Quantitative magneto-mechanical detection and control of the Barkhausen effect

Coherent correlation imaging for resolving fluctuating states of matter

Fluctuations and stochastic transitions are ubiquitous in nanometre-scale systems, especially in the presence of disorder. However, their direct observation has so far been impeded by a seemingly fundamental, signal-limited compromise between spatial and temporal resolution. Here we develop coherent correlation imaging (CCI) to overcome this dilemma. Our method begins by classifying recorded camera frames in Fourier space. Contrast and spatial resolution emerge by averaging selectively over same-state frames. Temporal resolution down to the acquisition time of a single frame arises independently from an exceptionally low misclassification rate, which we achieve by combining a correlation-based similarity metric^1,2 with a modified, iterative hierarchical clustering algorithm^3,4. We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state with nanometre-scale resolution. We uncover an intricate network of transitions between more than 30 discrete states. Our spatiotemporal data enable us to reconstruct the pinning energy landscape and to thereby explain the dynamics observed on a microscopic level. CCI massively expands the potential of emerging high-coherence X-ray sources and paves the way for addressing large fundamental questions such as the contribution of pinning^5-8 and topology^9-12 in phase transitions and the role of spin and charge order fluctuations in high-temperature superconductivity^13,14.

Causal analysis and visualization of magnetization reversal using feature extended landau free energy

The magnetization reversal in nanomagnets is causally analyzed using an extended Landau free-energy model. This model draws an energy landscape in the information space using physics-based features. Thus, the origin of the magnetic effect in macroscopic pinning phenomena can be identified. The microscopic magnetic domain beyond the hierarchy can be explained using energy gradient analysis and its decomposition. Structural features from the magnetic domains are extracted using persistent homology. Extended energy is visualized using ridge regression, principal component analysis, and Hadamard products. We found that the demagnetization energy concentration near a defect causes the demagnetization effect, which quantitatively dominates the pinning phenomenon. The exchange energy inhibits pinning, promotes saturation, and shows slight interactions with the defect. Furthermore, the energy distributions are visualized in real space. Left-position defects reduce the energy barrier and are useful for the topological inverse design of recording devices.

Magnetic Barkhausen Noise Transient Analysis for Microstructure Evolution Characterization with Tensile Stress in Elastic and Plastic Status

Stress affects the microstructure of the material to influence the durability and service life of the components. However, the previous work of stress measurement lacks quantification of the different variations in time and spatial features of micromagnetic properties affected by stress in elastic and plastic ranges, as well as the evolution of microstructure. In this paper, microstructure evolution under stress in elastic and plastic ranges is evaluated by magnetic Barkhausen noise (MBN) transient analysis. Based on a J-A model, the duration and the intensity are the eigenvalues for MBN transient analysis to quantify transient size and number of Barkhausen events under stress. With the observation of domain wall (DW) distribution and microstructure, the correlation between material microstructure and MBN transient eigenvalues is investigated to verify the ability of material status evaluation on the microscopic scale of the method. The results show that the duration and the intensity have different change trends in elastic and plastic ranges. The eigenvalue fusion of the duration and intensity distinguishes the change in microstructure under the stress in elastic and plastic deformation. The appearance of grain boundary (GB) migration and dislocation under the stress in the plastic range makes the duration and the intensity higher on the GB than those inside the grain. Besides, the reproducibility of the proposed method is investigated by evaluating microstructure evolution for silicon steel sheet and Q235 steel sheet. The proposed method investigates the correlation between the microstructure and transient micromagnetic properties, which has the potential for stress evaluation in elastic and plastic ranges for industrial materials.

Precision Magnetometers for Aerospace Applications: A Review

Aerospace technologies are crucial for modern civilization; space-based infrastructure underpins weather forecasting, communications, terrestrial navigation and logistics, planetary observations, solar monitoring, and other indispensable capabilities. Extraplanetary exploration—including orbital surveys and (more recently) roving, flying, or submersible unmanned vehicles—is also a key scientific and technological frontier, believed by many to be paramount to the long-term survival and prosperity of humanity. All of these aerospace applications require reliable control of the craft and the ability to record high-precision measurements of physical quantities. Magnetometers deliver on both of these aspects and have been vital to the success of numerous missions. In this review paper, we provide an introduction to the relevant instruments and their applications. We consider past and present magnetometers, their proven aerospace applications, and emerging uses. We then look to the future, reviewing recent progress in magnetometer technology. We particularly focus on magnetometers that use optical readout, including atomic magnetometers, magnetometers based on quantum defects in diamond, and optomechanical magnetometers. These optical magnetometers offer a combination of field sensitivity, size, weight, and power consumption that allows them to reach performance regimes that are inaccessible with existing techniques. This promises to enable new applications in areas ranging from unmanned vehicles to navigation and exploration.

Time-Response-Histogram-Based Feature of Magnetic Barkhausen Noise for Material Characterization Considering Influences of Grain and Grain Boundary under In Situ Tensile Test

Stress is the crucial factor of ferromagnetic material failure origin. However, the nondestructive test methods to analyze the ferromagnetic material properties’ inhomogeneity on the microscopic scale with stress have not been obtained so far. In this study, magnetic Barkhausen noise (MBN) signals on different silicon steel sheet locations under in situ tensile tests were detected by a high-spatial-resolution magnetic probe. The domain-wall (DW) motion, grain, and grain boundary were detected using a magneto-optical Kerr (MOKE) image. The time characteristic of DW motion and MBN signals on different locations was varied during elastic deformation. Therefore, a time-response histogram is proposed in this work to show different DW motions inside the grain and around the grain boundary under low tensile stress. In order to separate the variation of magnetic properties affected by the grain and grain boundary under low tensile stress corresponding to MBN excitation, time-division was carried out to extract the root-mean-square (RMS), mean, and peak in the optimized time interval. The time-response histogram of MBN evaluated the silicon steel sheet’s inhomogeneous material properties, and provided a theoretical and experimental reference for ferromagnetic material properties under stress.

Probing the pinning strength of magnetic vortex cores with sub-nanometer resolution

Understanding interactions of magnetic textures with defects is crucial for applications such as racetrack memories or microwave generators. Such interactions appear on the few nanometer scale, where imaging has not yet been achieved with controlled external forces. Here, we establish a method determining such interactions via spin-polarized scanning tunneling microscopy in three-dimensional magnetic fields. We track a magnetic vortex core, pushed by the forces of the in-plane fields, and discover that the core (~ 10⁴ Fe-atoms) gets successively pinned close to single atomic-scale defects. Reproducing the core path along several defects via parameter fit, we deduce the pinning potential as a mexican hat with short-range repulsive and long-range attractive part. The approach to deduce defect induced pinning potentials on the sub-nanometer scale is transferable to other non-collinear spin textures, eventually enabling an atomic scale design of defect configurations for guiding and reliable read-out in race-track type devices.

Magnetic vortices such as skyrmions are promising for spintronic applications, however, little is known about the pinning effects strongly influencing their dynamics. Here, the authors map the interaction potential between defects and vortex cores down to the sub-nanometer scale enabling the better control of these magnetic textures.

Quantum Acoustomechanics with a Micromagnet

We show theoretically how to strongly couple the center-of-mass motion of a micromagnet in a harmonic potential to one of its acoustic phononic modes. The coupling is induced by a combination of an oscillating magnetic field gradient and a static homogeneous magnetic field. The former parametrically couples the center-of-mass motion to a magnonic mode while the latter tunes the magnonic mode in resonance with a given acoustic phononic mode. The magnetic fields can be adjusted to either cool the center-of-mass motion to the ground state or to enter into the strong quantum coupling regime. The center of mass can thus be used to probe and manipulate an acoustic mode, thereby opening new possibilities for out-of-equilibrium quantum mesoscopic physics. Our results hold for experimentally feasible parameters and apply to levitated micromagnets as well as micromagnets deposited on a clamped nanomechanical oscillator.

Antiferromagnetic skyrmions overcoming obstacles in a racetrack

Topological objects interacting with lattice defects is an important topic in condensed matter physics. In this paper, we would like to explore the ballistic trajectory of an antiferromagnetic skyrmion in a racetrack to study processes such as collisions of skyrmions and holes in the magnetic sample. The skyrmion is impelled against the hole-obstacle by means of a spin polarized current. Depending on the skyrmion velocity (associated to the strength of the applied current) and the type of collision (frontal or lateral), it will be captured, scattered or completely destroyed by the hole. In some cases, this obstacle can shift the skyrmion center from a straight line to another one, and it appears as an effective way of manipulating skyrmion trajectories and dynamics.

Three-dimensional nanomagnetism

Magnetic nanostructures are being developed for use in many aspects of our daily life, spanning areas such as data storage, sensing and biomedicine. Whereas patterned nanomagnets are traditionally two-dimensional planar structures, recent work is expanding nanomagnetism into three dimensions; a move triggered by the advance of unconventional synthesis methods and the discovery of new magnetic effects. In three-dimensional nanomagnets more complex magnetic configurations become possible, many with unprecedented properties. Here we review the creation of these structures and their implications for the emergence of new physics, the development of instrumentation and computational methods, and exploitation in numerous applications.

Nanoscale magnetic devices play a key role in modern technologies but current applications involve only 2D structures like magnetic discs. Here the authors review recent progress in the fabrication and understanding of 3D magnetic nanostructures, enabling more diverse functionalities.

Nanocavity optomechanical torque magnetometry and radiofrequency susceptometry

Nanophotonic optomechanical devices allow the observation of nanoscale vibrations with a sensitivity that has dramatically advanced the metrology of nanomechanical structures and has the potential to impact studies of nanoscale physical systems in a similar manner. Here we demonstrate this potential with a nanophotonic optomechanical torque magnetometer and radiofrequency (RF) magnetic susceptometer. Exquisite readout sensitivity provided by a nanocavity integrated within a torsional nanomechanical resonator enables observations of the unique net magnetization and RF-driven responses of single mesoscopic magnetic structures in ambient conditions. The magnetic moment resolution is sufficient for the observation of Barkhausen steps in the magnetic hysteresis of a lithographically patterned permalloy island. In addition, significantly enhanced RF susceptibility is found over narrow field ranges and attributed to thermally assisted driven hopping of a magnetic vortex core between neighbouring pinning sites. The on-chip magnetosusceptometer scheme offers a promising path to powerful integrated cavity optomechanical devices for the quantitative characterization of magnetic micro- and nanosystems in science and technology.

Approaching the standard quantum limit of mechanical torque sensing

Reducing the moment of inertia improves the sensitivity of a mechanically based torque sensor, the parallel of reducing the mass of a force sensor, yet the correspondingly small displacements can be difficult to measure. To resolve this, we incorporate cavity optomechanics, which involves co-localizing an optical and mechanical resonance. With the resulting enhanced readout, cavity-optomechanical torque sensors are now limited only by thermal noise. Further progress requires thermalizing such sensors to low temperatures, where sensitivity limitations are instead imposed by quantum noise. Here, by cooling a cavity-optomechanical torque sensor to 25 mK, we demonstrate a torque sensitivity of 2.9 yNm/. At just over a factor of ten above its quantum-limited sensitivity, such cryogenic optomechanical torque sensors will enable both static and dynamic measurements of integrated samples at the level of a few hundred spins.

Cavity optomechanics enables measurement of torque at levels unattainable by previous techniques, but the main obstacle to improved sensitivity is thermal noise. Here the authors present cryogenic measurement of a cavity-optomechanical torsional resonator with unprecedented torque sensitivity of 2.9 yNm/√Hz.

Optomechanical measurement of photon spin angular momentum and optical torque in integrated photonic devices

Photons carry linear momentum and spin angular momentum when circularly or elliptically polarized. During light-matter interaction, transfer of linear momentum leads to optical forces, whereas transfer of angular momentum induces optical torque. Optical forces including radiation pressure and gradient forces have long been used in optical tweezers and laser cooling. In nanophotonic devices, optical forces can be significantly enhanced, leading to unprecedented optomechanical effects in both classical and quantum regimes. In contrast, to date, the angular momentum of light and the optical torque effect have only been used in optical tweezers but remain unexplored in integrated photonics. We demonstrate the measurement of the spin angular momentum of photons propagating in a birefringent waveguide and the use of optical torque to actuate rotational motion of an optomechanical device. We show that the sign and magnitude of the optical torque are determined by the photon polarization states that are synthesized on the chip. Our study reveals the mechanical effect of photon's polarization degree of freedom and demonstrates its control in integrated photonic devices. Exploiting optical torque and optomechanical interaction with photon angular momentum can lead to torsional cavity optomechanics and optomechanical photon spin-orbit coupling, as well as applications such as optomechanical gyroscopes and torsional magnetometry.

Creep turns linear in narrow ferromagnetic nanostrips

The motion of domain walls in magnetic materials is a typical example of a creep process, usually characterised by a stretched exponential velocity-force relation. By performing large-scale micromagnetic simulations, and analyzing an extended 1D model which takes the effects of finite temperatures and material defects into account, we show that this creep scaling law breaks down in sufficiently narrow ferromagnetic strips. Our analysis of current-driven transverse domain wall motion in disordered Permalloy nanostrips reveals instead a creep regime with a linear dependence of the domain wall velocity on the applied field or current density. This originates from the essentially point-like nature of domain walls moving in narrow, line- like disordered nanostrips. An analogous linear relation is found also by analyzing existing experimental data on field-driven domain wall motion in perpendicularly magnetised media.

Torsional optical spring effect in coupled nanobeam photonic crystal cavities

Compared to probe-tuned optomechanical cavity systems, coupled cavity systems have the merit of having much stronger optomechanical interactions. However, to date, the torsional optomechanical effects of coupled cavities have rarely been investigated. In this Letter, we report a torsional optical spring effect in coupled nanobeam photonic crystal cavities. One of the cavities is suspended by a multi-degree-of-freedom spring mechanism that supports torsional vibration modes. The cavities' light field acts in reverse on the selected torsional mode, thus generating a torsional optical spring effect. The experimental results show that the third-order torsional mode of the spring mechanism is optically stiffened and a maximum frequency increase of 77.1 Hz is obtained. The device provides a novel configuration for the optomechanical design of a new degree of freedom (torsional motion) and the coupled cavities are favorable for strong optomechanical interactions in the torsional direction.

Optomechanical photon shuttling between photonic cavities

Mechanical motion of photonic devices driven by optical forces provides a profound means of coupling between optical fields. The current focus of these optomechanical effects has been on cavity optomechanics systems in which co-localized optical and mechanical modes interact strongly to enable wave mixing between photons and phonons, and backaction cooling of mechanical modes. Alternatively, extended mechanical modes can also induce strong non-local effects on propagating optical fields or multiple localized optical modes at distances. Here, we demonstrate a multicavity optomechanical device in which torsional optomechanical motion can shuttle photons between two photonic crystal nanocavities. The resonance frequencies of the two cavities, one on each side of this 'photon see-saw', are modulated antisymmetrically by the device's rotation. Pumping photons into one cavity excites optomechanical self-oscillation, which strongly modulates the inter-cavity coupling and shuttles photons to the other empty cavity during every oscillation cycle in a well-regulated fashion.

Propagation of magnetic vortices using nanocontacts as tunable attractors

Magnetic vortices in thin films are in-plane spiral spin configurations with a core in which the magnetization twists out of the film plane. Vortices result from the competition between atomic-scale exchange forces and long-range dipolar interactions. They are often the ground state of magnetic dots, and have applications in medicine, microwave generation and information storage. The compact nature of the vortex core, which is 10-20 nm wide, makes it a suitable probe of magnetism at the nanoscale. However, thus far the positioning of a vortex has been possible only in confined structures, which prevents its transport over large distances. Here we show that vortices can be propagated in an unconstrained system that comprises electrical nanocontacts (NCs). The NCs are used as tunable vortex attractors in a manner that resembles the propelling of space craft with gravitational slingshots. By passing current from the NCs to a ferromagnetic film, circulating magnetic fields are generated, which nucleate the vortex and create a potential well for it. The current becomes spin polarized in the film, and thereby drives the vortex into gyration through spin-transfer torques. The vortex can be guided from one NC to another by tuning attractive strengths of the NCs. We anticipate that NC networks may be used as multiterminal sources of vortices and spin waves (as well as heat, spin and charge flows) to sense the fundamental interactions between physical objects and fluxes of the next-generation spintronic devices.

Probing the anharmonicity of the potential well for a magnetic vortex core in a nanodot

The anharmonicity of the potential well confining a magnetic vortex core in a nanodot is measured dynamically with a magnetic resonance force microscope (MRFM). The stray field of the MRFM tip is used to displace the equilibrium core position away from the nanodot center. The anharmonicity is then inferred from the relative frequency shift induced on the eigenfrequency of the vortex core translational mode. An analytical framework is proposed to extract the anharmonic coefficient from this variational approach. Traces of these shifts are recorded while scanning the tip above an isolated nanodot, patterned out of a single crystal FeV film. We observe a +10% increase of the eigenfrequency when the equilibrium position of the vortex core is displaced to about one-third of its radius. This calibrates the tunability of the gyrotropic mode by external magnetic fields.

Universal properties of magnetization dynamics in polycrystalline ferromagnetic films

We investigate the scaling behavior in the statistical properties of Barkhausen noise in ferromagnetic films. We apply the statistical treatment usually employed for bulk materials in experimental Barkhausen noise time series measured with the traditional inductive technique in polycrystalline ferromagnetic films having different thickness from 100 to 1000 nm and determine the scaling exponents. Based on this procedure, we group the samples in a single universality class, since the scaling behavior of Barkhausen avalanches is characterized by exponents τ∼1.5, α∼2.0, and 1/σνz∼ϑ∼2.0 for all the films. We interpret these results in terms of theoretical models and provide experimental evidence that a well-known mean-field model for the dynamics of a ferromagnetic domain wall in three-dimensional ferromagnets can be extended for films. We identify that the films present an universal three-dimensional magnetization dynamics, governed by long-range dipolar interactions, even at the smallest thicknesses, indicating that the two-dimensional magnetic behavior commonly verified for films cannot be generalized for all thickness ranges.