Search

Surfaces -- by breaking bulk symmetries, introducing roughness, or hosting defects -- can significantly influence magnetic order in magnetic materials. Determining their effect on the complex nanometer-scale phases present in certain non-centrosymmetric magnets is an outstanding problem requiring high-resolution magnetic microscopy. Here, we use scanning SQUID-on-tip microscopy to image the surface of bulk Cu$_2$OSeO$_3$ at low temperature and in a magnetic field applied along $\left\langle100\right\rangle$. Real-space maps measured as a function of applied field reveal the microscopic structure of the magnetic phases and their transitions. In low applied field, we observe a magnetic texture consistent with an in-plane stripe phase, pointing to the existence of a distinct surface state. In the low-temperature skyrmion phase, the surface is populated by clusters of disordered skyrmions, which emerge from rupturing domains of the tilted spiral phase. Furthermore, we displace individual skyrmions from their pinning sites by applying an electric potential to the scanning probe, thereby demonstrating local skyrmion control at the surface of a magnetoelectric insulator., Comment: 25 pages, 13 figures, including 1 appendix and references

Cascades are self-reinforcing processes underlying the systemic risk of many complex systems. Understanding the universal aspects of these phenomena is of fundamental interest, yet typically bound to numerical observations in ad-hoc models and limited insights. Here, we develop a unifying approach and show that cascades induced by a long-range propagation of local perturbations are characterized by two universality classes determined by the parity invariance of the underlying process. We provide hyperscaling arguments predicting hybrid critical exponents given by a combination of both mean-field spinodal exponents and $d$-dimensional corrections and we show how global symmetries influence the geometry and lifetime of avalanches. Simulations encompassing classic and novel cascade models validate our predictions, revealing fundamental principles of cascade phenomena amenable to experimental validation., Comment: 12 pages, 9 figures, methods and supplementary material included

Cascades are self-amplifying processes triggered by feedback mechanisms that may cause a substantial part of a macroscopic system to change its phase in response of a relatively small local event. The theoretical background for these phenomena is rich and interdisciplinary with interdependent networks providing a versatile "two-interactions" framework to study their multiscale evolution. Yet, physics experiments aimed at validating this ever-growing volume of predictions have remained elusive, hitherto hindered by the problem of identifying possible physical mechanisms realizing interdependent couplings. Here we develop and study the first experimental realization of an interdependent system as a multilayer network of two disordered superconductors separated by an insulating film. We show that Joule heating effects emerging at sufficiently large driving currents act as dependency links between the superconducting layers, igniting overheating cascades via adaptive back and forth electro-thermal feedbacks. Through theory and experiments, we unveil a rich phase diagram of mutual resistive transitions and cascading processes that physically realize and generalize interdependent percolation. The present work establishes the first physics laboratory bench for the manifestation of the theory of interdependent systems, enabling experimental studies to control and to further develop the multilayer phenomena of complex interdependent materials.

We use sensitive dynamic cantilever magnetometry to measure the magnetic hysteresis of individual magnetic Janus particles. These particles consist of hemispherical caps of magnetic material deposited on micrometer-scale silica spheres. The measurements, combined with corresponding micromagnetic simulations, reveal the magnetic configurations present in these individual curved magnets. In remanence, ferromagnetic Janus particles are found to host a global vortex state with vanishing magnetic moment. In contrast, a remanent onion state with significant moment is recovered by imposing an exchange bias to the system via an additional antiferromagnetic layer in the cap. A robust remanent magnetic moment is crucial for most applications of magnetic Janus particles, in which an external magnetic field actuates their motion., Comment: 6 pages, 3 figures, 9-page supplementary information

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., Comment: 17 pages, 4 figures, 6-page supplementary information

We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics $d\mathbf{X}_t = a(\mathbf{X}_t)dt + \mathbf{b}(\mathbf{X}_t)d\mathbf{W}_t$. We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form $u(\mathbf{x}) = \mathbb{E}^{\mathbf{x}}\left[\int_0^\tau g(\mathbf{X}_t)dt \right] + \mathbb{E}^{\mathbf{x}}\left[f(\mathbf{X}_\tau)\right]$ for a domain $\Omega$ and the exit stopping time $\tau = \inf_t \{t > 0 \; |\; \mathbf{X}_t \not\in \Omega\}$, where $f,g$ are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward-Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case $f = 0,\, g = 1$ where $u(\mathbf{x}) = \mathbb{E}^{\mathbf{x}}\left[\tau\right]$. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.

Interest in creating magnetic metamaterials has led to methods for growing superstructures of magnetic nanoparticles. Mesoscopic crystals of maghemite ($\gamma\text{-Fe}_2\text{O}_3$) nanoparticles can be arranged into highly ordered body-centered tetragonal lattices of up to a few micrometers. Although measurements on disordered ensembles have been carried out, determining the magnetic properties of individual mesoscopic crystals is challenging due to their small total magnetic moment. Here, we overcome these challenges by utilizing sensitive dynamic cantilever magnetometry to study individual micrometer-sized $\gamma\text{-Fe}_2\text{O}_3$ mesocrystals. These measurements reveal an unambiguous cubic anisotropy, resulting from the crystalline anisotropy of the constituent maghemite nanoparticles and their alignment within the mesoscopic lattice. The signatures of anisotropy and its orgins come to light because we combine the self-assembly of highly ordered mesocrystals with the ability to resolve their individual magnetism. This combination is promising for future studies of the magnetic anisotropy of other nanoparticles, which are too small to investigate individually., Comment: 13 pages, 12 figures

The orientation of N\'eel-type skyrmions in the lacunar spinels GaV$_4$S$_8$ and GaV$_4$Se$_8$ is tied to the polar axes of their underlying crystal structure through the Dzyaloshinskii-Moriya interaction. In these crystals, the skyrmion lattice phase exists for externally applied magnetic fields parallel to these axes and withstands oblique magnetic fields up to some critical angle. Here, we map out the stability of the skyrmion lattice phase in both crystals as a function of field angle and magnitude using dynamic cantilever magnetometry. The measured phase diagrams reproduce the major features predicted by a recent theoretical model, including a reentrant cycloidal phase in GaV$_4$Se$_8$. Nonetheless, we observe a greater robustness of the skyrmion phase to oblique fields, suggesting possible refinements to the model. Besides identifying transitions between the cycloidal, skyrmion lattice, and ferromagnetic states in the bulk, we measure additional anomalies in GaV$_4$Se$_8$ and assign them to magnetic states confined to polar structural domain walls., Comment: 11 pages and 7 figures

We report a magnetic state in GaV$_4$Se$_8$ which emerges exclusively in samples with mesoscale polar domains and not in polar mono-domain crystals. Its onset is accompanied with a sharp anomaly in the magnetic susceptibility and the magnetic torque, distinct from other anomalies observed also in polar mono-domain samples upon transitions between the cycloidal, the N\'eel-type skyrmion lattice and the ferromagnetic states. We ascribe this additional transition to the formation of magnetic textures localized at structural domain walls, where the magnetic interactions change stepwise and spin textures with different spiral planes, hosted by neighbouring domains, need to be matched. A clear anomaly in the magneto-current indicates that the domain-wall-confined magnetic states also have strong contributions to the magnetoelectric response. We expect polar domain walls to commonly host such confined magnetic edge states, especially in materials with long wavelength magnetic order.

We demonstrate the use of individual magnetic nanowires (NWs), grown by focused electron beam induced deposition (FEBID), as scanning magnetic force sensors. Measurements of their mechanical susceptibility, thermal motion, and magnetic response show that the NWs posses high-quality flexural mechanical modes and a strong remanent magnetization pointing along their long axis. Together, these properties make the NWs excellent sensors of weak magnetic field patterns, as confirmed by calibration measurements on a micron-sized current-carrying wire and magnetic scanning probe images of a permalloy disk. The flexibility of FEBID in terms of the composition, geometry, and growth location of the resulting NWs, makes it ideal for fabricating scanning probes specifically designed for imaging subtle patterns of magnetization or current density., Comment: Main text: 22 pages, 4 figures; Supplementary information: 8 pages, 6 figures

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and splitting schemes for the fourth-order governing equations in terms of a system of second-order elliptic operators. Using a Hodge decomposition, we develop methods for manifolds having spherical topology. We show the methods exhibit high-order convergence rates for solving hydrodynamic flows on curved surfaces. The methods also provide general high-order approximations for the metric, curvature, and other geometric quantities of the manifold and associated exterior calculus operators. The approaches also can be utilized to develop high-order solvers for other scalar-valued and vector-valued problems on manifolds.

We present a scanning magnetic force sensor based on an individual magnet-tipped GaAs nanowire (NW) grown by molecular beam epitaxy. Its magnetic tip consists of a final segment of single-crystal MnAs formed by sequential crystallization of the liquid Ga catalyst droplet. We characterize the mechanical and magnetic properties of such NWs by measuring their flexural mechanical response in an applied magnetic field. Comparison with numerical simulations allows the identification of their equilibrium magnetization configurations, which in some cases include magnetic vortices. To determine a NW's performance as a magnetic scanning probe, we measure its response to the field profile of a lithographically patterned current-carrying wire. The NWs' tiny tips and their high force sensitivity make them promising for imaging weak magnetic field patterns on the nanometer-scale, as required for mapping mesoscopic transport and spin textures or in nanometer-scale magnetic resonance., Comment: 8 pages, 5 figures

The reversal of a uniform axial magnetization in a ferromagnetic nanotube (FNT) has been predicted to nucleate and propagate through vortex domains forming at the ends. In dynamic cantilever magnetometry measurements of individual FNTs, we identify the entry of these vortices as a function of applied magnetic field and show that they mark the nucleation of magnetization reversal. We find that the entry field depends sensitively on the angle between the end surface of the FNT and the applied field. Micromagnetic simulations substantiate the experimental results and highlight the importance of the ends in determining the reversal process. The control over end vortex formation enabled by our findings is promising for the production of FNTs with tailored reversal properties., Comment: 20 pages, 13 figures

We use a scanning nanometer-scale superconducting quantum interference device to map the stray magnetic field produced by individual ferromagnetic nanotubes (FNTs) as a function of applied magnetic field. The images are taken as each FNT is led through magnetic reversal and are compared with micromagnetic simulations, which correspond to specific magnetization configurations. In magnetic fields applied perpendicular to the FNT long axis, their magnetization appears to reverse through vortex states, i.e.\ configurations with vortex end domains or -- in the case of a sufficiently short FNT -- with a single global vortex. Geometrical imperfections in the samples and the resulting distortion of idealized mangetization configurations influence the measured stray-field patterns., Comment: 14 pages, 4 figures

We image the remnant magnetization configurations of CoFeB and permalloy nanotubes (NTs) using x-ray magnetic circular dichroism photo-emission electron microscopy. The images provide direct evidence for flux-closure configurations, including a global vortex state, in which magnetization points circumferentially around the NT axis. Furthermore, micromagnetic simulations predict and measurements confirm that vortex states can be programmed as the equilibrium remnant magnetization configurations by reducing the NT aspect ratio., Comment: 14 pages, 4 figures, link to supplementary information

We investigate single CoFeB nanotubes with hexagonal cross-section using dynamic cantilever magnetometry (DCM). We develop both an analytical model based on the Stoner-Wohlfarth approximation and a broadly applicable numerical framework for analyzing DCM measurements of magnetic nanostructures. Magnetometry data show the presence of a uniformly magnetized configuration at high external fields with $\mu_0 M_s =1.3 \pm 0.1$ T and non-uniform configurations at low fields. In this low-field regime, comparison between numerical simulations and DCM measurements supports the existence of flux-closure configurations. Crucially, evidence of such configurations is only apparent because of the sensitivity of DCM to single nanotubes, whereas conventional measurements of ensembles are often obscured by sample-to-sample inhomogeneities in size, shape, and orientation, Comment: 16 pages, 9 figures

We used one-dimensional coupled sine-Gordon equations combined with heat diffusion equations to numerically investigate the thermal and electromagnetic properties of a $300\,\mu\mathrm{m}$ long intrinsic Josephson junction stack consisting of $N = 700$ junctions. The junctions in the stack are combined to $M$ segments where we assume that inside a segment all junctions behave identically. Most simulations are for $M = 20$. For not too high bath temperatures there is the appearence of a hot spot at high bias currents. In terms of electromagnetic properties, robust standing wave patterns appear in the current density and electric field distributions. These patterns come together with vortex/antivortex lines across the stack that correspond to $\pi$ kink states, discussed before in the literature for a homogeneous temperature distribution in the stack. We also discuss scaling of the thermal and electromagnetic properties with $M$, on the basis of simulations with $M$ between 10 and 350., Comment: 17 pages, 17 figures

Recently it has been found that, when operated at large input power, the linewidth of terahertz radiation emitted from intrinsic Josephson junction stacks can be as narrow as some megahertz. In this high-bias regime a hot spot coexists with regions which are still superconducting. Surprisingly, the linewidth was found to decrease with increasing bath temperature. We present a simple model describing the dynamics of the stack in the presence of a hot spot by two parallel arrays of pointlike Josephson junctions and an additional shunt resistor in parallel. Heat diffusion is taken into account by thermally coupling all elements to a bath at temperature T_b. We present current-voltage characteristics of the coupled system and calculations of the linewidth of the radiation as a function of T_b. In the presence of a spatial gradient of the junction parameters critical current and resistance, the linewidth deceases with increasing T_b, similar to the experimental observation., Comment: accepted in PRB

We have studied experimentally and numerically temperature profiles and the formation of hot spots in intrinsic Josephson junction stacks in Bi2Sr2CaCu2O8 (BSCCO). The superconducting stacks are biased in a state where all junctions are resistive. The formation of hot spots in this system is shown to arise mainly from the strongly negative temperature coefficient of the c-axis resistivity of BSCCO at low temperatures. This leads to situations where the maximum temperature in the hot spot can be below or above the superconducting transition temperature Tc. The numerical simulations are in good agreement with the experimental observations.

We report on measurements of the linewidth {\Delta}f of THz radiation emitted from intrinsic Josephson junction stacks, using a Nb/AlN/NbN integrated receiver for detection. Previous resolution limited measurements indicated that {\Delta}f may be below 1 GHz - much smaller than expected from a purely cavity-induced synchronization. While at low bias we found {\Delta}f to be not smaller than ? 500 MHz, at high bias, where a hotspot coexists with regions which are still superconducting, {\Delta}f turned out to be as narrow as 23 MHz. We attribute this to the hotspot acting as a synchronizing element. {\Delta}f decreases with increasing bath temperature, a behavior reminiscent of motional narrowing in NMR or ESR, but hard to explain in standard electrodynamic models of Josephson junctions., Comment: 4 figures, 5 pages

At high enough input power in stacks of Bi_2Sr_2CaCu_2O8 intrinsic Josephson junctions a hot spot (a region heated to above the superconducting transition temperature) coexists with regions still in the superconducting state. In the ``cold'' regions cavity resonances can occur, synchronizing the ac Josephson currents and giving rise to strong coherent THz emission. We investigate the interplay of hot spots and standing electromagnetic waves by low temperature scanning laser microscopy and THz emission measurements, using stacks of various geometries. For a rectangular and a arrow-shaped structure we show that the standing wave can be turned on and off in various regions of the stack structure, depending on the hot spot position. We also report on standing wave and hot spot formation in a disk shaped mesa structure.

We report on THz emission measurements and low temperature scanning laser imaging of Bi_2Sr_2CaCu_2O_8 intrinsic Josephson junction stacks. Coherent emission is observed at large dc input power, where a hot spot and a standing wave, formed in the "cold" part of the stack, coexist. By varying the hot spot size the cavity resonance frequency and the emitted radiation can be tuned. The linewidth of radiation is much smaller than expected from the quality factor of the cavity mode excited. Thus, an additional mechanism of synchronization seems to play a role, possibly arising from nonequilibrium processes at the hot spot edge., Comment: 4.1 pages, 5 figures

State education agencies (SEAs) are reframing their work to be more coordinated and strategic but talent in most SEAs continues to be in large part defined by federal programs and oriented toward the routines of compliance. Existing talent pipelines in SEAs are rooted in the historic functions of administering federal programs and doing little more. But, in an era of education reform, tight state budgets, and increasing public expectations, SEAs face new demands to: (1) More efficiently manage SEA initiatives and assess progress toward goals; (2) Improve data systems to more precisely track performance of students in local education agencies (LEAs) and schools; (3) Intensify and diversify efforts to support the improvement of LEAs and schools; and (4) Encourage and evaluate innovative models of teaching, learning, and school design.

Let B be a reductive Lie subalgebra of a semi-simple Lie algebra of the same rank both over the complex numbers. To each finite dimensional irreducible representation $V_\lambda$ of F we assign a multiplet of irreducible representations of B with m elements in each multiplet, where m is the index of the Weyl group of B in the Weyl group of F. We obtain a generalization of the Weyl character formula; our formula gives the character of $V_\lambda$ as a quotient whose numerator is an alternating sum of the characters in the multiplet associated to $V_\lambda$ and whose denominator is an alternating sum of the characters of the multiplet associated to the trivial representation of F., Comment: 5 pages, uses article.sty