Equilibrium Magnetic Configuration Research Articles

Highly tunable spin Hall magnetoresistance in room-temperature magnetoelectric multiferroic, Sr3Co2Fe24O41|Pt hybrids

We present spin transport studies on a low-field, room-temperature magnetoelectric multiferroic polycrystalline Sr3Co2Fe24O41|Pt heterostructure wherein a highly tunable transverse conical magnetic phase is responsible for static and dynamic magnetoelectric coupling. We measured angular dependence of spin Hall magnetoresistance (SMR) at constant magnetic fields (H) in the range; 50–100 kOe. Application of field below the critical value (Hc1 ≈ 2.5 kOe), yielded negative SMR and the H-evolution of normalized SMR ((ΔR∕R0) × 100 %) exhibited a negative gradient. Further, an increase in H resulted in the positive slope of (ΔR∕R0) × 100 % Vs. H and later at higher H around 14 kOe, a crossover from negative to positive SMR was observed. We employed a simple model for estimating the equilibrium magnetic configuration and computed the SMR modulation at various values of H. We argue that the tilting of the cone is dominant and in turn responsible for the observed nature of SMR below 2.5 kOe while, the closing of the cone-angle is pronounced at higher fields causing a reversal in sign of the SMR from negative to positive. Importantly, SMR experiments revealed that a change in the helicity with a reversal of the magnetic field has no influence on the observed SMR. Longitudinal spin Seebeck effect (LSSE) signal was measured to be ≈ 500 nV at 280 K, under application of thermal gradient, ΔT = 23 K and field, 60 kOe. The observed LSSE signal, originating from pure magnon spin current, showed a similar H-dependent behavior as that of the magnetization of Sr3Co2Fe24O41. Our detailed spin transport studies on polycrystalline Sr3Co2Fe24O41|Pt heterostructure demonstrate high tunability of the amplitude and the sign of the SMR, highlighting its potential for novel spintronic devices such as SMR-based spin valves and voltage-controlled spin transport devices.

Influence of Dzyaloshinskii–Moriya interaction and perpendicular anisotropy on spin waves propagation in stripe domain patterns and spin spirals

Texture-based magnonics focuses on the utilization of spin waves in magnetization textures to process information. Using micromagnetic simulations, we study how (1) the dynamic magnetic susceptibility, (2) dispersion relations, and (3) the equilibrium magnetic configurations in periodic magnetization textures in a ultrathin ferromagnetic film in remanence depend on the values of the Dzyaloshinskii–Moriya interaction and the perpendicular magnetocrystalline anisotropy. We observe that for large Dzyaloshinskii–Moriya interaction values, spin spirals with periods of tens of nanometers are the preferred state; for small Dzyaloshinskii–Moriya interaction values and large anisotropies, stripe domain patterns with over a thousand times larger period are preferable. We observe and explain the selectivity of the excitation of resonant modes by a linearly polarized microwave field. We study the propagation of spin waves along and perpendicular to the direction of the periodicity. For propagation along the direction of the periodicity, we observe a bandgap that closes and reopens, which is accompanied by a swap in the order of the bands. For waves propagating in the perpendicular direction, some modes can be used for unidirectional channeling of spin waves. Overall, our findings are promising in sensing and signal processing applications and explain the fundamental properties of periodic magnetization textures.

Efficient FEM-BEM Coupling Based on Argyris Element for Axi-Symmetric Open Boundary Magnetostatic Problems

This article describes a novel and accurate implementation of finite element method-boundary element method (FEM-BEM) coupling based on Argyris element (AE), for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C^{1}$ </tex-math></inline-formula> solution of axi-symmetric magnetostatic problems in open boundary domains. The aim of the work is twofold: 1) to provide novel, easy, and accurate way to compute the basis functions that is strongly not affected by accuracy errors and 2) to give a clear mathematical and numerical description of the FEM-BEM coupling based on AE. The first goal is achieved by shifting to the origin the physical triangular elements and computing the basis function in the shifted coordinate system. Second, AE-based FEM-BEM coupling relies on the boundary integral equations (BIEs) for poloidal flux and its partial derivatives of both first and second order, accurately computed by combining the analytical formula based on elliptic integrals together with high degree Gaussian cubature. The application of the proposed method to an advanced plasma equilibrium magnetic configuration, typical of magnetic confinement fusion (MCF) (i.e., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">snowflake configuration</i> ), highlights that, even in case of coarse triangulation, satisfactory results can be achieved, and the error on the boundary conditions (BCs) is well below machine working precision.

Magnetic excitations in assemblies of dipolar coupled nanoparticles

The equilibrium magnetization configurations and the associated microwave susceptibility spectra of dipolar coupled nanoplatelets are explored using three-dimensional (3D) micromagnetic simulations. First, the case of periodic arrangements of nanoplatelets on square arrays is considered. As a result, a macro-vortex state defined as a flux closure pattern spreading over the whole array with or without a vortex core can be stabilized starting from an initial orthoradial magnetization configuration. For macro-vortex states with a vortex core, the linear excitation spectrum exhibits a sub-GHz resonance line ascribed to the vortex core dynamics at the array center. The features of this line (spectral position and amplitude) depend on the array size and the strength of the dipolar coupling through the interplatelet spacing. This resonance is also observed for macro-vortex states without a vortex core but only in the regime of a strong dipolar coupling. The effect of disorder is then investigated by numerically generating assemblies of nanoplatelets with a position disorder and, shape and size distributions. The micromagnetic simulations reveal flux closure magnetization configurations as well but without a vortex core. A low-frequency resonance appears in the susceptibility spectra for quite high surface contents of nanoplatelets but its amplitude is weaker compared to the case of periodic arrays. This line arises from a collective mode extended over a few nanoplatelets. A large variety of static and dynamical behaviors is thus evidenced resulting in a great complexity even in such model systems.

Magnetic Force Sensing Using a Self-Assembled Nanowire.

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.

A Hybridizable Discontinuous Galerkin solver for the Grad–Shafranov equation

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad–Shafranov equation, the solution of which determines the poloidal component of the magnetic field. When the geometry of the confinement region is known, the problem becomes an interior Dirichlet boundary value problem. We propose a high order solver based on the Hybridizable Discontinuous Galerkin method. The resulting algorithm (1) provides high order of convergence for the flux function and its gradient, (2) incorporates a novel method for handling piecewise smooth geometries by extension from polygonal meshes, (3) can handle geometries with non-smooth boundaries and x-points, and (4) deals with the semi-linearity through an accelerated two-grid fixed-point iteration. The effectiveness of the algorithm is verified with computations for cases where analytic solutions are known on configurations similar to those of actual devices (ITER with single null and double null divertor, NSTX, ASDEX upgrade, and Field Reversed Configurations).

Effect of the dipolar coupling on the precessional magnetization switching in two-dimensional arrays of single-domain nano-ellipses

Various spintronic devices use single-domain magnetic nanoparticles as unit cells. Herein, we investigated interparticle dipole-dipole interactions in arrays of Permalloy single-domain nano-ellipses through micromagnetic simulations. In this study, the variation is introduced not only to the aspect ratio and the spacing between ellipses but to the magnetization distribution and the 2D lattice type as well. When integrating the Landau-Lifshitz-Gilbert equation with zero external magnetic field, equilibrium magnetic configurations were obtained for each array. For small values of the spacing between ellipses, they interact strongly, such that the shape anisotropy is locally modified by the distribution of the magnetization. Moreover, the effect of the dipolar coupling on the precessional magnetization reversal is also studied. The minimum field strength required to switch the magnetization depends on the magnetization distribution in a strongly interacting magnetic system. Consequently, we have assessed the minimum spacing between particles in which single-domain nano-ellipses becomes a non-interacting magnetic system.

A novel approach to studying transport in plasmas with magnetic islands

In magnetically confined experiments the presence of rational surfaces modifies the magnetic configuration with one or more islands embedded in the main plasma. The islands strongly modify particle and heat fluxes, hence their role must be included in the study of the transport properties. Two examples of this phenomenology are here presented: a cold pulse propagation in LHD with an RMP (1,1) island highlights a diffusivity reduction inside the island. A second study has been carried out on the RFX-mod reversed field pinch device where the transport on the ITB associated to a spontaneous m = 1 magnetic structure is discussed.To perform these studies a new approach in modeling transport in the presence of islands is presented: this new method, dubbed the multiple domains scheme (MDS), with some simplifying assumptions, is directly applicable to 1.5D transport codes. In the MDS different regions are identified inside the plasma all interfaced by the separatrix that acts as common boundary. In each domain a monotonic radial coordinate can be chosen and the metric elements can be computed accordingly. This scheme is independent of the equilibrium magnetic configuration hence it can be applied to either tokamaks, stellarators or reversed field pinches. The MDS has been implemented in a new numerical tool, dubbed the multiple axis solver.

Parallel ion compressibility effects on kinetic ballooning mode for different magnetic shears

Various gyrokinetic simulations suggest that the kinetic ballooning mode (KBM) instability is sensitive to the numerical implementation of equilibrium magnetic configuration in tokamaks. In this work, the gyrokinetic code GTC is employed to investigate the KBM's sensitivity to equilibrium plasma profiles. An outward radial shift of the radial mode is found for the normal magnetic shear case, but there is no shift if the shear is negative. The simulation results are explained by a linear eigenmode theory. It is found that the observed phenomenon is an effect of the parallel ion compressibility.

Magnetohydrodynamic equilibrium interpretation of low-aspect-ratio tokamak plasma

ABSTRACTIt is very important to calculate the equilibrium magnetic field configuration exactly and to estimate the parameters of the device needed for the equilibrium and stability in the design and operate the low-aspect-ratio tokamak, one of the axis-symmetrical torus devices which is widely used in the research of nuclear fusion using plasma. In the previous researches, there were the theoretical and numerical interpretation methods for the high-aspect-ratio tokamak plasma. But for the low-aspect-ratio tokamak plasma, numerical methods such as the finite element method and iteration method are usually used. In this research, we interpreted and examined the features of magnetohydrodynamic equilibrium of the low-aspect-ratio tokamak plasma in combination with the Green function method and finite element method which has high numerical value accuracy.

Impact of hydrogen isotope species on microinstabilities in helical plasmas

The impact of isotope ion mass on ion-scale and electron-scale microinstabilities such as ion temperature gradient (ITG) mode, trapped electron mode (TEM), and electron temperature gradient (ETG) mode in helical plasmas are investigated by using gyrokinetic Vlasov simulations with a hydrogen isotope and real-mass kinetic electrons. Comprehensive scans for the equilibrium parameters and magnetic configurations clarify the transition from ITG mode to TEM instability, where a significant TEM enhancement is revealed in the case of inward-shifted plasma compared to that in the standard configuration. It is elucidated that the ion-mass dependence on the ratio of the electron–ion collision frequency to the ion transit one, i.e. , leads to a stabilization of the TEM for heavier isotope ions. The ITG growth rate indicates a gyro-Bohm-like ion-mass dependence, where the mixing-length estimate of diffusivity yields . On the other hand, a weak isotope dependence of the ETG growth rate is identified. A collisionality scan also reveals that the TEM stabilization by the isotope ions becomes more significant for relatively higher collisionality in a banana regime.

Reconstruction of equilibrium magnetic configurations in the Globus-M spherical tokamak

The results of reconstruction of equilibrium magnetic configurations in the Globus-M spherical tokamak by means of the EFIT code and by the method of movable filaments with the use of the data from magnetic measurements are compared. The EFIT code allows one to completely reconstruct the magnetic configuration by solving the Grad−Shafranov equation. In the method of movable filaments, the distribution of the toroidal current flowing through the plasma is described by a set of infinitely thin current-carrying rings. In this method, the last closed magnetic surface (LCMS) and the open surfaces lying beyond the LCMS are calculated. Using both methods, the coordinates of the regions where the separatrix strikes the divertor plates were determined. The results obtained agree well with the distributions of the temperature over the tungsten divertor tiles measured using an IR camera.

Multi-stability in low-symmetry magnetic nanoparticles

The occurrence of equilibrium magnetic configurations in ferromagnetic low-symmetry nanoparticles has been investigated. T-shaped nanoparticles, which present strong configurational anisotropy, have been considered. It has been found that such particles exhibit four equilibrium magnetic states, whose stability at room temperature was estimated. The presence of structural imperfections, such as surface roughness, in those systems was also considered, resulting in no significant effects on the magnetic behavior of the particles. The present results are expected to be of relevance to magnetic storage.

The contrasting magnetic fields of superconducting pulsars and magnetars

We study equilibrium magnetic field configurations in a neutron star (NS) whose core has type-II superconducting protons. Unlike the equations for normal matter, which feature no special field strength, those for superconductors contain the lower critical field, of the order of 1015 G. We find that the ratio of this critical field to the smooth-averaged stellar field at the crust–core boundary is the key feature dictating the field geometry. Our results suggest that pulsar- and magnetar-strength fields have notably different configurations. Field decay for NSs with Bpole ∼ 1014 G could thus result in substantial internal rearrangements, pushing the toroidal field component out of the core; this may be related to observed magnetar activity. In addition, we calculate the magnetically induced ellipticities of our models.

Effect of hole shape on spin-wave band structure in one-dimensional magnonic antidot waveguide

We present the possibility of tuning the spin-wave band structure, particularly the bandgaps in a nanoscale magnonic antidot waveguide by varying the shape of the antidots. The effects of changing the shape of the antidots on the spin-wave dispersion relation in a waveguide have been carefully monitored. We interpret the observed variations by analysing the equilibrium magnetic configuration and the magnonic power and phase distribution profiles during spin-wave dynamics. The inhomogeneity in the exchange fields at the antidot boundaries within the waveguide is found to play a crucial role in controlling the band structure at the discussed length scales. The observations recorded here will be important for future developments of magnetic antidot based magnonic crystals and waveguides.

Comparison of Observed Divertor Heat Flux and Modeling Results at LHD

The divertor strike line pattern on the helical divertor of LHD was observed with an infra red camera. The derived heat flux pattern show multiple distinct strike lines depending on the equilibrium magnetic configuration. Predictions of such divertor heat loads thus require a modeling of the magnetic configuration and the heat transport in the magnetic edge. Equilibrium magnetic topologies were analyzed with HINT2, while the plasma fluid model code EMC3 was used to simulate the energy transport in the edge. The measured multi peak structure of the divertor heat flux is correlated to the intersection points of elongated loop shaped flux tubes of long LC field lines. But the fluid model could not recreate the total energy load and the multiple heat flux peaks on the divertor. A Variation in the plasma density ne as a transport parameter in order to fit the simulated heat flux to the measured one shows a contradicting tendency.

Magnetization configurations of a tri-layer nanopillar ferromagnet/nonmagnetic spacer/ferromagnet

The equilibrium magnetization configurations of tri-layer circular nanopillar are calculated within micromagnetic approach. Nanopillar is assumed to be a vertical stack of ferromagnetic/nonmagnetic/ferromagnetic layers. The regions of geometrical parameters of nanopillar (radius and thickness), where the magnetic vortices and single domain states appear in the ground state, are calculated analytically and checked by micromagnetic simulations. The interlayer magnetostatic coupling affects essentially the formation of vortices or single domain states in both ferromagnetic layers. A considerable influence of the thicknesses of the ferromagnetic layers and spacer on the stability of vortex states is found. The results can be applied to interpret experiments on spin torque induced magnetization dynamics in nanopillars and tunnel junctions and also to estimate the nanopillar ground states.

Three-Dimensional Simulations of Magnetic Reconnection with or Without Velocity Shears

The properties of spontaneous reconnection of a current sheet analyzed via direct three-dimensional simulations are presented. In particular the non-linear dynamics of resistive instabilities has been studied in absence or in presence of velocity shears. It is shown that full three-dimensional simulations allow the inclusion of a rich variety of (ideal) secondary instabilities which, depending on the initial equilibrium magnetic field configuration, determine the final fate of the system in the fully non linear regime. In particular in presence of a guide-field the dynamic is similar to what observed in two-dimensional simulations with energy driven toward both smaller and larger scales and energy spectra anisotropy. For different magnetic field configurations, the final state is characterized by the disruption of the coalesced structure created during the resistive phase and the system is characterized by a more chaotic state. A discussion on the importance of high-order numerical techniques in numerical simulations of magnetic reconnection is also present.

Relativistic models of magnetars: the twisted torus magnetic field configuration

We find general relativistic solutions of equilibrium magnetic field configurations in magnetars, extending previous results of Colaiuda et al. (2008). Our method is based on the solution of the relativistic Grad-Shafranov equation, to which Maxwell's equations can be reduced in some limit. We obtain equilibrium solutions with the toroidal magnetic field component confined into a finite region inside the star, and the poloidal component extending to the exterior. These so-called twisted-torus configurations have been found to be the final outcome of dynamical simulations in the framework of Newtonian gravity, and appear to be more stable than other configurations. The solutions include higher order multipoles, which are coupled to the dominant dipolar field. We use arguments of minimal energy to constrain the ratio of the toroidal to the poloidal field.

Interrelation of the spin, orbital, and charge degrees of freedom in half-doped manganites

Based on the double-exchange model in the tight-binding approximation, self-consistent energy-band-structure calculations are carried out for the first time for the orbital and charge ordering in La0.5Ca0.5MnO3-type manganites with 16 Mn ions in the unit cell under the assumption of a linear dependence of the Jahn-Teller splitting of the eg level on the occupancy of each ion. The equilibrium magnetic and orbital configurations are determined by minimizing the total energy with respect to the direction of the local magnetic moments and the orbital states of the Mn ions. The dependence of the splitting on the occupancy favors the stabilization of phases with charge separation. This separation is an important factor determining the magnetic structure of the ground state. The ground state can be an insulating antiferromagnetic structure of the CE or G type or a new ferrimagnetic structure with a magnetization lower than that of a saturated ferromagnet by a factor of 2. The existence and the width of the bandgap in the electronic energy spectrum of the CE phase depend on the ratio between the values of the Hund exchange and the splitting. When the splitting is sufficiently large, the Jahn-Teller effect stabilizes the insulating state. The finite value of the Hund coupling also favors the stabilization of the CE phase for the realistic values of the interionic exchange and the hopping integral of itinerant electrons.