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Flat band moir\'e graphene systems have emerged as a quintessential platform to investigate correlated phases of matter. A plethora of interaction-driven ground states have been proposed, and yet despite extensive experimental effort, there has been little direct evidence that distinguishes between the various phases, in particular near charge neutrality point. Here, we use a nanoscale scanning superconducting quantum interference device to image the local thermodynamic quantum oscillations in alternating-twist trilayer graphene at magnetic fields as low as 56 mT, which reveal ultrafine details of the density of states and of the renormalization of the single-particle band structure by Coulomb interactions. We find that the charging self-energy due to occupied electronic states, is critical in explaining the high carrier density physics. At half-filling of the conduction flat band, we observe a Stoner-like symmetry breaking, suggesting that it is the most robust mechanism in the hierarchy of phase transitions. On approaching charge neutrality, where the charging energy is negligible and exchange energy is dominant, we find the ground state to be a nematic semimetal which is favored over gapped states in the presence of heterostrain. In the revealed semimetallic phase, the flat-band Dirac cones migrate towards the mini-Brillouin zone center, spontaneously breaking the C_3 rotational symmetry. Our low-field local quantum oscillations technique presents an alluring avenue to explore the ground states of diverse strongly interacting van der Waals systems., Comment: 30 pages, 4 main text figures, 6 Extended Data figures

A unique attribute of atomically thin quantum materials is the in-situ tunability of their electronic band structure by externally controllable parameters like electrostatic doping, electric field, strain, electron interactions, and displacement or twisting of atomic layers. This unparalleled control of the electronic bands has led to the discovery of a plethora of exotic emergent phenomena. But despite its key role, there is currently no versatile method for mapping the local band structure in advanced 2D materials devices in which the active layer is commonly embedded in various insulating layers and metallic gates. Utilizing a scanning superconducting quantum interference device, we image the de Haas-van Alphen quantum oscillations in a model system, the Bernal-stacked trilayer graphene with dual gates, which displays multiple highly-tunable bands. By resolving thermodynamic quantum oscillations spanning over 100 Landau levels in low magnetic fields, we reconstruct the band structure and its controllable evolution with the displacement field with unprecedented precision and spatial resolution of 150 nm. Moreover, by developing Landau level interferometry, we reveal 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 Tesla, we detect naturally occurring pseudomagnetic fields as low as 1 mT corresponding to graphene twisting by just 1 millidegree over one {\mu}m distance, two orders of magnitude lower than the typical angle disorder in high-quality twisted bilayer graphene devices. This ability to resolve the local band structure and strain on the nanoscale opens the door to the characterization and utilization of tunable band engineering in practical van der Waals devices., Comment: Nature (2023)

Quantum oscillations originating from the quantization of the electron cyclotron orbits provide ultrasensitive diagnostics of electron bands and interactions in novel materials. We report on the first direct-space nanoscale imaging of the thermodynamic magnetization oscillations due to the de Haas-van Alphen effect in moir\'e graphene. Scanning by SQUID-on-tip in Bernal bilayer graphene crystal-axis-aligned to hBN reveals abnormally large magnetization oscillations with amplitudes reaching 500 {\mu}_B/electron in weak magnetic fields, unexpectedly low frequencies, and high sensitivity to the superlattice filling fraction. The oscillations allow us to reconstruct the complex band structure in exquisite detail, revealing narrow moir\'e bands with multiple overlapping Fermi surfaces separated by unusually small momentum gaps. We identify distinct sets of oscillations that violate the textbook Onsager Fermi surface sum rule, signaling formation of exotic broad-band particle-hole superposition states induced by coherent magnetic breakdown., Comment: 30 pages, 5 main text figures, 6 supplementary figures

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 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 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 the relative vibrations between the tip and the sample. The spectrum of the vibrations shows distinct resonant peaks with maximal power density of about 27 nm/Hz$^{1/2}$ in the in-plane direction. The performance of the SQUID-on-tip microscope is demonstrated by magnetic imaging of the MnBi$_2$Te$_4$ magnetic topological insulator, magnetization and current distribution imaging in a SrRuO$_3$ ferromagnetic oxide thin film, and by thermal imaging of dissipation in graphene., Comment: Submitted to Review of Scientific Instruments

Vortices are the hallmarks of hydrodynamic flow. Recent studies indicate that strongly-interacting electrons in ultrapure conductors can display signatures of hydrodynamic behavior including negative nonlocal resistance, Poiseuille flow in narrow channels, and a violation of the Wiedemann-Franz law. Here we provide the first visualization of whirlpools in an electron fluid. By utilizing a nanoscale scanning superconducting quantum interference device on a tip (SQUID-on-tip) we image the current distribution in a circular chamber connected through a small aperture to an adjacent narrow current carrying strip in high-purity type-II Weyl semimetal WTe2. In this geometry, the Gurzhi momentum diffusion length and the size of the aperture determine the vortex stability phase diagram. We find that the vortices are present only for small apertures, whereas the flow is laminar (non-vortical) for larger apertures, consistent with the theoretical analysis of the hydrodynamic regime and in contrast to the expectations of ballistic transport in WTe2 at low temperatures. Moreover, near the vortical-to-laminar transition, we observe a single vortex in the chamber splitting into two vortices, a behavior that can occur only in the hydrodynamic regime and cannot be sustained by ballistic transport. These findings suggest a novel mechanism of hydrodynamic flow: instead of the commonly considered electron-electron scattering at the bulk, which becomes extremely weak at low temperatures, the spatial diffusion of charge carriers' momenta is enabled by small-angle scattering at the planar surfaces of thin pure crystals. This surface-induced para-hydrodynamics opens new avenues for exploring and utilizing electron fluidics in high-mobility electron systems., Comment: Main text: 15 pages, 5 figures. Method: 18 pages, 9 Extended Data figures. Supplementary videos: 2

Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations. When the inversion and time reversal symmetries are broken by the substrate or by strong interactions, the degeneracy of the flavors can be lifted and their corresponding bands can be filled sequentially. Due to their non-trivial band topology and Berry curvature, each of the bands is classified by a topological Chern number, leading to the quantum anomalous Hall and Chern insulator states at integer fillings $\nu$ of the bands. It has been recently predicted, however, that depending on the local atomic-scale arrangements of the graphene and the encapsulating hBN lattices, rather than being a global topological invariant, the Chern number C may become position dependent, altering transport and magnetic properties of the itinerant electrons. Using a SQUID-on-tip, we directly image the nanoscale Berry-curvature-induced equilibrium orbital magnetism, the polarity of which is governed by the local Chern number, and detect its two constituent components associated with the drift and the self-rotation of the electronic wave packets. At $\nu=1$, we observe local zero-field valley-polarized Chern insulators forming a mosaic of microscopic patches of C=-1, 0, or 1, governed by the local sublattice polarization, consistent with predictions. Upon further filling, we find a first-order phase transition due to recondensation of electrons from valley K to K', which leads to irreversible flips of the local Chern number and the magnetization, and to the formation of valley domain walls giving rise to hysteretic global anomalous Hall resistance. The findings shed new light on the structure and dynamics of topological phases and call for exploration of the controllable formation of flavor domain walls and their utilization in twistronic devices., Comment: 29 pages, 5 main text figures and 8 supplementary figures

Van der Waals heterostructures display a rich variety of unique electronic properties. To identify novel transport mechanisms, nonlocal measurements have been widely used, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers. This approach was employed in search of dissipationless spin and valley transport, topological charge-neutral currents, hydrodynamic flows and helical edge modes. Monolayer, bilayer, and few-layer graphene, transition-metal dichalcogenides, and moire superlattices were found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated. Graphene, in particular, exhibits giant nonlocality at charge neutrality, a prominent behavior that attracted competing explanations. Utilizing superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging, we demonstrate that the commonly-occurring charge accumulation at graphene edges leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, while the edge conductance has little impact on the current flow in zero magnetic field, it leads to field-induced decoupling between edge and bulk transport at moderate fields. The resulting giant nonlocality both at charge neutrality and away from it produces exotic flow patterns in which charges can flow against the global electric field. We have visualized surprisingly intricate patterns of nonlocal currents, which are sensitive to edge disorder. The observed one-dimensional edge transport, being generic and nontopological, is expected to support nonlocal transport in many electronic systems, offering insight into numerous controversies in the literature and linking them to long-range guided electronic states at system edges., Comment: Main text: 14 pages, 4 figures. Methods and Supplementary information: 27 pages, 6 figures. Supplementary videos: 9

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 superconducting materials and alloys beyond the elemental superconductors employed in the existing thermal deposition methods, opening the route to greatly enhanced SOT characteristics and functionalities. Utilizing this method, we have developed MoRe SOT devices with sub-50 nm diameter, magnetic flux sensitivity of 1.2 $\mu\Phi_0/Hz^{1/2}$ up to 3 T at 4.2 K, and thermal sensitivity better than 4 $\mu K/Hz^{1/2}$ up to 5 T, about five times higher than any previous report, paving the way to nanoscale imaging of magnetic and spintronic phenomena and of dissipation mechanisms in previously inaccessible quantum states of matter.

The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $\theta_M \approx 1.1\deg$. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1$\deg$, little information is currently available on the distribution of the local twist angles in actual magic angle twisted bilayer graphene (MATBG) transport devices. Here we map the local $\theta$ variations in hBN encapsulated devices with relative precision better than 0.002$\deg$ and spatial resolution of a few moir$\'e$ periods. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels in the quantum Hall state in MATBG, which provides a highly sensitive probe of the charge disorder and of the local band structure determined by the local $\theta$. We find that even state-of-the-art devices, exhibiting high-quality global MATBG features including superconductivity, display significant variations in the local $\theta$ with a span close to 0.1$\deg$. Devices may even have substantial areas where no local MATBG behavior is detected, yet still display global MATBG characteristics in transport, highlighting the importance of percolation physics. The derived $\theta$ maps reveal substantial gradients and a network of jumps. We show that the twist angle gradients generate large unscreened electric fields that drastically change the quantum Hall state by forming edge states in the bulk of the sample, and may also significantly affect the phase diagram of correlated and superconducting states. The findings call for exploration of band structure engineering utilizing twist-angle gradients and gate-tunable built-in planar electric fields for novel correlated phenomena and applications.

The recently predicted topological magnetoelectric effect and the response to an electric charge that mimics an induced mirror magnetic monopole are fundamental attributes of topological states of matter with broken time reversal symmetry. Using a SQUID-on-tip, acting simultaneously as a tunable scanning electric charge and as ultrasensitive nanoscale magnetometer, we induce and directly image the microscopic currents generating the magnetic monopole response in a graphene quantum Hall electron system. We find a rich and complex nonlinear behavior governed by coexistence of topological and nontopological equilibrium currents that is not captured by the monopole models. Furthermore, by utilizing a tuning fork that induces nanoscale vibrations of the SQUID-on-tip, we directly image the equilibrium currents of individual quantum Hall edge states for the first time. We reveal that the edge states that are commonly assumed to carry only a chiral downstream current, in fact carry a pair of counterpropagating currents, in which the topological downstream current in the incompressible region is always counterbalanced by heretofore unobserved nontopological upstream current flowing in the adjacent compressible region. The intricate patterns of the counterpropagating equilibrium-state orbital currents provide new insights into the microscopic origins of the topological and nontopological charge and energy flow in quantum Hall systems.

Topology is a powerful recent concept asserting that quantum states could be globally protected against local perturbations. Dissipationless topologically protected states are thus of major fundamental interest as well as of practical importance in metrology and quantum information technology. Although topological protection can be robust theoretically, in realistic devices it is often fragile against various dissipative mechanisms, which are difficult to probe directly because of their microscopic origins. By utilizing scanning nanothermometry, we visualize and investigate microscopic mechanisms undermining the apparent topological protection in the quantum Hall state in graphene. Our simultaneous nanoscale thermal and scanning gate microscopy shows that the dissipation is governed by crosstalk between counterpropagating pairs of downstream and upstream channels that appear at graphene boundaries because of edge reconstruction. Instead of local Joule heating, however, the dissipation mechanism comprises two distinct and spatially separated processes. The work generating process that we image directly and which involves elastic tunneling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. The independently visualized heat and entropy generation process, in contrast, occurs nonlocally upon inelastic resonant scattering off single atomic defects at graphene edges, while not affecting the transport. Our findings offer a crucial insight into the mechanisms concealing the true topological protection and suggest venues for engineering more robust quantum states for device applications., Comment: Main text: 12 pages, 3 figures. Supplementary information: 19 pages, 9 figures

Accurate determination of microscopic transport and magnetization currents is of central importance for the study of the electric properties of low dimensional materials and interfaces, of superconducting thin films and of electronic devices. Current distribution is usually derived from the measurement of the perpendicular component of the magnetic field above the surface of the sample, followed by numerical inversion of the Biot-Savart law. The inversion is commonly obtained by deriving the current stream function $g$, which is then differentiated in order to obtain the current distribution. However, this two-step procedure requires filtering at each step and, as a result, oversmoothes the solution. To avoid this oversmoothing we develop a direct procedure for inversion of the magnetic field that avoids use of the stream function. This approach provides enhanced accuracy of current reconstruction over a wide range of noise levels. We further introduce a reflection procedure that allows for the reconstruction of currents that cross the boundaries of the measurement window. The effectiveness of our approach is demonstrated by several numerical examples.

Controlling energy flows in solids through switchable electron-lattice cooling can grant access to a range of interesting and potentially useful energy transport phenomena. Here we discuss a unique switchable electron-lattice cooling mechanism arising in graphene due to phonon emission mediated by resonant scattering on defects in crystal lattice, which displays interesting analogy to the Purcell effect in optics. This mechanism strongly enhances the electron-phonon cooling rate, since non-equilibrium carriers in the presence of momentum recoil due to disorder can access a larger phonon phase space and emit phonons more effciently. Resonant energy dependence of phonon emission translates into gate-tunable cooling rates, exhibiting giant enhancement of cooling occurring when the carrier energy is aligned with the electron resonance of the defect.

Conversion of electric current into heat involves microscopic processes that operate on nanometer length-scales and release minute amounts of power. While central to our understanding of the electrical properties of materials, individual mediators of energy dissipation have so far eluded direct observation. Using scanning nano-thermometry with sub-micro K sensitivity we visualize and control phonon emission from individual atomic defects in graphene. The inferred electron-phonon 'cooling power spectrum' exhibits sharp peaks when the Fermi level comes into resonance with electronic quasi-bound states at such defects, a hitherto uncharted process. Rare in the bulk but abundant at graphene's edges, switchable atomic-scale phonon emitters define the dominant dissipation mechanism. Our work offers new insights for addressing key materials challenges in modern electronics and engineering dissipation at the nanoscale.

Quantized magnetic vortices driven by electric current determine key electromagnetic properties of superconductors. While the dynamic behavior of slow vortices has been thoroughly investigated, the physics of ultrafast vortices under strong currents remains largely unexplored. Here we use a nanoscale scanning superconducting quantum interference device to image vortices penetrating into a superconducting Pb film at rates of tens of GHz and moving with velocities up to tens of km/s, which are not only much larger than the speed of sound but also exceed the pair-breaking speed limit of superconducting condensate. These experiments reveal formation of mesoscopic vortex channels which undergo cascades of bifurcations as the current and magnetic field increase. Our numerical simulations predict metamorphosis of fast Abrikosov vortices into mixed Abrikosov-Josephson vortices at even higher velocities. This work offers an insight into the fundamental physics of dynamic vortex states of superconductors at high current densities, crucial for many applications.

The symmetry of single-molecule magnets dictates their spin quantum dynamics, influencing how such systems relax via quantum tunneling of magnetization (QTM). By reducing a system's symmetry, through the application of a magnetic field or uniaxial pressure, these dynamics can be modified. We report measurements of the magnetization dynamics of a crystalline sample of the high-symmetry [Mn12O12(O2CMe)16(MeOH)4]MeOH single-molecule magnet as a function of uniaxial pressure applied either parallel or perpendicular to the sample's "easy" magnetization axis. At temperatures between 1.8 and 3.3 K, magnetic hysteresis loops exhibit the characteristic steplike features that signal the occurrence of QTM. After applying uniaxial pressure to the sample in situ, both the magnitude and field position of the QTM steps changed. The step magnitudes were observed to grow as a function of pressure in both arrangements of pressure, while pressure applied along (perpendicular to) the sample's easy axis caused the resonant-tunneling fields to increase (decrease). These observations were compared with simulations in which the system's Hamiltonian parameters were changed. From these comparisons, we determined that parallel pressure induces changes to the second-order axial anisotropy parameter as well as either the fourth-order axial or fourth-order transverse parameter, or to both. In addition, we find that pressure applied perpendicular to the easy axis induces a rhombic anisotropy E ~ D/2000 per kbar that can be understood as deriving from a symmetry-breaking distortion of the molecule., Comment: 18 pages, 7 figures, version accepted by Phys. Rev. B

Energy dissipation is a fundamental process governing the dynamics of physical, chemical, and biological systems. It is also one of the main characteristics distinguishing quantum and classical phenomena. In condensed matter physics, in particular, scattering mechanisms, loss of quantum information, or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Despite its vital importance the microscopic behavior of a system is usually not formulated in terms of dissipation because the latter is not a readily measureable quantity on the microscale. Although nanoscale thermometry is gaining much recent interest, the existing thermal imaging methods lack the necessary sensitivity and are unsuitable for low temperature operation required for study of quantum systems. Here we report a superconducting quantum interference nano-thermometer device with sub 50 nm diameter that resides at the apex of a sharp pipette and provides scanning cryogenic thermal sensing with four orders of magnitude improved thermal sensitivity of below 1 {\mu}K/Hz1/2. The non-contact non-invasive thermometry allows thermal imaging of very low nanoscale energy dissipation down to the fundamental Landauer limit of 40 fW for continuous readout of a single qubit at 1 GHz at 4.2 K. These advances enable observation of dissipation due to single electron charging of individual quantum dots in carbon nanotubes and reveal a novel dissipation mechanism due to resonant localized states in hBN encapsulated graphene, opening the door to direct imaging of nanoscale dissipation processes in quantum matter., Comment: Submitted to Nature

Miniaturization of superconducting quantum interference devices (SQUIDs) is of major importance for the development of sensitive scanning nanoscale magnetometry tools. The high sensitivity of nanoSQUIDs is restricted, however, to only particular periodic values of the applied magnetic field, making accurate measurements at intermediate values of the field impossible. We present a theoretical investigation of a multi-terminal, multi-junction SQUID (mSQUID) that lifts this limitation by providing electrical means for a continuous shift of the quantum interference pattern with respect to the applied field. Analysis of 4-terminal, 4-junction and 3-terminal, 3-junction mSQUIDs shows that operation at maximum sensitivity can be obtained at any value of the magnetic field by applying control current to the extra terminals. The model describes the variation and the shift of the interference pattern as a function of the control currents, junction asymmetries, and the mSQUID inductance. The mSQUID is also shown to provide a direct measurement of the current-phase relations of superconducting junctions. The derived model provides a quantitative description of the recently developed multi-terminal nanoSQUID-on-tip.

We present a new nanoscale superconducting quantum interference device (SQUID) whose interference pattern can be shifted electrically in-situ. The device consists of a nanoscale four-terminal/four-junction SQUID fabricated at the apex of a sharp pipette using a self-aligned three-step deposition of Pb. In contrast to conventional two-terminal/two-junction SQUIDs that display optimal sensitivity when flux biased to about a quarter of the flux quantum, the additional terminals and junctions allow optimal sensitivity at arbitrary applied flux, thus eliminating the magnetic field "blind spots". We demonstrate spin sensitivity of 5 to 8 $\mu_B/\text{Hz}^{1/2}$ over a continuous field range of 0 to 0.5 T, with promising applications for nanoscale scanning magnetic imaging.

Atomically sharp oxide heterostructures exhibit a range of novel physical phenomena that do not occur in the parent bulk compounds. The most prominent example is the appearance of highly conducting and superconducting states at the interface between the band insulators LaAlO3 and SrTiO3. Here we report a new emergent phenomenon at the LaMnO3/SrTiO3 interface in which an antiferromagnetic insulator abruptly transforms into a magnetic state that exhibits unexpected nanoscale superparamagnetic dynamics. Upon increasing the thickness of LaMnO3 above five unit cells, our scanning nanoSQUID-on-tip microscopy shows spontaneous formation of isolated magnetic islands of 10 to 50 nm diameter, which display random moment reversals by thermal activation or in response to an in-plane magnetic field. Our charge reconstruction model of the polar LaMnO3/SrTiO3 heterostructure describes the sharp emergence of thermodynamic phase separation leading to nucleation of metallic ferromagnetic islands in an insulating antiferromagnetic matrix. The model further suggests that the nearby superparamagnetic-ferromagnetic transition can be gate tuned, holding potential for applications in magnetic storage and spintronics.

The dynamics of quantized magnetic vortices and their pinning by materials defects determine electromagnetic properties of superconductors, particularly their ability to carry non-dissipative currents. Despite recent advances in the understanding of the complex physics of vortex matter, the behavior of vortices driven by current through a multi-scale potential of the actual materials defects is still not well understood, mostly due to the scarcity of appropriate experimental tools capable of tracing vortex trajectories on nanometer scales. Using a novel scanning superconducting quantum interference microscope we report here an investigation of controlled dynamics of vortices in lead films with sub-Angstrom spatial resolution and unprecedented sensitivity. We measured, for the first time, the fundamental dependence of the elementary pinning force of multiple defects on the vortex displacement, revealing a far more complex behavior than has previously been recognized, including striking spring softening and broken-spring depinning, as well as spontaneous hysteretic switching between cellular vortex trajectories. Our results indicate the importance of thermal fluctuations even at 4.2 K and of the vital role of ripples in the pinning potential, giving new insights into the mechanisms of magnetic relaxation and electromagnetic response of superconductors., Comment: 15 pages and 5 figures (main text) + 15 pages and 11 figures (supplementary material)

Nanoscale superconducting quantum interference devices (SQUIDs) demonstrate record sensitivities to small magnetic moments, but are typically sensitive only to the field component that is normal to the plane of the SQUID and out-of-plane with respect to the scanned surface. We report on a nanoscale three-junction Pb SQUID which is fabricated on the apex of a sharp tip. Because of its three-dimensional structure, it exhibits a unique tunable sensitivity to both in-plane and out-of-plane fields. We analyze the two-dimensional interference pattern from both numerical and experimental points of view. This device is integrated into a scanning microscope and its ability to independently measure the different components of the magnetic field with outstanding spin sensitivity better than $5\ \frac{\mu_B}{\mathrm{Hz}^{1/2}}$ is demonstrated. This highlights its potential as a local probe of nanoscale magnetic structures.

We report spatially resolved, time-dependent, magnetization reversal measurements of an Fe$_{8}$ single molecular magnet using a microscopic Hall bar array. We found that under some conditions the molecules reverse their spin direction at a resonance field in the form of an avalanche. The avalanche front velocity is of the order of $1$m/sec and is sensitive to field gradients and sweep rates. We also measured the propagation velocity of a heat pulse and found that it is much slower than the avalanche velocity. We therefore conclude that in Fe$_{8}$, the avalanche front propagates without thermal assistance.

The emerging field of complex oxide interfaces is generically built on one of the most celebrated substrates - strontium titanate (SrTiO3). This material hosts a range of phenomena, including ferroelasticity, incipient ferroelectricity, and most puzzlingly, contested giant piezoelectricity. Although these properties may markedly influence the oxide interfaces, especially on microscopic length scales, the lack of local probes capable of studying such buried systems has left their effects largely unexplored. Here we use a scanning charge detector - a nanotube single-electron transistor - to noninvasively image the electrostatic landscape and local mechanical response in the prototypical LaAlO3/SrTiO3 system with unprecedented sensitivity. Our measurements reveal that on microscopic scales SrTiO3 exhibits large anomalous piezoelectricity with curious spatial dependence. Through electrostatic imaging we unravel the microscopic origin for this extrinsic piezoelectricity, demonstrating its direct, quantitative connection to the motion of locally ordered tetragonal domains under applied gate voltage. These domains create striped potential modulations that can markedly influence the two-dimensional electron system at the conducting interface. Our results have broad implications to all complex oxide interfaces built on SrTiO3 and demonstrate the importance of microscopic structure to the physics of electrons at the LaAlO3/SrTiO3 interface., Comment: MH and JAS contributed equally to this work; supplementary information included

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 {\mu}B 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 {\mu}m). 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 n{\Phi}0/Hz^1/2, representing almost two orders of magnitude improvement in spin sensitivity, down to 0.38 {\mu}B/Hz^1/2. In addition, the devices operate over a wide range of magnetic fields with 0.6 {\mu}B/Hz^1/2 sensitivity even at 1 T. We demonstrate magnetic imaging of vortices in type II superconductor that are 120 nm apart and scanning measurements of AC magnetic fields down to 50 nT. The unique geometry of these nano-SQUIDs that reside on the apex of a sharp tip allows approaching the sample to within a few nm, which paves the way to a new class of single-spin resolved scanning probe microscopy., Comment: 10 pages, 9 figures (including supplementary material), Nature Nanotechnology in press

The local effect of the Josephson vortices on the vortex lattice melting process in \BSCCO crystals in the presence of an in-plane field $H_{ab}$ is studied by differential magneto-optical imaging. The melting process is found to commence along the Josephson vortex stacks, forming a mesomorphic phase of periodic liquid and solid lamellas, the direction and spacing of which are controlled by $H_{ab}$. The reduction of the local melting field $H_m$ along the Josephson vortex stacks is more than an order of magnitude larger than the reduction of the average bulk $H_m$ by $H_{ab}$., Comment: 5 pages, 3 figures (low res). Higher resolution can be found in the Phys. Rev. Lett. equivalent paper

Differential magneto-optics are used to study the effect of dc in-plane magnetic field on hysteretic behavior due to geometrical barriers in $Bi_2Sr_2CaCu_2O_{8+\delta}$ crystals. In absence of in-plane field a vortex dome is visualized in the sample center surrounded by barrier-dominated flux-free regions. With in-plane field, stacks of Josephson vortices form vortex chains which are surprisingly found to protrude out of the dome into the vortex-free regions. The chains are imaged to extend up to the sample edges, thus providing easy channels for vortex entry and for drain of the dome through geometrical barrier, suppressing the magnetic hysteresis. Reduction of the vortex energy due to crossing with Josephson vortices is evaluated to be about two orders of magnitude too small to account for the formation of the protruding chains. We present a model and numerical calculations that qualitatively describe the observed phenomena by taking into account the demagnetization effects in which flux expulsion from the pristine regions results in vortex focusing and in the chain protrusion. Comparative measurements on a sample with narrow etched grooves provide further support to the proposed model., Comment: 12 figures (low res.) Higher resolution figures are available at the Phys Rev B version. Typos corrected

A nanometer-sized superconducting quantum interference device (nanoSQUID) is fabricated on the apex of a sharp quartz tip and integrated into a scanning SQUID microscope. A simple self-aligned fabrication method results in nanoSQUIDs with diameters down to 100 nm with no lithographic processing. An aluminum nanoSQUID with an effective area of 0.034 $\mu$m$^2$ displays flux sensitivity of 1.8$\cdot 10^{-6}$ $\Phi_0/\mathrm{Hz}^{1/2} and operates in fields as high as 0.6 T. With projected spin sensitivity of 65 $\mu_B/\mathrm{Hz}^{1/2}$ and high bandwidth, the SQUID on a tip is a highly promising probe for nanoscale magnetic imaging and spectroscopy., Comment: 14 manuscript pages, 5 figures

Superconductors often contain quantized microscopic whirlpools of electrons, called vortices, that can be modeled as one-dimensional elastic objects. Vortices are a diverse playground for condensed matter because of the interplay between thermal fluctuations, vortex-vortex interactions, and the interaction of the vortex core with the three-dimensional disorder landscape. While vortex matter has been studied extensively, the static and dynamic properties of an individual vortex have not. Here we employ magnetic force microscopy (MFM) to image and manipulate individual vortices in detwinned, single crystal YBa2Cu3O6.991 (YBCO), directly measuring the interaction of a moving vortex with the local disorder potential. We find an unexpected and dramatic enhancement of the response of a vortex to pulling when we wiggle it transversely. In addition, we find enhanced vortex pinning anisotropy that suggests clustering of oxygen vacancies in our sample and demonstrates the power of MFM to probe vortex structure and microscopic defects that cause pinning.

A low concentration of columnar defects is reported to transform a first-order vortex lattice melting line in BSCCO crystals into alternating segments of first-order and second-order transitions separated by two critical points. As the density of CDs is increased, the critical points shift apart and the range of the intermediate second-order transition expands. A third, low temperature critical point was also observed in one sample. The measurement of equilibrium magnetization and the mapping of the melting line down to 27K was made possible by employment of the shaking technique., Comment: 5 pages, 3 figures

Vortex matter phase transitions in the high-temperature superconductor Bi2Sr2CaCu2O8 were studied using local magnetization measurements combined with a vortex 'shaking' technique. The measurements revealed thermodynamic evidence of a first-order transition along the second magnetization peak line, at temperatures below the apparent critical point Tcp. We found that the first-order transition line does not terminate at Tcp, but continues down to at least 30 K. This observation suggests that the ordered vortex lattice phase is destroyed through a unified first-order transition that changes its character from thermally induced melting at high temperatures to a disorder-induced transition at low temperatures. At intermediate temperatures the transition line shows an upturn, which implies that the vortex matter displays 'inverse' melting behavior., Comment: 9 pages, 6 figures, Physica C, in press

Inverse melting, in which a crystal reversibly transforms into a liquid or amorphous phase upon decreasing the temperature, is considered to be very rare in nature. The search for such an unusual equilibrium phenomenon is often hampered by the formation of nonequilibrium states which conceal the thermodynamic phase transition, or by intermediate phases, as was recently shown in a polymeric system. Here we report a first-order inverse melting of the magnetic flux line lattice in Bi2Sr2CaCu2O8 superconductor. At low temperatures, the material disorder causes significant pinning of the vortices, which prevents observation of their equilibrium properties. Using a newly introduced 'vortex dithering' technique we were able to equilibrate the vortex lattice. As a result, direct thermodynamic evidence of inverse melting transition is found, at which a disordered vortex phase transforms into an ordered lattice with increasing temperature. Paradoxically, the structurally ordered lattice has larger entropy than the disordered phase. This finding shows that the destruction of the ordered vortex lattice occurs along a unified first-order transition line that gradually changes its character from thermally-induced melting at high temperatures to a disorder-induced transition at low temperatures., Comment: 13 pages, 4 figures, Nature, In press

Large BSCCO crystals with electrical contacts positioned far from the edges are studied by transport measurements, then cut into the common narrow strip geometry, and remeasured. Instead of showing larger resistance, the narrow strip samples display a dramatic drop in the resistance, enhanced activation energies, and nonlinear characteristics due to strong surface barriers. The surface barriers also dominate the resistive drop at the first-order phase transition. Because the surface barriers are avoided in large crystals, we are able to probe the solid phase and find good agreement with the recent predictions of Bragg glass theory., Comment: 4 pages, 5 figures, submitted to PRL

The vortex matter phase diagram of BSCCO crystals is analyzed by investigating vortex penetration through the surface barrier in the presence of a transport current. The strength of the effective surface barrier, its nonlinearity, and asymmetry are used to identify a possible new ordered phase above the first-order transition. This technique also allows sensitive determination of the depinning temperature. The solid phase below the first-order transition is apparently subdivided into two phases by a vertical line extending from the multicritical point., Comment: 11 pages, 3 figures, accepted for publication in PRL

A new measurement technique for investigation of vortex dynamics is introduced. The distribution of the transport current across a crystal is derived by a sensitive measurement of the self-induced magnetic field of the transport current. We are able to clearly mark where the flow of the transport current is characterized by bulk pinning, surface barrier, or a uniform current distribution. One of the novel results is that in BSCCO crystals most of the vortex liquid phase is affected by surface barriers resulting in a thermally activated apparent resistivity. As a result the standard transport measurements in BSCCO do not probe the dynamics of vortices in the bulk, but rather measure surface barrier properties., Comment: 11 pages, 4 figures, accepted for publication in Nature