The coexistence of multiple types of orders is a common thread in condensed matter physics and unconventional superconductors. The nature of superconducting orders may be unveiled by analyzing local perturbations such as vortices. For thin films, the vortex magnetic profile is characterized by the Pearl-length $Λ$ Λ , which is inversely proportional to the 2D superfluid density; hence, normally, also inversely proportional to the film thickness, $$d$$ d . Here we employ the scanning SQUID-on-tip microscopy to measure $Λ$ Λ in NbSe 2 flakes with thicknesses ranging from $$N=3$$ N = 3 to $$53$$ 53 layers. For $$N\, > \,10$$ N > 10 , we find the expected dependence $$Λ\propto 1/d$$ Λ ∝ 1 / d . However, six-layer films show a sharp increase of $Λ$ Λ deviating by a factor of three from the expected value. This value remains fixed for $$N=3$$ N = 3 to $$6$$ 6 . This unexpected behavior suggests the competition between two orders; one residing only on the first and last layers of the film while the other prevails in all layers.

Nano‐patterned magnetic materials have opened new venues for the investigation of strongly correlated phenomena including artificial spin‐ice systems, geometric frustration, and magnetic monopoles, for technologically important applications such as reconfigurable ferromagnetism. With the advent of atomically thin 2D van der Waals (vdW) magnets, a pertinent question is whether such compounds could make their way into this realm where interactions can be tailored so that unconventional states of matter can be assessed. Here, it is shown that square islands of CrGeTe 3 vdW ferromagnets distributed in a grid manifest antiferromagnetic correlations, essential to enable frustration resulting in an artificial spin‐ice. By using a combination of SQUID‐on‐tip microscopy, focused ion beam lithography, and atomistic spin dynamic simulations, it is shown that a square array of CGT island as small as 150 × 150 × 60 nm 3 have tunable dipole–dipole interactions, which can be precisely controlled by their lateral spacing. There is a crossover between non‐interacting islands and significant inter‐island anticorrelation depending on how they are spatially distributed allowing the creation of complex magnetic patterns not observable at the isolated flakes. These findings suggest that the cross‐talk between the nano‐patterned magnets can be explored in the generation of even more complex spin configurations where exotic interactions may be manipulated in an unprecedented way.

Contrary to conventional nanoparticle, we report an increasing coercivity of magnetic nanoparticles with decreasing size. Our results show that the anomaly in coercivity can be attributed to a magnetic edge state.

A gel consists of a network of particles or molecules formed for example using the sol-gel process, by which a solution transforms into a porous solid. Particles or molecules in a gel are mainly organized on a scaffold that makes up a porous system. Quantized vortices in type-II superconductors mostly form spatially homogeneous ordered or amorphous solids. Here we present high-resolution imaging of the vortex lattice displaying dense vortex clusters separated by sparse or entirely vortex-free regions in β-Bi2Pd superconductor. We find that the intervortex distance diverges upon decreasing the magnetic field and that vortex lattice images follow a multifractal behavior. These properties, characteristic of gels, establish the presence of a novel vortex distribution, distinctly different from the well-studied disordered and glassy phases observed in high-temperature and conventional superconductors. The observed behavior is caused by a scaffold of one-dimensional structural defects with enhanced stress close to the defects. The vortex gel might often occur in type-II superconductors at low magnetic fields. Such vortex distributions should allow to considerably simplify control over vortex positions and manipulation of quantum vortex states.

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 selfaligned deposition of In and Sn, have resulted in SOT with a flux noise of 42 n0Hz–1/2, yielding a record low spin noise of 0.29 µBHz–1/2. In addition, the new SOTs function at sub-Kelvin temperatures and in high magnetic fields of over 2.5 T. Integrating the SOTs into a scanning probe microscope allowed us to image the stray field of a single Fe3O4 nanocube at 300 mK. Our results show that the easy magnetization axis direction undergoes a transition from the (111) direction at room temperature to an in-plane orientation, which could be attributed to the Verwey phase transition in Fe3O4.

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 of 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.

Simultaneous transport and scanning nanoSQUID-on-tip magnetic imaging studies in Cr-(Bi,Sb)(2)Te-3 modulation-doped films reveal the presence of superparamagnetic order within the quantum anomalous Hall regime. In contrast to the expectation that a long-range ferromagnetic order is required for establishing the quantum anomalous Hall state, superparamagnetic dynamics of weakly interacting nanoscale magnetic islands is observed both in the plateau transition regions, as well as within the fully quantized C = +/- 1 Chern plateaus. Modulation doping of the topological insulator films is found to give rise to significantly larger superparamagnetic islands as compared to uniform magnetic doping, evidently leading to enhanced robustness of the quantum anomalous Hall effect. Nonetheless, even in this more robust quantum state, attaining full quantization of transport coefficients requires magnetic alignment of at least 95% of the superparamagnetic islands. The superparamagnetic order is also found within the incipient C = 0 zero Hall plateau, which may host an axion state if the top and bottom magnetic layers are magnetized in opposite directions. In this regime, however, a significantly lower level of island alignment is found in our samples, hindering the formation of the axion state. Comprehension and control of superparamagnetic dynamics is thus a key factor in apprehending the fragility of the quantum anomalous Hall state and in enhancing the endurance of the different quantized states temperatures for utilization of robust topological protection in novel devices.

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 pipet 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/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 are absent in the parent compounds. A prominent example is the appearance of highly conducting and superconducting states at the interface between LaAlO3 and SrTiO3. Here we report an emergent phenomenon at the LaMnO3/ SrTiO3 interface where an antiferromagnetic Mott insulator abruptly transforms into a nanoscale inhomogeneous magnetic state. Upon increasing the thickness of LaMnO3, our scanning nanoSQUID-on-tip microscopy shows spontaneous formation of isolated magnetic nanoislands, which display thermally activated moment reversals in response to an in-plane magnetic field. The observed superparamagnetic state manifests the emergence of thermodynamic electronic phase separation in which metallic ferromagnetic islands nucleate in an insulating antiferromagnetic matrix. We derive a model that captures the sharp onset and the thickness dependence of the magnetization. Our model suggests that a nearby superparamagnetic-ferromagnetic transition can be gate tuned, holding potential for applications in magnetic storage and spintronics.

Energy dissipation is a fundamental process governing the dynamics of physical, chemical and biological systems. It is also one of the main characteristics that distinguish quantum from classical phenomena. In particular, in condensed matter physics, 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. Yet the microscopic behaviour of a system is usually not formulated in terms of dissipation because energy dissipation is not a readily measurable quantity on the micrometre scale. Although nanoscale thermometry has gained much recent interest(1-15), existing thermal imaging methods are not sensitive enough for the study of quantum systems and are also unsuitable for the low-temperature operation that is required. Here we report a nano-thermometer based on a superconducting quantum interference device with a diameter of less than 50 nanometres that resides at the apex of a sharp pipette: it provides scanning cryogenic thermal sensing that is four orders of magnitude more sensitive than previous devices-below 1 mu K Hz(-1/2). This non contact, non-invasive thermometry allows thermal imaging of very low intensity, nanoscale energy dissipation down to the fundamental Landauer limit(16-18) of 40 femtowatts for continuous readout of a single qubit at one gigahertz at 4.2 kelvin. These advances enable the observation of changes in dissipation due to single-electron charging of individual quantum dots in carbon nanotubes. They also reveal a dissipation mechanism attributable to resonant localized states in graphene encapsulated within hexagonal boron nitride, opening the door to direct thermal imaging of nanoscale dissipation processes in quantum matter.

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.

Quantized Hall conductance is a generic feature of two-dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is believed to be broken by long-range ferromagnetic order, with quantized resistance observed even at zero external magnetic field. We use scanning nanoSQUID (nano-superconducting quantum interference device) magnetic imaging to provide a direct visualization of the dynamics of the quantum phase transition between the two anomalous Hall plateaus in a Cr-doped (Bi, Sb)(2)Te-3 thin film. Contrary to naive expectations based on macroscopic magnetometry, our measurements reveal a superparamagnetic state formed by weakly interacting magnetic domains with a characteristic size of a few tens of nanometers. The magnetic phase transition occurs through random reversals of these local moments, which drive the electronic Hall plateau transition. Surprisingly, we find that the electronic system can, in turn, drive the dynamics of the magnetic system, revealing a subtle interplay between the two coupled quantum phase transitions.