraphic technique to estimate the growth rate of a ferromanganese crust using scanning SQUID (superconducting quantum interference device) microscope (SSM). SSM is designed to map the magnetic field across thins sections with sub-millimeter resolution. The crust sample was taken from the Takuyo–Daigo Seamount, northwestern Pacific, and recorded a limited supply of dust and sediment from continents. After drift correction and removal of spike noises, the magnetic field values were stacked within the areas of high signal-to-noise ratios. By correlating the obtained profiles with a standard geomagnetic polarity timescale, we obtained an average growth rate of 3.37 ± 0.06 mm/m.y., which is consistent with that obtained by 10Be/9Be geochronology (2.93 ± 0.15 mm/m.y.). S-ratio mapping shows low values after ~3 Ma, associated with voids between columnar structures.

Nondestructive Evaluation Using a High-<italic>T</italic>cSQUID Microscope

We report the application of a scanning high- $T_{{\rm{c}}}$ SQUID (superconducting quantum interference device) microscope with a ferromagnetic flux guide for the nondestructive evaluation of weld seams and wear tracks and scars on austenitic stainless steel plates as well as measurement of magnetic stray fields distribution above patterned by electron lithography 30-nm-thick cobalt films. A soft magnetic amorphous Vitrovac foil was used to guide the flux from the samples, which were held at room temperature, to the liquid-nitrogen-cooled SQUID-sensor and back. The flux guide passes through a hole in the $\text{1 mm}\times \text{2.5 mm}$ pick-up loop of the high- $T_{{\rm{c}}}$ SQUID sensor, thereby providing improved coupling of the magnetic flux from the object to the SQUID. In order to avoid the influence of the SQUID biasing the magnetic field on the object under investigation, a modulation and feedback coil was coupled to the pick-up loop of the SQUID directly and beyond the ferromagnetic flux guide. Such decoupling of feedback coil from soft magnetic flux antenna ensures that the high- $T_{{\rm{c}}}$ SQUID microscope does not disturb the sample magnetization during image recording. The SQUID microscope can be used to measure the spatial distribution of the z -component of the stray field above a specimen without mechanical contact to it.

Ultra-high sensitivity moment magnetometry of geological samples using magnetic microscopy

Paleomagnetically useful information is expected to be recorded by samples with moments up to three orders of magnitude below the detection limit of standard superconducting rock magnetometers. Such samples are now detectable using recently developed magnetic microscopes, which map the magnetic fields above room-temperature samples with unprecedented spatial resolutions and field sensitivities. However, realizing this potential requires the development of techniques for retrieving sample moments from magnetic microscopy data. With this goal, we developed a technique for uniquely obtaining the net magnetic moment of geological samples from magnetic microscopy maps of unresolved or nearly unresolved magnetization. This technique is particularly powerful for analyzing small, weakly magnetized samples such as meteoritic chondrules and terrestrial silicate crystals like zircons. We validated this technique by applying it to field maps generated from synthetic sources and also to field maps measured using a superconducting quantum interference device (SQUID) microscope above geological samples with moments down to 10^-15 Am2. For the most magnetic rock samples, the net moments estimated from the SQUID microscope data are within error of independent moment measurements acquired using lower sensitivity standard rock magnetometers. In addition to its superior moment sensitivity, SQUID microscope net moment magnetometry also enables the identification and isolation of magnetic contamination and background sources, which is critical for improving accuracy in paleomagnetic studies of weakly magnetic rocks.

Scanning SQUID susceptometers with sub-micron spatial resolution.

Superconducting QUantum Interference Device (SQUID) microscopy has excellent magnetic field sensitivity, but suffers from modest spatial resolution when compared with other scanning probes. This spatial resolution is determined by both the size of the field sensitive area and the spacing between this area and the sample surface. In this paper we describe scanning SQUID susceptometers that achieve sub-micron spatial resolution while retaining a white noise floor flux sensitivity of ≈2μΦ0/Hz1/2. This high spatial resolution is accomplished by deep sub-micron feature sizes, well shielded pickup loops fabricated using a planarized process, and a deep etch step that minimizes the spacing between the sample surface and the SQUID pickup loop. We describe the design, modeling, fabrication, and testing of these sensors. Although sub-micron spatial resolution has been achieved previously in scanning SQUID sensors, our sensors not only achieve high spatial resolution but also have integrated modulation coils for flux feedback, integrated field coils for susceptibility measurements, and batch processing. They are therefore a generally applicable tool for imaging sample magnetization, currents, and susceptibilities with higher spatial resolution than previous susceptometers.

SQUID Microscope With Hollow-Structured Cryostat for Magnetic Field Imaging of Room Temperature Samples

We have developed a high-spatial-resolution superconducting quantum interference device (SQUID) microscope for magnetic field imaging of rock samples at room temperature, using a hollow-structured cryostat. A directly coupled low-temperature SQUID with a $200 \mu\text{m} \times 200 \mu\text{m}$ pickup loop, which is mounted on a sapphire conical rod, is separated from room temperature by a thin sapphire window. Precise and repeatable adjustment of the vacuum gap between the SQUID and the sapphire window is performed by rotating a micrometer spindle connected to the sapphire rod through the hollow portion of the cryostat. A spacing of 230 $\mu\text{m}$ between the SQUID and a sample has been achieved. We demonstrated the imaging of the magnetic field on a zircon containing magnetic grains.