Nonuniform Magnetization Research Articles

Effects of the Winding Cross-Section Shape on the Magnetic Field Uniformity of the High Field Circular Helmholtz Coil Systems

Massive windings must be used for strong magnetic field applications, which results in low magnetic field uniformity. In this paper, a simple circular Helmholtz coil system is analyzed to identify the main causes of the problems, which arise for high intensity uniform magnetic field applications. Here, dominant deformations of the circular solenoid winding cross-section shape and its dimensions effects on the generated magnetic field and its uniformity are analyzed. These analyses can be applied to the modified Helmholtz coil and multi-axial systems, as well. The system dimensions are optimized and normalized to easily scale the given results for any desired uniform magnetic field and workspace without doing further laborious calculations. The optimized dimensions increase the magnetic field uniformity in a large portion of the available workspace and realize the desired magnetic field at the center of the system. Also, the necessary conductor mass and the total electrical power are reduced. To verify the given analyses, two small-scale Helmholtz coil systems have been implemented and their generated magnetic fields and nonuniformities have been measured under a variety of conditions.

Perpendicular magnetic tunneling junction switching dynamic modes, extreme events, and performance scaling

The performance of the state-of-the-art perpendicular magnetic tunneling junction (pMTJ) device is fundamentally determined by the physics of material “extreme events.” A dynamic mode approach is used to study “extreme events” of stochastic nonlinear magnetization switching, including magnetic interactions and non-uniform magnetization dynamics. Our theory and experiment show that the magnetization switching “extreme events” are well characterized by the dynamic modes of interacting magnetic systems. The dynamic modes provide a clear understanding of the physical processes of the magnetization switching “extreme events.” We predict markedly different pMTJ scaling behaviors for spin transfer torque, spin-orbit-interaction torque, and thermal fluctuations at different operation speeds and bit error rate conditions. Understanding these scaling behaviors is critical for existing and emerging pMTJ device applications.

Simulation of therapeutic electron beam tracking through a non-uniform magnetic field using finite element method.

IntroductionIn radiotherapy, megaelectron volt (MeV) electrons are employed for treatment of superficial cancers. Magnetic fields can be used for deflection and deformation of the electron flow. A magnetic field is composed of non-uniform permanent magnets. The primary electrons are not mono-energetic and completely parallel. Calculation of electron beam deflection requires using complex mathematical methods. In this study, a device was made to apply a magnetic field to an electron beam and the path of electrons was simulated in the magnetic field using finite element method.MethodsA mini-applicator equipped with two neodymium permanent magnets was designed that enables tuning the distance between magnets. This device was placed in a standard applicator of Varian 2100 CD linear accelerator. The mini-applicator was simulated in CST Studio finite element software. Deflection angle and displacement of the electron beam was calculated after passing through the magnetic field. By determining a 2 to 5cm distance between two poles, various intensities of transverse magnetic field was created. The accelerator head was turned so that the deflected electrons became vertical to the water surface. To measure the displacement of the electron beam, EBT2 GafChromic films were employed. After being exposed, the films were scanned using HP G3010 reflection scanner and their optical density was extracted using programming in MATLAB environment. Displacement of the electron beam was compared with results of simulation after applying the magnetic field.ResultsSimulation results of the magnetic field showed good agreement with measured values. Maximum deflection angle for a 12 MeV beam was 32.9° and minimum deflection for 15 MeV was 12.1°. Measurement with the film showed precision of simulation in predicting the amount of displacement in the electron beam.ConclusionA magnetic mini-applicator was made and simulated using finite element method. Deflection angle and displacement of electron beam were calculated. With the method used in this study, a good prediction of the path of high-energy electrons was made before they entered the body.

Nanoscale interface confinement of ultrafast spin transfer torque driving non-uniform spin dynamics

Spintronics had a widespread impact over the past decades due to transferring information by spin rather than electric currents. Its further development requires miniaturization and reduction of characteristic timescales of spin dynamics combining the sub-nanometre spatial and femtosecond temporal ranges. These demands shift the focus of interest towards the fundamental open question of the interaction of femtosecond spin current (SC) pulses with a ferromagnet (FM). The spatio-temporal properties of the impulsive spin transfer torque exerted by ultrashort SC pulses on the FM open the time domain for probing non-uniform magnetization dynamics. Here we employ laser-generated ultrashort SC pulses for driving ultrafast spin dynamics in FM and analysing its transient local source. Transverse spins injected into FM excite inhomogeneous high-frequency spin dynamics up to 0.6 THz, indicating that the perturbation of the FM magnetization is confined to 2 nm.

Equilibrium bi-domain configuration in cylindrical magnetic microparticles

This report is on the equilibrium bi-domain structure in magnetic microparticles of cylindrical shape with circular or elliptic cross-section and finite thickness. The model is for two coaxial 180 degree domains. The dependence of the inner domain dimensions on bias magnetic field was estimated for a series of particle aspect ratios. It is shown that a change in bias field leads to significant variation in the inner domain radius and that such variations occur at decreasing field strength as the particle height increases. Results of our model are of importance for magnetic particles ground state calculations and analysis of spin-wave oscillations in ferrite micro- and nano-resonators with non-uniform internal magnetization.

The Characteristics of Observation of the Non-uniform Magnetization on the Surface of the Thin Magnetic Films in Ta/CoFeB/MgO/CoFeB/Ta Multilayers

The Characteristics of Observation of the Non-uniform Magnetization on the Surface of the Thin Magnetic Films in Ta/CoFeB/MgO/CoFeB/Ta Multilayers

Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work we study the effect of a space dependent Weyl node separation, which we interpret as an emergent background axial vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or non-uniform magnetization and can also be engineered in cold-atomic systems. Using a semiclassical approach we show that the resulting axial magnetic field $\mathbf{B}_{5}$ is observable through an enhancement of the conductivity as $\sigma\sim \mathbf{B}_{5} ^{2}$ due to an underlying chiral pseudo magnetic effect. We then use two lattice models to analyze the effect of $\mathbf{B}_5$ on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau level structure for different spatial profiles of $\mathbf{B}_5$, revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as $n=0$ pseudo-Landau levels resulting from a $\mathbf{B}_5$ confined to the surface (ii) as a consequence of position-momentum locking a bulk $\mathbf{B}_5$ creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces and (iii) there are equilibrium bound currents proportional to $\mathbf{B}_{5}$ that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

On the exact solutions of nonlinear Schrödinger equation with spin current

An integrable nonlinear Schrödinger (NLS) equation driven by spin polarized current governing the magnetization dynamics of a ferromagnetic nanowire is considered. The exact soliton solution of the NLS equation propagating along the direction of wire axis which is also the current direction along which nonuniform magnetization occurs is obtained through the application of exponential function method. The solution of the system admits a class of solitons such as kink and periodic solitons in the nanowire along the direction of the electric current.

Surface morphology driven non-uniform magnetism in epitaxial BiMnO3

Thin films of BiMnO3 were grown on (001) SrTiO3 substrates by fine tuning the growth conditions. The films are epitaxial and impurity-free, but show island growth mode. From detailed magnetization measurements and surface analysis, we found evidence of morphology driven non-uniform magnetism. The non-uniform magnetism resulted in reduced saturation magnetization, reduced Curie temperature (TC), and nonlinear Arrott plots. In spite of non-uniform magnetism, the temperature dependence of magnetization showed conventional mean field behavior near TC. Our data suggest that non-uniform strain leads to coexistence of separate ferromagnetic and ferroelectric regions in BiMnO3 films which is not observed in bulk samples.

Quantitative analysis of the relationship between non-uniform stresses and residual magnetizations under geomagnetic fields

The quantitative relationship between non-uniform stresses and stress-induced residual magnetizations in ferromagnetic materials under geomagnetic fields was investigated. A ferromagnetic steel specimen with two symmetric notches was stretched to generate a non-uniform stress distribution. The residual leakage magnetic field and surface strain of the specimen were detected. Stress distribution was calculated according to the tested stress–strain curve of the material. The residual magnetization inside the specimen was reconstructed using residual leakage magnetic field signals. The quantitative relationship between stress and stress-induced residual magnetization was then established. Stress-induced residual magnetization was observed along the stress direction, and the intensity of the residual magnetization increased almost linearly with increasing stress.

Magnetization reversal in magnetic dot arrays: Nearest-neighbor interactions and global configurational anisotropy

Various proposals for future magnetic memories, data processing devices, and sensors rely on a precise control of the magnetization ground state and magnetization reversal process in periodically patterned media. In finite dot arrays, such control is hampered by the magnetostatic interactions between the nanomagnets, leading to the non-uniform magnetization state distributions throughout the sample while reversing. In this paper, we evidence how during reversal typical geometric arrangements of dots in an identical magnetization state appear that originate in the dominance of either Global Configurational Anisotropy or Nearest-Neighbor Magnetostatic interactions, which depends on the fields at which the magnetization reversal sets in. Based on our findings, we propose design rules to obtain the uniform magnetization state distributions throughout the array, and also suggest future research directions to achieve non-uniform state distributions of interest, e.g., when aiming at guiding spin wave edge-modes through dot arrays. Our insights are based on the Magneto-Optical Kerr Effect and Magnetic Force Microscopy measurements as well as the extensive micromagnetic simulations.

Disruptive effect of Dzyaloshinskii-Moriya interaction on the magnetic memory cell performance

In order to increase the thermal stability of a magnetic random access memory cell, materials with high spin-orbit interaction are often introduced in the storage layer. As a side effect, a strong Dzyaloshinskii-Moriya interaction (DMI) may arise in such systems. Here, we investigate the impact of DMI on the magnetic cell performance, using micromagnetic simulations. We find that DMI strongly promotes non-uniform magnetization states and non-uniform switching modes of the magnetic layer. It appears to be detrimental for both the thermal stability of the cell and its switching current, leading to considerable deterioration of the cell performance even for a moderate DMI amplitude.

Skyrmionic magnetization configurations at chiral magnet/ferromagnet heterostructures

We consider magnetization configurations at chiral magnet (CM)/ferromagnet (FM) heterostructures. In the CM, magnetic skyrmions and spin helices emerge due to the Dzyaloshinskii-Moriya interaction, which then penetrate into the adjacent FM. However, because the non-uniform magnetization structures are energetically unfavorable in the FM, the penetrated magnetization structures are deformed, resulting in exotic three-dimensional configurations, such as skyrmion cones, sideways skyrmions, and twisted helices and skyrmions. We discuss the stability of possible magnetization configurations at the CM/FM and CM/FM/CM hybrid structures within the framework of the variational method, and find that various magnetization configurations appear in the ground state, some of which cause nontrivial emergent magnetic field.

Double-Q spin-density wave in iron arsenide superconductors

Elucidating the nature of the magnetic ground state of iron-based superconductors is of paramount importance in unveiling the mechanism behind their high temperature superconductivity. Until recently, it was thought that superconductivity emerges only from an orthorhombic antiferromagnetic stripe phase, which can in principle be described in terms of either localized or itinerant spins. However, we recently reported that tetragonal symmetry is restored inside the magnetically ordered state of a hole-doped BaFe2As2. This observation was interpreted as indirect evidence of a new double-Q magnetic structure, but alternative models of orbital order could not be ruled out. Here, we present Mossbauer data that show unambiguously that half of the iron sites in this tetragonal phase are non-magnetic, establishing conclusively the existence of a novel magnetic ground state with a non-uniform magnetization that is inconsistent with localized spins. We show that this state is naturally explained as the interference between two spin-density waves, demonstrating the itinerant character of the magnetism of these materials and the primary role played by magnetic over orbital degrees of freedom.

Vestigial chiral and charge orders from bidirectional spin-density waves: Application to the iron-based superconductors

Recent experiments in optimally hole-doped iron arsenides have revealed a novel magnetically ordered ground state that preserves tetragonal symmetry, consistent with either a charge-spin density wave (CSDW), which displays a non-uniform magnetization, or a spin-vortex crystal (SVC), which displays a non-collinear magnetization. Here we show that, similarly to the partial melting of the usual stripe antiferromagnet into a nematic phase, either of these phases can also melt in two stages. As a result, intermediate paramagnetic phases with vestigial order appears: a checkerboard charge density-wave for the CSDW ground state, characterized by an Ising-like order parameter, and a remarkable spin-vorticity density-wave for the SVC ground state -- a triplet d-density wave characterized by a vector chiral order parameter. We propose experimentally detectable signatures of these phases, show that their fluctuations can enhance the superconducting transition temperature, and discuss their relevance to other correlated materials.

Transport in selectively magnetically doped topological insulator wires

We study the electronic and transport properties of a topological insulator nanowire including selective magnetic doping of its surfaces. We use a model which is appropriate to describe materials like Bi$_2$Se$_3$ within a k.p approximation and consider nanowires with a rectangular geometry. Within this model the magnetic doping at the (111) surfaces induces a Zeeman field which opens a gap at the Dirac cones corresponding to the surface states. For obtaining the transport properties in a two terminal configuration we use a recursive Green function method based on a tight-binding model which is obtained by discretizing the original continuous model. For the case of uniform magnetization of two opposite nanowire (111) surfaces we show that the conductance can switch from a quantized value of $e^2/h$ (when the magnetizations are equal) to a very small value (when they are opposite). We also analyze the case of non-uniform magnetizations in which the Zeeman field on the two opposite surfaces change sign at the middle of the wire. For this case we find that conduction by resonant tunneling through a chiral state bound at the middle of the wire is possible. The resonant level position can be tuned by imposing an Aharonov-Bohm flux through the nanowire cross section.

Magnetic field-dependent shape anisotropy in small patterned films studied using rotating magnetoresistance.

Based on the electric rotating magnetoresistance method, the shape anisotropy of a Co microstrip has been systematically investigated. We find that the shape anisotropy is dependent not only on the shape itself, but also on the magnetization distribution controlled by an applied magnetic field. Together with micro-magnetic simulations, we present a visualized picture of how non-uniform magnetization affects the values and polarities of the anisotropy constants and . From the perspective of potential appliantions, our results are useful in designing and understanding the performance of micro- and nano-scale patterned ferromagnetic units and the related device properties.

Kinetic modelling of runaway electron avalanches in tokamak plasmas

Runaway electrons can be generated in tokamak plasmas if the accelerating force from the toroidal electric field exceeds the collisional drag force owing to Coulomb collisions with the background plasma. In ITER, disruptions are expected to generate runaway electrons mainly through knock-on collisions (Hender et al 2007 Nucl. Fusion 47 S128–202), where enough momentum can be transferred from existing runaways to slow electrons to transport the latter beyond a critical momentum, setting off an avalanche of runaway electrons. Since knock-on runaways are usually scattered off with a significant perpendicular component of the momentum with respect to the local magnetic field direction, these particles are highly magnetized. Consequently, the momentum dynamics require a full 3D kinetic description, since these electrons are highly sensitive to the magnetic non-uniformity of a toroidal configuration. For this purpose, a bounce-averaged knock-on source term is derived. The generation of runaway electrons from the combined effect of Dreicer mechanism and knock-on collision process is studied with the code LUKE, a solver of the 3D linearized bounce-averaged relativistic electron Fokker–Planck equation (Decker and Peysson 2004 DKE: a fast numerical solver for the 3D drift kinetic equation Report EUR-CEA-FC-1736, Euratom-CEA), through the calculation of the response of the electron distribution function to a constant parallel electric field. The model, which has been successfully benchmarked against the standard Dreicer runaway theory now describes the runaway generation by knock-on collisions as proposed by Rosenbluth (Rosenbluth and Putvinski 1997 Nucl. Fusion 37 1355–62). This paper shows that the avalanche effect can be important even in non-disruptive scenarios. Runaway formation through knock-on collisions is found to be strongly reduced when taking place off the magnetic axis, since trapped electrons can not contribute to the runaway electron population. Finally, the relative importance of the avalanche mechanism is investigated as a function of the key parameters for runaway electron formation, namely the plasma temperature and the electric field strength. In agreement with theoretical predictions, the LUKE simulations show that in low temperature and electric field the knock-on collisions becomes the dominant source of runaway electrons and can play a significant role for runaway electron generation, including in non-disruptive tokamak scenarios.

Magnetic field induced spin-wave energy focusing

Local temperature variations induced by spin-wave propagation are studied using a model that couples nonuniform magnetization dynamics and heat flow. We show that the remote heating at the sample edge reported recently [T. An et al., Nat. Mater. 12, 549 (2013)] is due to the geometry-induced gradual reduction of the effective field. We demonstrate that the same effect can be achieved by a reduction in the external field instead of a constriction at the edge and, furthermore, that both the location and the amount of energy to be delivered to the lattice can be controlled accurately this way.

Magnetic Properties of NiFe and FeCuNbSiB Thin Films: Effect of Thickness on Static Permeability

The magnetic static permeability of sputtered FeCuNbSiB and electrodeposited NiFe patterns with thicknesses varying from 0.1 to 8 μm has been studied. The permeability varies proportionally with the pattern size/thickness ratio, like for uniformly magnetized patterns. Different hypothesis on this variation have been investigated and a critical analysis favors a demagnetizing effect. The comparison between experimental results and the theoretical value of the demagnetizing factor of squares plates confirms MOKE imaging, i.e. large magnetic domains but a non-uniform magnetization in the samples.