Applied Field Angle Research Articles

Magnetization dynamics of a CoFe/Co2MnSi magnetic bilayer structure

Half-metallic Heusler alloys are receiving significant attention for spintronic applications utilizing magnetic tunnel junctions and requiring large spin polarization. Co2MnSi (CMS) is one of the most promising candidates for this purpose. Here, we report the magnetization dynamics of a thin, epitaxial CMS film in a magnetic CoFe/CMS bilayer structure sputtered on an MgO substrate. The magnetic precession frequency response of the CoFe/CMS bilayer shows a fourfold symmetry with respect to the azimuthal applied field angle, reflecting the crystal symmetry of the CMS layer and not the underlying CoFe film. Moreover, the effective Gilbert damping parameter exhibits inhomogeneous broadening at lower applied magnetic fields. At large fields, however, the azimuthal angle dependence disappears, and the intrinsic Gilbert damping is observed. This study provides insight into the dynamics of a magnetic bilayer structure that forms an integral element in spintronic applications.

S-shaped configurational magnetic states in mesoscale square permalloy particles

Experimental detection of multiple stable magnetic configurational states in isolated square permalloy particles of side length on the order of 200 nm is reported. The magnetic states are characterized using the anisotropic magnetoresistance via four-terminal resistance measurements of individual particles, and results are corroborated with micromagnetic simulations. The particles tend to relax into a ground state U-shaped “buckle” configuration at larger sizes and for an applied field swept parallel to the particle's edge, but assume an S-shaped configuration at smaller sizes and for slight variations in the applied field angle. The occurrence of this metastable state at room temperature indicates that typical models characterizing such particles in terms of energy landscapes or local effective fields may not be sufficient to accurately describe systems at this scale.

Analysis of Adjacent Track Erasure in the HAMR Media

Writing closely spaced tracks in the cross-track direction helps increase the storage density but leads to erasure of the adjacent tracks. This phenomenon is called adjacent track erasure (ATE). This article aims to establish the presence and numerical extent of ATE in different heat-assisted magnetic recording (HAMR) media. We find that thermal exchange coupled composite (ECC) media can be more susceptible to ATE compared with single layer FePt media of equivalent thickness. We implement optimization techniques to reduce the ATE in different media and increase the recording signal to noise ratio (SNR) in this process. While the ATE in single layer FePt media seems to be relatively impervious to changes in the applied field angle, small field angles appear to reduce the ATE for the high $T_{c}$ thermal ECC media. However, small angle also reduces the SNR, leading to the conclusion that 30° actually yields the best SNR even in the presence of overwrite. Introducing a finite intergranular exchange coupling improves the writing performance of the single layer FePt and reduces the ATE. We rigorously calculate the thermal decay constant and use it to evaluate the performance of pulsed laser recording. Finally, we establish a hypothesis that helps explain the presence of ATE in different HAMR media. We believe the ATE is proportional to the thermal stability factor at a temperature just below the write temperature. The proposed hypothesis correctly predicts the ATE in the single layer FePt media assuming coherent rotation. Our results can help increase the HAMR storage density and make HAMR media resistant to the ATE.

Formation of zero-field skyrmion arrays in asymmetric superlattices

We demonstrate the formation of metastable Néel-type skyrmion arrays in Pt/Co/Ni/Ir multi-layers at zero-field following the ex situ application of an in-plane magnetic field using Lorentz transmission electron microscopy. The resultant skyrmion texture is found to depend on both the strength and misorientation of the applied field as well as the interfacial Dzyaloshinskii–Moriya interaction. To demonstrate the importance of the applied field angle, we leverage bend contours in the specimens, which coincide with transition regions between skyrmion and labyrinth patterns. The subsequent application of a perpendicular magnetic field near these regions reveals the unusual situation where skyrmions with opposite magnetic polarities are stabilized in close proximity.

Planar Hall Driven Torque in a Ferromagnet/Nonmagnet/Ferromagnet System

An important goal of spintronics is to covert a charge current into a spin current with a controlled spin polarization that can exert torques on an adjacent magnetic layer. Here we demonstrate such torques in a two ferromagnet system. A CoNi multilayer is used as a spin current source in a sample with structure CoNi/Au/CoFeB. Spin torque ferromagnetic resonance is used to measure the torque on the CoFeB layer. The response as a function of the applied field angle and current is consistent with the symmetry expected for a torque produced by the planar Hall effect originating in CoNi. We find the strength of this effect to be comparable to that of the spin Hall effect in platinum, indicating that the planar Hall effect holds potential as a spin current source with a controllable polarization direction.

Linear chains of nanomagnets: engineering the effective magnetic anisotropy.

This paper investigates the control of effective magnetic anisotropy in Permalloy linear chain arrays, achieved by tuning the symmetry arrangement of the ellipsoidal nanomagnets and the film thickness. When the ellipsoidal nanomagnets are coupled along their easy axis, stronger effective magnetic anisotropy is achieved compared to when the nanomagnets are coupled along their hard axis. A clear transition from a single domain state to a combination of complex flux closure states such as a vortex or double vortices is observed at different applied field angles when the film thickness is varied in the range from 20 nm to 100 nm. Tunable microwave absorption spectra, obtained by ferromagnetic resonance spectroscopy, established the complex interplay between the shape anisotropy and magnetostatic interactions, which becomes more intriguing at different film thicknesses and applied field angles. The micromagnetic simulations are in good agreement with the experimental results. Our results demonstrate possible ways of manipulating the effective magnetic anisotropy in arrays of nanomagnets for magnonic and microwave applications.

Auto-oscillating Spin-Wave Modes of Constriction-Based Spin Hall Nano-oscillators in Weak In-Plane Fields

We experimentally study the auto-oscillating spin-wave modes in NiFe/$\beta-$W constriction-based spin Hall nano-oscillators as a function of bias current, in-plane applied field strength, and azimuthal field angle, in the low-field range of 40-80 mT. We observe two different spin-wave modes: i) a linear-like mode confined to the minima of the internal field near the edges of the nanoconstriction, with weak frequency dependencies on the bias current and the applied field angle, and ii) a second, lower frequency mode that has significantly higher threshold current and stronger frequency dependencies on both bias current and the external field angle. Our micromagnetic modeling qualitatively reproduces the experimental data and reveals that the second mode is a spin-wave bullet and that the SHNO mode hops between the two modes, resulting in a substantial increase in linewidths. In contrast to the linear-like mode, the bullet is localized in the middle of the constriction and shrinks with increasing bias current. Utilizing intrinsic frequency doubling at zero field angle we can reach frequencies above 9 GHz in fields as low as 40 mT, which is important for the development of low-field spintronic oscillators with applications in microwave signal generation and neuromorphic computing.

The dynamic resistance of YBCO coated conductor wire: effect of DC current magnitude and applied field orientation

Dynamic resistance, which occurs when a HTS coated conductor carries a DC current under an AC magnetic field, can have critical implications for the design of HTS machines. Here, we report measurements of dynamic resistance in a commercially available SuperPower 4 mm-wide YBCO coated conductor, carrying a DC current under an applied AC magnetic field of arbitrary orientation. The reduced DC current, It/Ic0, ranged from 0.01 to 0.9, where It is the DC current level and Ic0 is the self-field critical current of the conductor. The field angle (the angle between the magnetic field and the normal vector of the conductor wide-face) was varied between 0° and 90° at intervals of 10°. We show that the effective width of the conductor under study is ∼12% less than the physical wire width, and we attribute this difference to edge damage of the wire during or after manufacture. We then examine the measured dynamic resistance of this wire under perpendicular applied fields at very low DC current levels. In this regime we find that the threshold field, Bth, of the conductor is well described by the nonlinear equation of Mikitik and Brandt. However, this model consistently underestimates the threshold field at higher current levels. As such, the dynamic resistance in a coated conductor under perpendicular magnetic fields is best described using two different equations for each of the low and high DC current regimes, respectively. At low DC currents where It/Ic0 ≤ 0.1, the nonlinear relationship of Mikitik and Brandt provides the closest agreement with experimental data. However, in the higher current regime where It/Ic0 ≥ 0.2, closer agreement is obtained using a simple linear expression which assumes a current-independent penetration field. We further show that for the conductor studied here, the measured dynamic resistance at different field angles is dominated by the perpendicular magnetic field component, with negligible contribution from the parallel component. Our findings now enable the dynamic resistance of a single conductor to be analytically determined for a very wide range of DC currents and at all applied field angles.

Effective demagnetizing tensors in arrays of magnetic nanopillars

A model describing the effect of magnetic dipolar interactions on the susceptibility of magnetic nanopillars is presented. It is an extension of a recently reported model for three-dimensional randomlike dispersions of nearly spherical nanoparticles in equilibrium [S\'anchez et al., Phys. Rev. B 95, 134421 (2017)], to well-ordered arrays of nanoparticles out of equilibrium. To test it, a high-quality benchmark consisting of a two-dimensional hexagonal arrangement of quasi-identical parallel nickel nanopillars embedded in a porous alumina template was fabricated. This model is based on an effective demagnetizing tensor, which only depends on a few morphological parameters of the sample, as the nearest-neighbor distance between pillars and the volume fraction of pillars in the specimen. It allows us to obtain the nanopillar intrinsic susceptibility tensor from the magnetic response of the nanopillar ensemble. The values of the in-plane and normal-to-plane susceptibility of the sample are successfully predicted by the model. Furthermore, the model reproduces the susceptibility in the applied field direction, measured for different applied field angles. In this way, it provides a simple and accurate treatment to account for the complex magnetic effects produced by dipolar interactions.

Magnetic solitons and magnetic phase diagram of the hexagonal chiral crystal CrNb3S6 in oblique magnetic fields

We investigate the magnetic torque and magnetoresistance (MR) responses in oblique magnetic fields in micrometer-sized specimens of the hexagonal chiral magnetic crystal ${\mathrm{CrNb}}_{3}{\mathrm{S}}_{6}$. The results exhibit hysteresis over a wide range of applied field angles, while reversible behavior appears only when the magnetic field is closely aligned to the helical axis of the crystal. Stepwise changes of the magnetic torque and MR detected in the hysteresis region indicate the existence of chiral solitons in the oblique magnetic fields. A magnetic phase diagram is derived from the experimental results, and the stability of the chiral magnetic phases, such as the chiral soliton lattice and chiral conical phase, and the nature of the phase transition between them are discussed.

Reliable Propagation of Magnetic Domain Walls in Cross Structures for Advanced Multiturn Sensors

We develop and analyze an advanced concept for domain wall based sensing of rotations. Moving domain walls in n closed loops with n-1 intersecting convolutions by rotating fields, we can sense n rotations. By combining loops with coprime numbers of rotations, we create a sensor system allowing for the total counting of millions of turns of a rotating applied magnetic field. We analyze the operation of the sensor and identify the intersecting cross structures as the critical component for reliable operation. In particular depending on the orientation of the applied field angle with the magnetization in the branches of the cross, a domain wall is found to propagate in an unwanted direction yielding failures and counting errors in the device. To overcome this limiting factor, we introduce a specially designed syphon structure to achieve the controlled pinning of the domain wall before the cross and depinning and propagation only for a selected range of applied field angles. By adjusting the syphon and the cross geometry, we find that the optimized combination of both structures prevents failures in the full sensor structure yielding robust operation. Our modeling results show that the optimized element geometry allows for the realization of the sensor with cross-shaped intersections and operation that is tolerant to inaccuracies of the fabrication.

High Recording Performance of Bit-Patterned Media With Two-Layer Inclined Anisotropy ECC Dots

A simplified exchange coupled composite (ECC) dot structure with a reduced switching field and small applied field angle dependence in the switching field is proposed. It was found from a spin model analysis that a reduced switching field as well as a small applied field angle dependence of the field is obtainable even for two-layer ECC dot when the anisotropy axis is weakly inclined with an increased anisotropy for the soft layer. The switching properties of the two-layer ECC dots were confirmed using a micromagnetic simulation. A minimum normalized switching field of 0.51 was obtained for a two-layer ECC dot model of stacked cubes with a size of 5 nm and an anisotropy inclination angle of 10°. Recording simulation on a bit-pattered medium of the two-layer ECC dot array suggested the possibility of a high areal density recording beyond 4 Tdot/in 2 by shingled recording. It was also confirmed by simulation that the proposed inclined anisotropy ECC dot could be applicable to granular media for narrow track recoding.

Stress and Strain Analysis in an Fe-Ga Alloy Single Crystal

We carried out in situ x-ray diffraction measurements of magnetostriction in an Fe-18at%Ga alloy single crystal under magnetic fields. The sample studied here was a Goss-oriented square plate (dimensions: 10 mm × 10 mm × 1 mm height) cutting from as-grown single crystal ingot produced by the Czochralski method. In-plain magnetic fields were applied with various directions in this study. The influence of magnetic field direction on the stress/strain states was precisely analyzed by using our original x-ray single crystal stress/strain measurement method. As a result, applied field angle dependence of tri-axial magnetostriction states was successfully obtained. Thereby, we found that the singular anisotropic mechanical properties of this material play an important role for its magnetostriction properties.

Theoretical Study of the Charge-Transfer State Separation within Marcus Theory: The C60-Anthracene Case Study

We study, within Marcus theory, the possibility of the charge-transfer (CT) state splitting at organic interfaces and a subsequent transport of the free charge carriers to the electrodes. As a case study we analyze model anthracene-C60 interfaces. Kinetic Monte Carlo (KMC) simulations on the cold CT state were performed at a range of applied electric fields, and with the fields applied at a range of angles to the interface to simulate the action of the electric field in a bulk heterojunction (BHJ) interface. The results show that the inclusion of polarization in our model increases CT state dissociation and charge collection. The effect of the electric field on CT state splitting and free charge carrier conduction is analyzed in detail with and without polarization. Also, depending on the relative orientation of the anthracene and C60 molecules at the interface, CT state splitting shows different behavior with respect to both applied field strength and applied field angle. The importance of the hot CT in helping the charge carrier dissociation is also analyzed in our scheme.

Fabrication and Manipulation of Ciliary Microrobots with Non-reciprocal Magnetic Actuation.

Magnetically actuated ciliary microrobots were designed, fabricated, and manipulated to mimic cilia-based microorganisms such as paramecia. Full three-dimensional (3D) microrobot structures were fabricated using 3D laser lithography to form a polymer base structure. A nickel/titanium bilayer was sputtered onto the cilia part of the microrobot to ensure magnetic actuation and biocompatibility. The microrobots were manipulated by an electromagnetic coil system, which generated a stepping magnetic field to actuate the cilia with non-reciprocal motion. The cilia beating motion produced a net propulsive force, resulting in movement of the microrobot. The magnetic forces on individual cilia were calculated with various input parameters including magnetic field strength, cilium length, applied field angle, actual cilium angle, etc., and the translational velocity was measured experimentally. The position and orientation of the ciliary microrobots were precisely controlled, and targeted particle transportation was demonstrated experimentally.

Field angle dependent change of the magnetization reversal mode in epitaxial Co (0001) films

The magnetic field dependent reorientation phase transition of epitaxial Co (0001) films with perpendicular magnetic anisotropy is studied as a function of the applied field angle. The experimental data reveal an abrupt qualitative change of the magnetization reversal path at a critical angle between in-plane and out-of-plane field orientation, which is caused by a change in the domain formation process occurring concurrently with the phase transition. By means of our experiments and model calculations, we demonstrate that the observations are due to a transition from instability driven magnetization reversal occurring near in-plane field orientation to domain nucleation processes, which occur near out-of-plane orientation of the magnetic field.

Approaching the Grain-Size Limit for Jitter Using FeRh/FePt in Heat-Assisted Magnetic Recording

Composite FeRh/FePt for heat-assisted magnetic recording media is investigated with micromagnetic simulation. It is found to potentially lower recording temperature, while retaining high anisotropy field gradient. The transition width is predicted to depend on the media cooling rate. The thickness of the FeRh layer and the applied field can significantly affect the switching time of the FePt layer, and therefore alter recording performance. Applied field magnitudes and angles are identified that allow successful switching within 100 ps. It is shown that using up to 15 nm of FeRh with 6 nm of FePt, the jitter for 5.6 nm grains can be nearly equal to the grain-size limited value, for head velocities as high as 20 m/s.

High-Areal Density Recording Simulation of Three-Layered ECC Bit-Patterned Media With a Shielded Planar Head

Magnetic parameters of the previously proposed three-layer exchange coupled composite (ECC) dot were modified to compensate the additional perpendicular anisotropy from the shape and the stacking of the layers. The modification in the magnetic parameters resulted in a minimum switching field and applied field angle dependence of the field. Recording simulation using a multistepped shielded planar head field on the bit-patterned media with modified three-layer ECC dots suggested possibility of a high-areal density recording above 4 T dot/in\(^{2}\) with no energy assist scheme. It was also concluded that magnetic parameter compensation for additional shape and stacking anisotropy is indispensable for ECC dots.

Effect of magnetocrystalline anisotropy on the magnetic properties of electrodeposited Co–Pt nanowires

We report on the influence of the magnetocrystalline anisotropy on the easy magnetization axis, magnetization reversal and magnetic domain configurations of electrodeposited Co–Pt nanowires with lengths in the range of 4–6 µm and a diameter of 250 nm. The transmission electron microscopy and the X-ray diffractions revealed that the nanowires are composed of an intermixture of hcp- and fcc-textured crystal structures. The crystallographic orientations of both phases were such that the $$\left[ {00\bar{1}} \right]$$ of the hcp phase and the [111] of the fcc phase are pointing almost perpendicular to the nanowire axis. This observation allows us to understand the perpendicular easy magnetization axis of the nanowire arrays measured with vibrating sample magnetometry. Analytical calculations of the angular dependence of the coercivity revealed that the magnetization reversal changes from vortex to transverse mode at the applied field angle θ = 30°. Fitting of the experiment to these calculations results in a perpendicular effective anisotropy constant (K eff = 2.6 × 104 J/m3) in nanowires which can be ascribed to the strong magnetocrystalline anisotropy. Furthermore, the magnetic domain configurations of individual nanowires of length range 4 < L < 6 µm are studied using magnetic force microscopy. This reveals a spatial magnetization modulation along the length of the nanowires, which was found to be length dependent. Such an intrinsic modulation is attributed to the competition between the magnetocrystalline anisotropy and the shape anisotropy in the nanowires. We believe that this interplay between anisotropies gives rise to a magnetic configuration involving vortex-like structure with alternating chirality along the length of the nanowires.

Magnetization reversal of in-plane uniaxial Co films and its dependence on epitaxial alignment

This work studies the influence of crystallographic alignment onto magnetization reversal in partially epitaxial Co films. A reproducible growth sequence was devised that allows for the continuous tuning of grain orientation disorder in Co films with uniaxial in-plane anisotropy by the controlled partial suppression of epitaxy. While all stable or meta-stable magnetization states occurring during a magnetic field cycle exhibit a uniform magnetization for fully epitaxial samples, non-uniform states appear for samples with sufficiently high grain orientation disorder. Simultaneously with the occurrence of stable domain states during the magnetization reversal, we observe a qualitative change of the applied field angle dependence of the coercive field. Upon increasing the grain orientation disorder, we observe a disappearance of transient domain wall propagation as the dominating reversal process, which is characterized by an increase of the coercive field for applied field angles away from the easy axis for well-ordered epitaxial samples. Upon reaching a certain disorder threshold level, we also find an anomalous magnetization reversal, which is characterized by a non-monotonic behavior of the remanent magnetization and coercive field as a function of the applied field angle in the vicinity of the nominal hard axis. This anomaly is a collective reversal mode that is caused by disorder-induced frustration and it can be qualitatively and even quantitatively explained by means of a two Stoner-Wohlfarth particle model. Its predictions are furthermore corroborated by Kerr microscopy and by Brillouin light scattering measurements.