Identifying the symmetry of the superconducting order parameter in the recently-discovered ferro-oxypnictide family of superconductors, RFeAsO$_{1-x}$F$_{y}$, where $R$ is a rare earth, is a high priority. Many of the proposed order parameters have internal $π$ phase shifts, like the d-wave order found in the cuprates, which would result in direction-dependent phase shifts in tunnelling. In dense polycrystalline samples, these phase shifts in turn would result in spontaneous orbital currents and magnetization in the superconducting state. We perform scanning SQUID microscopy on a dense polycrystalline sample of \NdFeAsO$_{0.94}$F$_{0.06}$ with $T_c=48$ K and find no such spontaneous currents, ruling out many of the proposed order parameters.
In this paper we discuss design concepts for increasing the spatial resolution, improving the sensitivity, and reducing the invasiveness in scanning Superconducting Quantum Interference Device (SQUID) microscope sensors with integrated flux pickup loops. This can be done not only by reducing the ground-rule line widths and spacings, but also by taking advantage of planarization, reducing flux noise through reducing the SQUID inductance, and reducing back-action through dispersive readouts or on-chip filtering.
In type-1.5 superconductors, vortices emerge in clusters, which grow in size with increasing magnetic field. These novel vortex clusters and their field dependence are directly visualized by scanning SQUID microscopy at very low vortex densities in MgB2 single crystals. Our observations are elucidated by simulations based on a two-gap Ginzburg-Landau theory in the type-1.5 regime.
We use a scanning superconducting quantum interference device (SQUID) to image the magnetic flux produced by a superconducting device designed for quantum computing. The nanometer-scale SQUID-on-tip probe reveals the flow of superconducting current through the circuit as well as the locations of trapped magnetic flux. In particular, maps of current flowing out of a flux-control line in the vicinity of a qubit show how these elements are coupled, providing insight on how to optimize qubit control.
Scanning SQUID susceptometry images the local magnetization and susceptibility of a sample. By accurately modeling the SQUID signal we can determine the physical properties such as the penetration depth and permeability of superconducting samples. We calculate the scanning SQUID susceptometry signal for a superconducting slab of arbitrary thickness with isotropic London penetration depth, on a non-superconducting substrate, where both slab and substrate can have a paramagnetic response that is linear in the applied field. We derive analytical approximations to our general expression in a numbe…
Scanning Superconducting QUantum Interference Device (SQUID) microscopy is a powerful tool for imaging local magnetic properties of materials and devices, but it requires a low-vibration cryogenic environment, traditionally achieved by thermal contact with a bath of liquid helium or the mixing chamber of a "wet" dilution refrigerator. We mount a SQUID microscope on the 3 K plate of a Bluefors cryocooler and characterize its vibration spectrum by measuring SQUID noise in a region of sharp flux gradient. By implementing passive vibration isolation, we reduce relative sensor-sample vibrations to …
We developed a scanning DC SQUID microscope with novel readout electronics capable of wideband sensing RF magnetic fields from 50 to 200 MHz and simultaneously providing closed-loop response at kHz frequencies. To overcome the 20 MHz bandwidth limitation of traditional closed-loop SQUIDs, a flux-modulated closed loop simultaneously locks the SQUID quasi-static flux and flux-biases the SQUID for amplification of the RF flux up to $Φ_0/4$ in amplitude. Demodulating the SQUID voltage with a double lock-in technique yields a signal representative of both the amplitude and phase of the RF flux. Thi…
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 $\approx 2μΦ_0/Hz^{1/2}$. This high spatial resolution is accomplished by deep sub-micron feature sizes, well shie…
We investigate the magnetic field distribution near the surface of a magnetic superconductor when a magnetic source is placed close to the superconductor. The magnetic field distribution can be measured by magnetic force microscopy and scanning SQUID microscopy, from which one can extract both the penetration depth $λ_L$ and magnetic susceptibility $χ$. When the magnetic moments are parallel to the surface, one extracts $λ_L/\sqrt{1-4πχ}$. When the moments are perpendicular to the surface, one obtains $λ_L$. By changing the orientation of the crystal, one thus is able to extract both $χ$ and $…
We measure changes in the penetration depth $λ$ of the $T_c \approx 6$ K superconductor LaFePO. In the process scanning SQUID susceptometry is demonstrated as a technique for accurately measuring {\it local} temperature-dependent changes in $λ$, making it ideal for studying early or difficult-to-grow materials. $λ$ of LaFePO is found to vary linearly with temperature from 0.36 to $\sim$2 K, with a slope of 143$\pm$15 Å/K, suggesting line nodes in the superconducting order parameter. The linear dependence up to $\sim T_c/3$ is similar to the cuprate superconductors, indicating well-developed no…
Correlating DC SQUID Performance with the Location of Trapped Magnetic Flux Using Scanning SQUID Microscopy
National Institute of Standards and Technology（美国国家标准与技术研究院）；University of Colorado Boulder（科罗拉多大学博尔德分校）；SUN Magnetics (RF) (Pty) Ltd（SUN Magnetics (RF) 私人有限公司）；Stellenbosch University（斯泰伦博斯大学）
The Dirac semimetal PdTe${}_2$ becomes superconducting at a temperature $T_{c}=1.6$~K. Thermodynamic and muon spin rotation experiments support type-I superconductivity, which is unusual for a binary compound. A key property of a type-I superconductor is the intermediate state which presents a coexistence of superconducting and normal domains (flux structures) at magnetic fields lower than the thermodynamic critical field $H_{c}$. By means of scanning SQUID microscopy (SSM) we observe flux structures in the superconducting state of PdTe${}_2$. The flux structures are strongly history dependent…
The glass-like vortex distribution in pulsed laser deposited YBCO thin films is observed by scanning superconducting quantum interference device microscopy and analysed for ordering after cooling in magnetic fields significantly smaller than the Earth's field. Autocorrelation calculations on this distribution show a weak short-range positional order, while Delaunay triangulation shows a near-complete lack of orientational order. The distribution of these vortices is finally characterised as an isotropic vortex glass. Abnormally closely spaced groups of vortices, which are statistically unlikel…
One of the critical milestones in the intensive pursuit of quantitative nanoscale magnetic imaging tools is achieving the level of sensitivity required for detecting the field generated by the spin magnetic moment μB of a single electron. Superconducting quantum interference devices (SQUIDs), which were traditionally the most sensitive magnetometers, could not hitherto reach this goal because of their relatively large effective size (of the order of 1 μm). Here we report self-aligned fabrication of nano-SQUIDs with diameters as small as 46 nm and with an extremely low flux noise of 50 nΦ0/Hz^1…
We designed and fabricated a new type of superconducting quantum interference device (SQUID) susceptometers for magnetic imaging of quantum materials. The 2-junction SQUID sensors employ 3D Nb nano-bridges fabricated using electron beam lithography. The two counter-wound balanced pickup loops of the SQUID enable gradiometric measurement and they are surrounded by a one-turn field coil for susceptibility measurements. The smallest pickup loop of the SQUIDs were 1 $μm$ in diameter and the flux noise was around 1 $μΦ_0/\sqrt{Hz}$ at 100 Hz. We demonstrate scanning magnetometry, susceptometry and …
Recently, advances in film synthesis methods have enabled a study of extremely overdoped $La_{2-x}Sr_{x}CuO_{4}$. This has revealed a surprising behavior of the superfluid density as a function of doping and temperature, the explanation of which is vividly debated. One popular class of models posits electronic phase separation, where the superconducting phase fraction decreases with doping, while some competing phase (e.g. ferromagnetic) progressively takes over. A problem with this scenario is that all the way up to the dome edge the superconducting transition remains sharp, according to mutu…
The diamagnetic susceptibility of a superconductor is directly related to its superfluid density. Mutual inductance is a highly sensitive method for characterizing thin films; however, in traditional mutual inductance measurements, the measured response is a non-trivial average over the area of the mutual inductance coils, which are typically of millimeter size. Here we image localized, isolated features in the diamagnetic susceptibility of δ-doped SrTiO3, the 2-DES at the interface between LaAlO3 and SrTiO3, and Nb superconducting thin film systems using scanning superconducting quantum inter…
We present scanning SQUID microscopy data on the superconductors Sr2RuO4 (Tc = 1.5 K) and PrOs$_4$Sb$_{12}$ (Tc = 1.8 K). In both of these materials, superconductivity-related time-reversal symmetry-breaking fields have been observed by muon spin rotation; our aim was to visualize the structure of these fields. However in neither Sr$_2$RuO$_4$ nor PrOs$_4$Sb$_{12}$ do we observe spontaneous superconductivity-related magnetization. In Sr$_2$RuO$_4$, many experimental results have been interpreted on the basis of a $px \pm ipy$ superconducting order parameter. This order parameter is expected to…
Scanning Superconducting Quantum Interference Device (SQUID) Susceptometry simultaneously images the local magnetic fields and susceptibilities above a sample with sub-micron spatial resolution. Further development of this technique requires a thorough understanding of the current, voltage, and flux characteristics of scanning SQUID susceptometers. These sensors often have striking anomalies in their current-voltage characteristics, which we believe to be due to electromagnetic resonances. The effect of these resonances on the performance of these SQUIDs is unknown. To explore the origin and i…
In the past, magnetic images acquired using scanning Superconducting Quantum Interference Device (SQUID) microscopy have been interpreted using simple models for the sensor point spread function. However, more complicated modeling is needed when the characteristic dimensions of the field sensitive areas in these sensors become comparable to the London penetration depth. In this paper we calculate the response of SQUIDs with deep sub-micron pickup loops to different sources of magnetic fields by solving coupled London's and Maxwell's equations using the full sensor geometry. Tests of these calc…
We have designed and characterized a micro-SQUID with dispersive readout for use in low temperature scanning probe microscopy systems. The design features a capacitively shunted RF SQUID with a tunable resonance frequency from 5 to 12 GHz, micrometer spatial resolution and integrated superconducting coils for local application of magnetic fields. The SQUID is operated as a nonlinear oscillator with a flux- and power-dependent resonance frequency. Measurements for device characterization and noise benchmarking were carried out at 4 K. The measured flux noise above 10 kHz at 4 K is $80\;\mathrm{…
Scanning superconducting quantum interference device (SQUID) microscopy is a magnetic imaging technique combining high-field sensitivity with nanometer-scale spatial resolution. State-of-the-art SQUID-on-tip probes are now playing an important role in mapping correlation phenomena, such as superconductivity and magnetism, which have recently been observed in two-dimensional van der Waals materials. Here, we demonstrate a scanning probe that combines the magnetic and thermal imaging provided by an on-tip SQUID with the tip-sample distance control and topographic contrast of a non-contact atomic…
Direct observation of vortices by the scanning SQUID microscopy was made on large mesoscopic disks of an amorphous MoGe thin film. Owing to the weak pinning nature of the amorphous film, vortices are able to form geometry induced, (quasi-)symmetric configurations of polygons and concentric shells in the large disks. Systematic measurements made on selected disks allow us to trace not only how the vortex pattern evolves with magnetic field, but also how the vortex polygons change in size and rotate with respect to the disk center. The results are in good agreement with theoretical consideration…
We describe a new type of scanning probe microscope based on a superconducting quantum interference device (SQUID) that resides on the apex of a sharp tip. The SQUID-on-tip is glued to a quartz tuning fork which allows scanning at a tip-sample separation of a few nm. The magnetic flux sensitivity of the SQUID is 1.8 μ_0/Hz^{1/2} and the spatial resolution is about 200 nm, which can be further improved. This combination of high sensitivity, spatial resolution, bandwidth, and the very close proximity to the sample provides a powerful tool for study of dynamic magnetic phenomena on the nanoscale.…
Superconducting Quantum Interference Devices (SQUIDs) can have excellent spin sensitivity depending on their magnetic flux noise, pick-up loop diameter, and distance from the sample. We report a family of scanning SQUID susceptometers with terraced tips that position the pick-up loops 300 nm from the sample. The 600 nm - 2 um pickup loops, defined by focused ion beam, are integrated into a 12-layer optical lithography process allowing flux-locked feedback, in situ background subtraction and optimized flux noise. These features enable a sensitivity of ~70 electron spins per root Hertz at 4K.
In this review I discuss the application of scanning magnetic imaging to fundamental studies of superconductors, concentrating on three scanning magnetic microscopies - scanning SQUID microscopy (SSM), scanning Hall bar microscopy (SHM), and magnetic force microscopy (MFM). I briefly discuss the history, sensitivity, spatial resolution, invasiveness, and potential future developments of each technique. I then discuss a selection of applications of these microscopies.
We use low-temperature scanning electron microscopy combined with SQUID detection of magnetic flux to image vortices and to investigate low-frequency flux noise in YBa$_2$Cu$_3$O$_7$ thin film SQUIDs. The low-frequency flux noise shows a nonlinear increase with magnetic cooling field up to 60 $μ$T. This effect is explained by the surface potential barrier at the SQUID hole. By correlating flux noise data with the spatial distribution of vortices, we obtain information on spatial fluctuations of vortices on a microscopic scale, e.g. an average vortex hopping length of approximately 10 nm.
Superconducting Quantum Interference Devices (SQUIDs) are one of the most popular devices in superconducting electronics. They combine the Josephson effect with the quantization of magnetic flux in superconductors. This gives rise to one of the most beautiful manifestations of macroscopic quantum coherence in the solid state. In addition, SQUIDs are extremely sensitive sensors allowing to transduce magnetic flux into measurable electric signals. As a consequence, any physical observable that can be converted into magnetic flux, e.g., current, magnetization, magnetic field or position, becomes …
Scanning nanoscale superconducting quantum interference devices (nanoSQUIDs) are of growing interest for highly sensitive quantitative imaging of magnetic, spintronic, and transport properties of low-dimensional systems. Utilizing specifically designed grooved quartz capillaries pulled into a sharp pipette, we have fabricated the smallest SQUID-on-tip (SOT) devices with effective diameters down to 39 nm. Integration of a resistive shunt in close proximity to the pipette apex combined with self-aligned deposition of In and Sn, have resulted in SOT with a flux noise of 42 n$Φ_0$Hz$^{-1/2}$, yiel…
We examine the collective behavior of two-dimensional nonlinear superconducting metamaterials using a non-contact spatially resolved imaging technique. The metamaterial is made up of sub-wavelength nonlinear oscillators in a strongly coupled 27x27 planar array of radio-frequency Superconducting QUantum Interference Devices (rf SQUIDs). By using low-temperature laser scanning microscopy we image microwave currents in the driven SQUIDs while in non-radiating dark modes and identify the clustering and uniformity of like-oscillating meta-atoms. We follow the rearrangement of coherent patterns due …
Scanning nanoscale superconducting quantum interference devices (SQUIDs) are gaining interest as highly sensitive microscopic magnetic and thermal characterization tools of quantum and topological states of matter and devices. Here we introduce a novel technique of collimated differential-pressure magnetron sputtering for versatile self aligned fabrication of SQUID on tip (SOT) nanodevices, which cannot be produced by conventional sputtering methods due to their diffusive, rather than the required directional point-source, deposition. The new technique provides access to a broad range of super…
Magic-angle twisted bilayer graphene (MATBG) hosts a number of correlated states of matter that can be tuned by electrostatic doping. Superconductivity has drawn considerable attention and the mechanism behind it is a topic of active discussion. MATBG has been experimentally characterized by numerous transport and scanning-probe experiments. The material has also emerged as a versatile platform for superconducting electronics, as proven by the realization of monolithic Josephson junctions. However, even though phase-coherent phenomena have been measured, no control of the superconducting phase…
A scanning superconducting quantum interference device (SQUID) microscope (SSM) is used to study the magnetic imaging of dynamic motion of quantized interlayer vortices induced by the Lorentz force in anisotropic high-Tc La_(1.87)Sr_(0.13)CuO_4 single crystals. It is found that 3 modes of flux motion switch depending on the transport current. By increasing the current a transition from the creep-like behavior of vortices to a steady flow of vortices was observed. Even higher current induced a continuous expansion of vortex-flow area indicating an inhomogeneous distribution of various pinning c…
When an electron beam strikes a superconducting thin film near a pinned vortex, it locally increases the temperature-dependent London penetration depth and perturbs the circulating supercurrent, thereby distorting the vortex's magnetic field toward the heated spot. This phenomenon has been used to visualize vortices pinned in SQUIDs using low-temperature scanning electron microscopy. In this paper I develop a quantitative theory to calculate the displacement of the vortex-generated magnetic-flux distribution as a function of the distance of the beam spot from the vortex core. The results are c…
We use magnetic force microscopy (MFM) and scanning SQUID susceptometry to measure the local superfluid density $ρ_{s}$ in Ba(Fe$_{0.95}$Co$_{0.05}$)$_2$As$_2$ single crystals from 0.4 K to the critical temperature $T_c=18.5$ K. We observe that the penetration depth $λ$ varies about ten times more slowly with temperature than previously published, with a dependence that can be well described by a clean two-band fully gapped model. We demonstrate that MFM can measure the important and hard-to-determine absolute value of $λ$, as well as obtain its temperature dependence and spatial homogeneity. …
A single-sample synthesis concept based on multi-element ceramic samples can produce a variety of local products. When applied to cuprate superconductors (SC), statistical modelling predicts the occurrence of possible compounds in a concentration range of about 50 ppm. In samples with such low concentrations, determining which compositions are superconducting is a challenging task and requires local probes or separation techniques. Here, we report results from samples with seven components: BaO2, CaCO3, SrCO3, La2O3, PbCO3, ZrO2 and CuO oxides and carbonates, starting from different grain size…
MgB2 superconducting wires were produced by the Mg diffusion method. Scanning electron microscopy (SEM), optical microscopy, dispersive x-ray analysis (EDS) and XRD diffraction were used to study the physical structure and content of the wires. Magnetic properties (Tcm, Hc1, Hc2, Jc by the Bean model) were obtained with a SQUID magnetometer, and transport properties (Tcr, Hc2, resistivity and residual resistivity ratio) were measured using a standard four-lead configuration. The V-I characteristics of the wires close to the critical temperature showed a staircase response, which was attributed…
Strontium ruthenate (Sr$_2$RuO$_4$) is a multiband superconductor that displays evidence of topological superconductivity, although a model of the order parameter that is consistent with all experiments remains elusive. We integrated a piezoelectric-based strain apparatus with a scanning superconducting quantum interference device (SQUID) microscope to map the diamagnetic response of single-crystal Sr$_2$RuO$_4$ as a function of temperature, uniaxial pressure, and position with micron-scale spatial resolution. We thereby obtained local measurements of the superconducting transition temperature…
We report experiments in which one dimensional (1D) and two dimensional (2D) arrays of YBa2Cu3O7-x-Nb pi-rings are cooled through the superconducting transition temperature of the Nb in various magnetic fields. These pi-rings have degenerate ground states with either clockwise or counter-clockwise spontaneous circulating supercurrents. The final flux state of each ring in the arrays was determined using scanning SQUID microscopy. In the 1D arrays, fabricated as a single junction with facets alternating between alignment parallel to a [100] axis of the YBCO and rotated 90 degrees to that axis, …
Superconductors separated by a thin tunneling barrier exhibit the Josephson effect that allows charge transport at zero voltage, typically with no phase shift between the superconductors in the lowest energy state. Recently, Josephson junctions with ground state phase shifts of pi proposed by theory three decades ago have been demonstrated. In superconducting loops, pi-junctions cause spontaneous circulation of persistent currents in zero magnetic field, analogous to spin-1/2 systems. Here we image the spontaneous zero-field currents in superconducting networks of temperature-controlled pi-jun…
