Local Magnetic Direction Research Articles

Chirality Control of Magnetic Vortices in Ferromagnetic Disk–Nanowire System

The results of experimental studies and micromagnetic modeling of magnetic states in a one-dimensional array are presented. The array has the form of a chain of ferromagnetic disks coupled with a ferromagnetic nanowire made of the same material. The disks are located on opposite sides of the nanowire, which makes it possible to obtain distributions when the chiralities of the magnetic vortex shells in neighboring disks alternate, which can find application in vortex spin nanooscillators. Using the application in situ of a magnetic field to an excited objective lens using Lorentz transmission electron microscopy, it is shown that in this system it is possible to control the chiralities of the shells of magnetic vortices, which is realized by magnetization in the sample plane along various azimuthal directions. When wire magnetized along a nanowire, vortex states with opposite chiralities are realized in disks located on opposite sides of it. An antivortex is formed in the nanowire itself at the boundary with the disk, since the local direction of magnetization in the wire and in the disk are anticollinear. When magnetized perpendicular to the nanowire, states with the same chirality are realized in all disks. In this case, two perpendicular domain walls are formed between the disks in the nanowire, and the vortex in the disk is shifted to one of the edges along the nanowire.

Transformations of borehole magnetic data in the frequency domain and estimation of the total magnetization direction: A case study from the Mengku iron-ore deposit, Northwest China

Borehole magnetic prospecting measures the three components of the magnetic field and is sensitive to the vertical depth of the magnetic source, which plays an important role in deep mineral exploration. Magnetic field transformations in the frequency domain constitute common and important processing for ground and airborne data but are rarely applied to borehole magnetic data. Here, we deduce component transformation and magnetization-direction transformation formulas for borehole data. It is found that the transformation factors differ from those of ground and airborne data. The new formulas depend on the position of the drillholes. The transformed data are then used to estimate the total magnetization direction by computing the correlation coefficient between the transformed components and the amplitude anomaly. The advantages of this method are that the borehole data yield a local and accurate magnetization direction and the total amplitude anomaly is computed directly from the individual anomalies in the observed components. The frequency-domain transformation is tested on the synthetic data, and the estimated directions are consistent with the true values. The processing procedure is applied to borehole data collected at the Mengku iron-ore deposit in Northwest China, where magnetic surveys from 55 boreholes have been acquired. The estimated magnetization directions yield good approximations of the results from the ground magnetic data and the physical property measurements of rock samples.

Quartic asymmetric exchange for two-dimensional ferromagnets with trigonal prismatic symmetry

We suggest a possible origin of noncollinear magnetic textures in ferromagnets (FMs) with the $D_{3h}$ point group symmetry. The suggested mechanism is different from the Dzyaloshinskii-Moriya interaction (DMI) and its straightforward generalizations. The considered symmetry class is important because a large fraction of all single-layer intrinsic FMs should belong to it. In particular, so does a monolayer Fe$_3$GeTe$_2$. At the same time, DMI vanishes identically in materials described by this point group, in the continuous limit. We use symmetry analysis to identify the only possible contribution to the free energy density in two dimensions that is of the fourth order with respect to the local magnetization direction and linear with respect to its spatial derivatives. This contribution predicts long-range conical magnetic spirals with both the average magnetization and the average chirality dependent on the spiral propagation direction. We relate the predicted spirals to a recent experiment on Fe$_3$GeTe$_2$. Finally, we demonstrate that, for easy-plane materials, the same mechanism may stabilize bimerons.

Helical phase in two-dimensional magnets due to four-spin interactions

We demonstrate that in ferromagnets with the D3h point group of symmetry a possible origin of phase transition from a collinear ferromagnetic state to a non-collinear state can be the fourth order contributions to the free energy density that are allowed by this point group of symmetry. At the same time, Dzyaloshinskii-Moria interaction vanishes in such materials. Via symmetry analysis we derive seven possible fourth order contributions to the free energy density with respect to the unit vector of the local magnetization direction but only two of them can be considered as independent. Moreover, for two-dimensional systems only one survives. Considered symmetry class is essential because a large group of two-dimensional intrinsic ferromagnets belongs to it, for example a monolayer Fe3GeTe2. The four-spin chiral exchange does also manifest itself in peculiar magnon spectra and favors spin waves.

Dynamical and current-induced Dzyaloshinskii-Moriya interaction: Role for damping, gyromagnetism, and current-induced torques in noncollinear magnets

Both applied electric currents and magnetization dynamics modify the Dzyaloshinskii-Moriya interaction (DMI), which we call current-induced DMI (CIDMI) and dynamical DMI (DDMI), respectively. We report a theory of CIDMI and DDMI. The inverse of CIDMI consists in charge pumping by a time-dependent gradient of magnetization $\partial^2 M(r,t)/\partial r\partial t$, while the inverse of DDMI describes the torque generated by $\partial^2 M(r,t)/\partial r\partial t$. In noncollinear magnets CIDMI and DDMI depend on the local magnetization direction. The resulting spatial gradients correspond to torques that need to be included into the theories of Gilbert damping, gyromagnetism, and current-induced torques (CITs) in order to satisfy the Onsager reciprocity relations. CIDMI is related to the modification of orbital magnetism induced by magnetization dynamics, which we call dynamical orbital magnetism (DOM), and spatial gradients of DOM contribute to charge pumping. We present applications of this formalism to the CITs and to the torque-torque correlation in textured Rashba ferromagnets.

Chiral ferromagnetism beyond Lifshitz invariants

We consider a contribution $w_{\text{ch}}$ to the micromagnetic energy density that is linear with respect to the first spatial derivatives of the local magnetization direction. For a generalized 2D Rashba ferromagnet, we present a microscopic analysis of this contribution and, in particular, demonstrate that it cannot be expressed through Lifshitz invariants beyond the linear order in the spin-orbit coupling (SOC) strength. Terms in $w_{\text{ch}}$ beyond Lifshitz invariants emerge as a result of spin rotation symmetry breaking caused by SOC. Effects of these terms on the phase diagram of magnetic states and spin-wave dispersion are discussed. Finally, we present a classification of terms in $w_{\text{ch}}$, allowed by symmetry, for each crystallographic point group.

Laser-induced spin dynamics in the iron-yttrium garnet film doped with Si ions

A continuous increase in the volume of stored and processed data leads to stricter requirements for storage media. The most common information storage technology is currently based on magnetic materials, where information in the form of 0 and 1 is associated with the local direction of magnetization, determined by the external magnetic field created by the recording device. It is known that this approach has fundamental limitations on the recording speed which is almost achieved. The requirements for energy efficiency of storage media are also being made stricter. These circumstances lead to the development of alternative approaches to recording information. One of these approaches has been demonstrated in the field of ultrafast opto-magnetism, which has been booming over the past 20 years. It consists in recording information with short optical pulses without the application of an external magnetic field. However, it requires fundamental studies of physical processes, as well as materials, in which magnetization can be controlled by short optical pulses. In this paper, we consider the spin dynamics in a magnetic dielectric: a film of iron - yttrium garnet doped with silicon. The studies were carried out using the pump – probe technique over a time range of up to 800 ns. The spot size was 30 μm, the optical pulse duration was 35 fs, and the pump fluence was about 50 mJ/cm 2 . It is shown that a change in the magnetocrystalline anisotropy constants due to the action of a pump pulse on the structure causes a long-decaying magnetization precession with a period of about 200 ps. The dependences of the amplitude, phase, and decay of the precession on the magnitude of the external magnetic field in the range up to 1.84 kOe were obtained and analyzed. The studied processes can be considered on the basis of the Landau-Lifshitz-Gilbert model, and be of interest for the optical switching of magnetization, as well as the creation of various spintronic devices. It is shown that films of iron-yttrium garnet doped with silicon are a promising material for magnetic information carriers based on ultrafast opto-magnetism.

A Stable Adaptive Observer for Hard-Iron and Soft-Iron Bias Calibration and Compensation for Two-Axis Magnetometers: Theory and Experimental Evaluation

This letter addresses the problem of on-line estimation and compensation of the hard-iron and soft-iron biases of a 2-axis magnetometer under dynamic motion, utilizing only biased measurements from a 2-axis magnetometer. The proposed adaptive observer formulates the relation between the true magnetic field vector and the magnetometer measurements as an algebraic system where the unknown biases enter linearly. The observer is shown to be globally stable. When the magnetometer measurements are persistently exciting (PE), the system is shown to be globally asymptotically stable, and the biases are shown to converge to their true values. The estimated biases are used to provide a calibrated magnetic field direction vector which is utilized to estimate magnetic geodetic heading. The adaptive observer is evaluated in a numerical simulation and a full-scale vehicle trial. For the proposed observer: $(i)$ knowledge of the instrument attitude is not required for sensor bias estimation, $(ii)$ zero a priori knowledge of the local magnetic field vector magnitude or vector direction is needed, $(iii)$ the system is shown to be globally stable, $(iv)$ the error system is shown to be globally asymptotically stable when the measured magnetometer signal is PE. $(v)$ magnetometer hard-iron and soft-iron bias compensation is shown to dramatically improve dynamic heading estimation accuracy.

Skyrmion–electron interaction in the separated spin-up and spin-down quantum hydrodynamics approach

Abstract The Berry gauge field associated with adiabatic quantum evolution represents a very interesting area of research, especially for the description of non-relativistic fermions coupled to a skyrmion texture. We construct a quantum hydrodynamics model that describes the electron–skyrmion interactions, with separate descriptions of spin-up and spin-down electrons as two different fluids. The quantum effects, represented by the quantum Bohm potential, are taken into account. We investigate the electron gas moving in a smooth magnetic texture, where the magnetic moments adjust to the local magnetization direction of the skyrmion, and derive the equations of motion and evolution of spin density for two fluids of electrons in the emergent gauge fields. Applying the separated spin evolution quantum hydrodynamics to the 2D electron gas, traveling on the background of the Berry gauge field in plane samples, located in an external magnetic field, we predict a wave of a new kind in the electron gas. This novel wave appears as an influence of emergent fields and quantum effects.

Magnetometer Calibration and Field Mapping through Thin Plate Splines.

While the undisturbed Earth’s magnetic field represents a fundamental information source for orientation purposes, magnetic distortions have been mostly considered as a source of error. However, when distortions are temporally stable and spatially distinctive, they could provide a unique magnetic landscape that can be used in different applications, from indoor localization to sensor fusion algorithms for attitude estimation. The main purpose of this work, therefore, is to present a method to characterize the 3D magnetic vector in every point of the measurement volume. The possibility of describing the 3D magnetic field map through Thin Plate Splines (TPS) interpolation is investigated and demonstrated. An algorithm for the simultaneous estimation of the parameters related to magnetometer calibration and those describing the magnetic map, is proposed and tested on both simulated and real data. Results demonstrate that an accurate description of the local magnetic field using TPS interpolation is possible. The proposed procedure leads to errors in the estimation of the local magnetic direction with a standard deviation lower than 1 degree. Magnetometer calibration and magnetic field mapping could be integrated into different algorithms, for example to improve attitude estimation in highly distorted environments or as an aid to indoor localization.

Voltage control of magnetic single domains in Ni discs on ferroelectric BaTiO3

For 1 µm-diameter Ni discs on a BaTiO3 substrate, the local magnetization direction is determined by ferroelectric domain orientation as a consequence of growth strain, such that single-domain discs lie on single ferroelectric domains. On applying a voltage across the substrate, ferroelectric domain switching yields non-volatile magnetization rotations of 90°, while piezoelectric effects that are small and continuous yield non-volatile magnetization reversals that are non-deterministic. This demonstration of magnetization reversal without ferroelectric domain switching implies reduced fatigue, and therefore represents a step towards applications.

Detailed modeling of local anisotropy and transverse K u interplay regarding hysteresis loop in FeCuNbSiB nanocrystalline ribbons

This article focuses on the modeling of the hysteresis loop featured by Fe-Cu-Nb-Si-B nanocrystalline alloys with transverse induced anisotropy. The magnetization reversal process of a magnetic correlated volume (CV), characterized by the induced anisotropy Ku, and a deviation of the local easy magnetization direction featuring the effect of a local incoherent anisotropy Ki, is analyzed, taking account of magnetostatic interactions. Solving the equations shows that considering a unique typical kind of CV does not enable accounting for both the domain pattern and the coercivity. Actually, the classical majority CVs obeying the random anisotropy model explains well the domain pattern but considering another kind of CVs, minority, mingled with classical ones, featuring a magnitude of Ki comparable to Ku, is necessary to account for coercivity. The model has been successfully compared with experimental data.

Development of Kerr Effect Microscope with Detection of Local Magnetization Direction and Its Application to Spatial Magnetic Field Detection

Development of Kerr Effect Microscope with Detection of Local Magnetization Direction and Its Application to Spatial Magnetic Field Detection

Photographic observation of magnetic domain structure with three-dimensional local magnetization direction

The direction of magnetization of a magnetic material is possibly oriented three-dimensionally because of the presence of magnetic anisotropy field, self-demagnetizing field, and stray field. Therefore, the three-dimensional detection of the direction of magnetization is required. The method of magnetic domain observation by photographic imaging utilizing the Kerr effect is widely used. If the perpendicular magnetization components exist, there is a problem that obliquely incident light has superimposed longitudinal Kerr and polar Kerr effects. To perform the three-dimensional detection of magnetization direction, it is necessary to eliminate the influence of the polar Kerr effect from the Kerr effect of obliquely incident light. We report the photographic observation of the magnetic domain structure and the detection of the three-dimensional local magnetization direction using the Kerr effect, applying only an in-plane saturation magnetic field.

Centimeter-order view for magnetic domain imaging with local magnetization direction by longitudinal Kerr effect

An observation system of centimeter-order of view of magnetic domain with local magnetization direction was developed by designing a telecentric optical system of finite design through the extension of microscope technology. The field of view realized in the developed system was 1.40 × 1.05 cm as suppressing defocus and distortion. Detection of the local magnetization direction has become possible by longitudinal Kerr observation from the orthogonal two directions. This system can be applied to the domain observation of rough surface samples and time resolved analysis for soft magnetic materials such as amorphous foil strips and soft magnetic thin films.

Spin-sensitive shape asymmetry of adatoms on noncollinear magnetic substrates

The spin-resolved density of states of Co atoms on a noncollinear magnetic support displays a distinct shape contrast, which is superimposed on the regular height contrast in spin-polarized scanning tunneling microscopy. The apparent atom height follows the well-known cosine dependence on the angle formed by the tip and adatom local magnetization directions, whereas the shape contrast exhibits a sine dependence. We explain this effect in terms of a noncollinear spin density induced by the substrate, which in our case is the spin spiral of the Mn monolayer on W(110). The two independent contrast channels, apparent height and shape, are identified with the Co magnetization projections onto two orthogonal axes. As a result, all components of the overall atom magnetic moment vector can be determined with a single spin-sensitive tip in the absence of an external magnetic field. This result should be general for any atom deposited on noncollinear magnetic layers.

Метод полевого трассирования охранных зон проектируемых ЛЭП относительно магнитных меридианов местного геомагнитного поля

Abstract: There is a possibility of using the local magnetic field of the Earth in field tracing linear objects in the course of engineering survey. You can find the results of the field of tracing in the Saint-Petersburg region, which are projected by Electricity Transmission Line 110 kV using the local magnetic azimuth direction angle instead of the local coordinate system. There is a possibility of appraisal of using these works for an international model of the main magnetic field of the Earth IGRF-11 on the basis of the results obtained.

Real-space Berry phases: Skyrmion soccer (invited)

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.

Study of Ferrite by Mössbauer Spectroscopy Zinc-Iron: the Influence of Directional Order

The Mossbauer spectroscopy has revealed the directional order that forms in the ferrites due to anisotropic distribution of Fe2+ and Fe3+ to the local direction of magnetization. We undertook to conduct a study on ferrites of composition: Fe3x2(1+x) Fe2+0.2-2.7x Zn0.8-0.3x ◊ = vacancies, 0 < x ≤ 0.07. The spectra were made on two kinds of samples: quenched and slowly cooled at different temperatures. The results show that it is possible to distinguish at least three sites according to the values of x: an octahedral site (O) occupied by the Fe3+ ion, which will be designated by (Fe 3+)O, a tetrahedral site (T) or (Fe2+)T, and a tetrahedral site (T) or (Fe3+)T. The variation of intensity of the site (Fe3+)O according to x, and the differences of variation according to the cooling conditions suggest the existence of a partial order among the nearest neighbors of the site (Fe3+)O of an ion (Fe3+)T, which will make good account of the directional order.

The alphabet of spin in nanostructures

In a ferromagnetic nanostructure, a domain wall is a transition region that separates two different but uniformly magnetized regions. Moving a domain wall with an electrical current instead of a magnetic field is of great appeal to researchers; it could lead to spin-based devices in which information is stored and processed in domain walls. Such storage, memory, and logic devices could potentially be more flexible, efficient, and scalable. The mechanism underlying this motion is called the spin-transfer torque, in which conduction electrons transfer a spin angular momentum to the local magnetization. The torque comes in an adiabatic and a so-called nonadiabatic part. There is much debate regarding the magnitude [1–5], microscopic origin [6–8], and even the existence [9] of the nonadiabatic term. In a paper in Physical Review Letters, Lutz Heyne and co-workers at the Universitat Konstanz in Germany, along with collaborators in Switzerland, the US, and Germany [10], tell us how they measure the torque with a scheme [11] that involves displacing a single magnetic vortex by electrical current. They find a surprisingly large nonadiabaticity—favorable for spintronic devices based on domain walls—that not only dictates how quickly a domain wall moves but allows it to do so in the absence of applied magnetic fields, even for very small currents. An intuitive phenomenological theory addresses the underlying physics. The Landau-Lifshitz-Gilbert (LLG) equation describes the evolution of magnetization in time: the magnetization vector precesses around any magnetic field that is present, eventually aligning with it as energy dissipates through dampening of the precession. In addition to the magnetization and the magnetic field, two quantities come into play: γ, the gyromagnetic ratio that determines the frequency of precession, and α, the parameter that describes the damping efficiency. As a spin-polarized current flows through a ferromagnet, the traveling spins tend to align with the magnetization. If the local magnetization direction changes, such as in a domain wall, angular momentum conservation requires the spins to exert a torque on the magnetization. This may result in domain-wall motion. This interaction is intricate, and two spin-transfer torque terms had to be incorporated into the LLG equation to describe it [6, 12]. The first term is adiabatic: it describes the effect of spins as they move and adapt to locally varying magnetization. It is an “antidamping” term that is, like standard damping, proportional to α, and contains no free spin-torque parameters. As noted in the paragraph above, the origin of the second term is unfortunately less clear. It has, for instance, been attributed to spin-flip scattering, which prevents the conduction electron spins from fully aligning with the magnetization [6] (hence dubbed “nonadiabatic”). This term introduces β [12], the nonadiabaticity parameter, which is expected to be large for large magnetization gradients or narrow domain walls. The spintronics community is intrigued by both the absolute sizes as well as the ratio of these two terms, as illustrated by the large number of ongoing theoretical and experimental studies. These two terms determine the ease with which domain walls can be pushed along by current pulses.