Scanning Superconducting Quantum Interference Device Research Articles

Restoration of Vector Magnetization Image from Vector Scanning-SQUID Microscope Measurement

Abstract A generalized mathematical framework to treat image data measured by the scanning superconducting quantum interference device (SQUID) microscope using a three-dimensional vector pickup coil is presented. The blurring of the images originating from the effects of diamagnetism due to the superconductivity of the sensor, the non-zero sensor size, and the finite sensor-to-sample separation are numerically reduced. We use a lattice model of the measurement system, and singular value decomposition and the Moore-Penrose pseudo-inverse matrix are employed to handle ill-conditioned matrices we encounter in the numerical processes. Based on a numerical model, measurement of the vector magnetization distributed on a sample surface, and the image restoration using the present procedure are demonstrated.

Visualizing thickness-dependent magnetic textures in few-layer Cr2Ge2Te6

Magnetic ordering in two-dimensional (2D) materials has recently emerged as a promising platform for data storage, computing, and sensing. To advance these developments, it is vital to gain a detailed understanding of how the magnetic order evolves on the nanometer-scale as a function of the number of atomic layers and applied magnetic field. Here, we image few-layer Cr2Ge2Te6 using a combined scanning superconducting quantum interference device and atomic force microscopy probe. Maps of the material’s stray magnetic field as a function of applied magnetic field reveal its magnetization per layer as well as the thickness-dependent magnetic texture. Using a micromagnetic model, we correlate measured stray-field patterns with the underlying magnetization configurations, including labyrinth domains and skyrmionic bubbles. Comparison between real-space images and simulations demonstrates that the layer dependence of the material’s magnetic texture is a result of the thickness-dependent balance between crystalline and shape anisotropy. These findings represent an important step towards 2D spintronic devices with engineered spin configurations and controlled dependence on external magnetic fields.

Imaging quantum oscillations and millitesla pseudomagnetic fields in graphene

The exceptional control of the electronic energy bands in atomically thin quantum materials has led to the discovery of several emergent phenomena1. However, at present there is no versatile method for mapping the local band structure in advanced two-dimensional materials devices in which the active layer is commonly embedded in the insulating layers and metallic gates. Using a scanning superconducting quantum interference device, here we image the de Haas–van Alphen quantum oscillations in a model system, the Bernal-stacked trilayer graphene with dual gates, which shows several highly tunable bands2–4. By resolving thermodynamic quantum oscillations spanning more than 100 Landau levels in low magnetic fields, we reconstruct the band structure and its evolution with the displacement field with excellent precision and nanoscale spatial resolution. Moreover, by developing Landau-level interferometry, we show shear-strain-induced pseudomagnetic fields and map their spatial dependence. In contrast to artificially induced large strain, which leads to pseudomagnetic fields of hundreds of tesla5–7, we detect naturally occurring pseudomagnetic fields as low as 1 mT corresponding to graphene twisting by 1 millidegree, two orders of magnitude lower than the typical angle disorder in twisted bilayer graphene8–11. This ability to resolve the local band structure and strain at the nanoscale level enables the characterization and use of tunable band engineering in practical van der Waals devices.

The on-chip scanning probe with dual niobium nitride nanoscale superconducting quantum interference devices for magnetic imaging at the high temperature

The scanning superconducting quantum interference device (SQUID) microscope is a powerful tool for investigating the microscale magnetic properties of quantum materials. However, the low operating temperature of SQUIDs limits the application of the microscope. In this work, we developed an on-chip probe with dual niobium nitride (NbN) nano-SQUIDs for scanning SQUID microscope. The working temperature of the NbN nano-SQUID on-chip probe was up to 8 K, and it enabled the magnetic imaging of samples at the temperature up to 128 K. We used a gradiometric readout scheme for dual nano-SQUIDs in one probe to reduce the influence of the background magnetic field. Furthermore, we demonstrated the capabilities of both topographic and current imaging by the on-chip probe with spatial resolutions of 1 μm and 2 μm, respectively. The advantage of the probe at the high temperature was also demonstrated by the investigation of the superconducting vortices distribution in the yttrium-barium-copper-oxide film.

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.

Vortex dynamics induced by scanning SQUID susceptometry

We measured the local magnetic response of a niobium thin film by applying a millitesla-scale AC magnetic field using a micron-scale field coil and detecting the response with a micron-scale pickup loop in a scanning superconducting quantum interference device (SQUID) susceptometry measurement. Near the film's critical temperature, we observed a step-like nonlinear and dissipative magnetic response due to the dynamics of a small number of vortex-antivortex pairs induced in the film by the local applied AC field. We modeled the dynamics of the measurement using a combined two-dimensional London-Maxwell and time-dependent Ginzburg-Landau approach, allowing us to construct a detailed real-space picture of the vortex motion causing the observed dissipative response. This work pushes scanning SQUID susceptometry of two-dimensional superconductors beyond the regime of linear response and lays the foundation for microscopic studies of vortex dynamics and pinning in superconducting devices and more exotic materials systems.

Superconducting vortices carrying a temperature-dependent fraction of the flux quantum.

Magnetic field penetrates type-II bulk superconductors by forming quantum vortices that enclose a magnetic flux equal to the magnetic flux quantum. The flux quantum is a universal quantity that depends only on fundamental constants. In this study, we investigated isolated vortices in the hole-overdoped Ba1-xKxFe2As2 (x = 0.77) by using scanning superconducting quantum interference device (SQUID) magnetometry. In many locations, we observed objects that carried only part of a flux quantum, with a magnitude that varied continuously with temperature. We demonstrated mobility and manipulability of these objects and interpreted them as quantum vortices with nonuniversally quantized (fractional) magnetic flux whose magnitude is determined by the temperature-dependent parameters of a multicomponent superconductor.

Scanning SQUID-on-tip microscope in a top-loading cryogen-free dilution refrigerator.

The scanning superconducting quantum interference device (SQUID) fabricated on the tip of a sharp quartz pipette (SQUID-on-tip) has emerged as a versatile tool for the nanoscale imaging of magnetic, thermal, and transport properties of microscopic devices of quantum materials. We present the design and performance of a scanning SQUID-on-tip microscope in a top-loading probe of a cryogen-free dilution refrigerator. The microscope is enclosed in a custom-made vacuum-tight cell mounted at the bottom of the probe and is suspended by springs to suppress vibrations caused by the pulse tube cryocooler. Two capillaries allow for the in situ control of helium exchange gas pressure in the cell that is required for thermal imaging. A nanoscale heater is used to create local temperature gradients in the sample, which enables quantitative characterization of relative vibrations between the tip and the sample. The spectrum of the vibrations shows distinct resonant peaks with a maximal power density of about 27 nm/Hz1/2 in the in-plane direction. The performance of the SQUID-on-tip microscope is demonstrated by magnetic imaging of the MnBi2Te4 magnetic topological insulator, magnetization and current distribution imaging in a SrRuO3 ferromagnetic oxide thin film, and thermal imaging of dissipation in graphene.

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.

Helical Luttinger Liquid on the Edge of a Two-Dimensional Topological Antiferromagnet

A boundary helical Luttinger liquid (HLL) with broken bulk time-reversal symmetry belongs to a unique topological class that may occur in antiferromagnets (AFM). Here, we search for signatures of HLL on the edge of a recently discovered topological AFM, MnBi2Te4 even-layer. Using a scanning superconducting quantum interference device, we directly image helical edge current in the AFM ground state appearing at its charge neutral point. Such a helical edge state accompanies an insulating bulk which is topologically distinct from the ferromagnetic Chern insulator phase, as revealed in a magnetic field driven quantum phase transition. The edge conductance of the AFM order follows a power law as a function of temperature and source-drain bias which serves as strong evidence for HLL. Such HLL scaling is robust at finite fields below the quantum critical point. The observed HLL in a layered AFM semiconductor represents a highly tunable topological matter compatible with future spintronics and quantum computation.

Local imaging of diamagnetism in proximity-coupled niobium nanoisland arrays on gold thin films

In this work we study the effect of engineered disorder on the local magnetic response of proximity coupled superconducting island arrays by comparing scanning Superconducting Quantum Interference Device (SQUID) susceptibility measurements to a model in which we treat the system as a network of one-dimensional (1D) superconductor-normal metal-superconductor (SNS) Josephson junctions, each with a Josephson coupling energy $E_J$ determined by the junction length or distance between islands. We find that the disordered arrays exhibit a spatially inhomogeneous diamagnetic response which, for low local applied magnetic fields, is well described by this junction network model, and we discuss these results as they relate to inhomogeneous two-dimensional (2D) superconductors. Our model of the static magnetic response of the arrays does not fully capture the onset of nonlinearity and dissipation with increasing applied field, as these effects are associated with vortex motion due to the dynamic nature of the scanning SQUID susceptometry measurement. This work demonstrates a model 2D superconducting system with engineered disorder and highlights the impact of dissipation on the local magnetic properties of 2D superconductors and Josephson junction arrays.

SQUID maps magnetic fields of superconducting qubit circuits

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

Magnetic imaging of superconducting qubit devices with scanning SQUID-on-tip

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.

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.

Tunable magnetic scattering and ferroelectric switching at the LaAlO3/EuTiO3/Sr0.99Ca0.01TiO3 interface

Ferroelectric and ferromagnetic orders rarely coexist, and magnetoelectric coupling is even more scarce. A possible avenue for combining these orders is by interface design, where orders formed at the constituent materials can overlap and interact. Using a combination of magnetotransport and scanning superconducting quantum interference device measurements, we explore the interactions between ferroelectricity, magnetism, and the two-dimensional electron system (2DES) formed at the novel ${\mathrm{LaAlO}}_{3}/{\mathrm{EuTiO}}_{3}/{\mathrm{Sr}}_{0.99}{\mathrm{Ca}}_{0.01}{\mathrm{TiO}}_{3}$(001) heterostructure. We find that the electrons at the interface experience magnetic scattering appearing along with a diverging Curie-Weiss-type behavior in the ${\mathrm{EuTiO}}_{3}$ layer. The 2DES is also affected by the switchable ferroelectric polarization at the ${\mathrm{Sr}}_{0.99}{\mathrm{Ca}}_{0.01}{\mathrm{TiO}}_{3}$ bulk. While the 2DES interacts with both magnetism and ferroelectricity, we show that the presence of the conducting electrons has no effect on magnetization in the ${\mathrm{EuTiO}}_{3}$ layer. Our results provide a first step towards realizing a new multiferroic system where magnetism and ferroelectricity can interact via an intermediate conducting layer.

Magnetic, Thermal, and Topographic Imaging with a Nanometer-Scale SQUID-On-Lever Scanning Probe

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 force microscope (AFM). We pattern the nanometer-scale SQUID, including its weak-link Josephson junctions, via focused ion beam milling at the apex of a cantilever coated with Nb, yielding a sensor with an effective diameter of 365 nm, field sensitivity of 9.5 $\text{nT}/\sqrt{\text{Hz}}$ and thermal sensitivity of 620 $\text{nK}/\sqrt{\text{Hz}}$, operating in magnetic fields up to 1.0 T. The resulting SQUID-on-lever is a robust AFM-like scanning probe that expands the reach of sensitive nanometer-scale magnetic and thermal imaging beyond what is currently possible.

Studying Quantum Materials with Scanning SQUID Microscopy

Electronic correlations give rise to fascinating macroscopic phenomena such as superconductivity, magnetism, and topological phases of matter. Although these phenomena manifest themselves macroscopically, fully understanding the underlying microscopic mechanisms often requires probing on multiple length scales. Spatial modulations on the mesoscopic scale are especially challenging to probe, owing to the limited range of suitable experimental techniques. Here, we review recent progress in scanning superconducting quantum interference device (SQUID) microscopy. We demonstrate how scanning SQUID combines unmatched magnetic field sensitivity and highly versatile designs, by surveying discoveries in unconventional superconductivity, exotic magnetism, topological states, and more. Finally, we discuss how SQUID microscopy can be further developed to answer the increasing demand for imaging new quantum materials.

Nanopatterning of oxide 2-dimensional electron systems using low-temperature ion milling

We present a ‘top-down’ patterning technique based on ion milling performed at low-temperature, for the realization of oxide two-dimensional electron system devices with dimensions down to 160 nm. Using electrical transport and scanning Superconducting QUantum Interference Device measurements we demonstrate that the low-temperature ion milling process does not damage the 2DES properties nor creates oxygen vacancies-related conducting paths in the STO substrate. As opposed to other procedures used to realize oxide 2DES devices, the one we propose gives lateral access to the 2DES along the in-plane directions, finally opening the way to coupling with other materials, including superconductors.

Improving spatial resolution of scanning SQUID microscopy with an on-chip design

Scanning superconducting quantum interference device (sSQUID) microscopy is currently one of the most effective methods for direct and sensitive magnetic flux imaging on the mesoscopic scale. A SQUID-on-chip (SOC) design allows integration of field coils for susceptometry in a gradiometer setup which is very desirable for measuring magnetic responses of quantum matter. However, the spatial resolution of such a design has largely been limited to micrometers due to the difficulty in approaching the sample. Here, we used electron beam lithography technology in the fabrication of the 3D nano-bridge-based SQUID devices to prepare pick-up coils with diameters down to 150 nm. Furthermore, we integrated the deep silicon etching process in order to minimize the distance between the pick-up coil and the wafer edge. Combined with a tuning-fork-based scanning head, the sharpness of the etched chip edge enables a precision of 5 nm in height control. By scanning measurements on niobium chessboard samples using these improved SQUID devices, we demonstrate sub-micron spatial resolutions in both magnetometry and susceptometry, significantly better than our previous generations of nano-SQUIDs. Such improvement in spatial resolution of SOC is a valuable progress for magnetic imaging of quantum materials and devices in various modes.