In-plane Materials Research Articles

The In-Plane Anisotropy of WTe2 Investigated by Angle-Dependent and Polarized Raman Spectroscopy.

Tungsten ditelluride (WTe2) is a semi-metallic layered transition metal dichalcogenide with a stable distorted 1T phase. The reduced symmetry of this system leads to in-plane anisotropy in various materials properties. We have systemically studied the in-plane anisotropy of Raman modes in few-layer and bulk WTe2 by angle-dependent and polarized Raman spectroscopy (ADPRS). Ten Raman modes are clearly resolved. Their intensities show periodic variation with sample rotating. We identify the symmetries of the detected modes by quantitatively analyzing the ADPRS results based on the symmetry selection rules. Material absorption effect on the phonon modes with high vibration frequencies is investigated by considering complex Raman tensor elements. We also provide a rapid and nondestructive method to identify the crystallographic orientation of WTe2. The crystallographic orientation is further confirmed by the quantitative atomic-resolution force image. Finally, we find that the atomic vibrational tendency and complexity of detected modes are also reflected in the shrinkage degree defined based on ADPRS, which is confirmed by corresponding density functional calculation. Our work provides a deep understanding of the interaction between WTe2 and light, which will benefit in future studies about the anisotropic physical properties of WTe2 and other in-plane anisotropic materials.

Geometrically pinned magnetic domain wall for multi-bit per cell storage memory.

Spintronic devices currently rely on magnetic switching or controlled motion of domain walls (DWs) by an external magnetic field or a spin-polarized current. Controlling the position of DW is essential for defining the state/information in a magnetic memory. During the process of nanowire fabrication, creating an off-set of two parts of the device could help to pin DW at a precise position. Micromagnetic simulation conducted on in-plane magnetic anisotropy materials shows the effectiveness of the proposed design for pinning DW at the nanoconstriction region. The critical current for moving DW from one state to the other is strongly dependent on nanoconstricted region (width and length) and the magnetic properties of the material. The DW speed which is essential for fast writing of the data could reach values in the range of hundreds m/s. Furthermore, evidence of multi-bit per cell memory is demonstrated via a magnetic nanowire with more than one constriction.

Geometric control of the magnetization reversal in antidot lattices with perpendicular magnetic anisotropy

While the magnetic properties of nanoscaled antidot lattices in in-plane magnetized materials have widely been investigated, much less is known about the microscopic effect of hexagonal antidot lattice patterning on materials with perpendicular magnetic anisotropy. By using a combination of first-order reversal curve measurements, magnetic x-ray microscopy, and micromagnetic simulations we elucidate the microscopic origins of the switching field distributions that arise from the introduction of antidot lattices into out-of-plane magnetized GdFe thin films. Depending on the geometric parameters of the antidot lattice we find two regimes with different magnetization reversal processes. For small antidots, the reversal process is dominated by the exchange interaction and domain wall pinning at the antidots drives up the coercivity of the system. On the other hand, for large antidots the dipolar interaction is dominating which leads to fragmentation of the system into very small domains that can be envisaged as a basis for a bit patterned media.

Constricted nanowire with stabilized magnetic domain wall

Domain wall (DW)-based magnetic memory offers the possibility for increasing the storage capacity. However, stability of DW remains the major drawback of this scheme. In this letter, we propose a stepped nanowire for pinning DW in a desirable position. From micromagnetic simulation, the proposed design applied to in-plane magnetic anisotropy materials shows that by adjusting the nanowire step size and its width it is possible to stabilize DW for a desirable current density range. In contrast, only a movement of DW could be seen for conventional nanowire. An extension to a multi-stepped nanowire could be used for multi-bit per cell magnetic memory.

Micromagnetic Study of Spin-Transfer-Driven Vortex Dipole and Vortex Quadrupole Dynamics

Vortices and antivortices are typical non uniform magnetization configurations that can be achieved in spin-torque oscillators with in-plane materials. Dynamics of a vortex-antivortex pair, namely vortex dipole, were predicted and already observed. In this paper, we present a systematic micromagnetic study on that kind of dynamics in different spin-valves where the current is injected through a nano-aperture. Rotation and translation of vortex dipoles and rotation of vortex quadrupoles are shown depending on the shape and the size of the spin-valve. The origin of the different behaviors is explained within a micromagnetic framework.

Wave vector dependent Rashba coefficient and nonlinear Rashba spin splitting in AlGaN/GaN quantum wells

By considering the energy dispersion of the conduction subband, we found the corrected Rashba coefficient (α׳) in AlGaN/GaN quantum wells (QWs) decreases with the in-plane wave vector k//, and the corrected Rashba spin splitting (ΔE׳) increases nonlinearly as a function of k//. Moreover, the correction to the Rashba spin splitting also increases with k//, since the ratio of the kinetic energy in the effective band gap increases. The effect of energy dispersion on the correction to the Rashba spin splitting will be greater for large in-plane wave vectors and materials with narrow band gap. Although the band gap of the barrier increases with Al content (x), we found the corrections to the Rashba coefficient and Rashba spin splitting at the Fermi level in AlxGa1−xN/GaN QWs increase with x, since the expansion region of the envelope functions decrease, and the polarized electric field in the well increases rapidly.

Development of perpendicularly magnetized Ta|CoFeB|MgO-based tunnel junctions at IBM (invited)

The discovery of perpendicular magnetic anisotropy (PMA) in Ta|CoFeB|MgO and the subsequent development of perpendicularly magnetized tunnel junctions at IBM is reviewed. The fast-turn-around method used for screening materials for interface PMA by measuring the moment/area and anisotropy field of in-plane materials as a function of CoFeB thickness is presented, including the data as a function of seed-layer material which led to the discovery of PMA in Ta|CoFeB|MgO. Magnetic and electrical data are reported for the first PMA magnetic tunnel junction we made using this material. By inserting a thin Fe layer at the Ta|CoFeB interface, a substantial increase in the PMA energy density was obtained. Pure Fe layers (which required the use of a TaMg seed) greatly improved the thermal stability, allowing annealing up to 400 °C.

Membrane Curvatures and Stress-strain Full Fields of Axisymmetric Bulge Tests from 3D-DIC Measurements. Theory and Validation on Virtual and Experimental results

The bulge test is mostly used to analyze equibiaxial tensile stress state at the pole of inflated isotropic membranes. Three-dimensional digital image correlation (3D-DIC) technique allows the determination of three-dimensional surface displacements and strain fields. In this paper, a method is proposed to determine also the membrane stress tensor fields for in-plane isotropic materials, independently of any constitutive equation. Stress-strain state is then known at any surface point which enriches greatly experimental data deduced from the axisymmetric bulge tests. Our method consists, first in calculating from the 3D-DIC experimental data the membrane curvature tensor at each surface point of the bulge specimen. Then, curvature tensor fields are used to investigate axisymmetry of the test. Finally in the axisymmetric case, membrane stress tensor fields are determined from meridional and circumferential curvatures combined with the measurement of the inflating pressure. Our method is first validated for virtual 3D-DIC data, obtained by numerical simulation of a bulge test using a hyperelastic material model. Afterward, the method is applied to an experimental bulge test performed using as material a silicone elastomer. The stress-strain fields which are obtained using the proposed method are compared with results of the finite element simulation of this overall bulge test using a neo-Hookean model fitted on uniaxial and equibiaxial tensile tests.

Current-induced domain wall motion in nanoscale ferromagnetic elements

We review the details of domain wall (DW) propagation due to spin-polarized currents that could potentially be used in magnetic data storage devices based on domains and DWs. We discuss briefly the basics of the underlying spin torque effect and show how the two torques arising from the interaction between the spin-polarized charge carriers and the magnetization lead to complex dynamics of a spin texture such as a DW. By direct imaging we show how confined DWs in nanowires can be displaced using currents in in-plane soft-magnetic materials, and that when using short pulses, fast velocities can be attained. For high-anisotropy out-of-plane magnetized wires with narrow DWs we present approaches to deducing the torque terms and show that in these materials potentially more efficient domain wall motion could be achieved.

Two-dimensional Green's function tensor and projected local density of states for TM and TE modes in dispersive and anisotropic photonic crystals

A multiple-scattering method for two-dimensional TM modes is extended to calculate the electric Green's function tensor for TE modes of a finite-size photonic crystal consisting of infinite-length cylinders of dispersive and in-plane anisotropic materials. We investigate the frequency and spatial dependence of the projected local density of states for TM and TE modes of the system. The large enhancement factor of the projected local density of states has been observed for dispersive finite photonic crystals.

Quantitative analysis of domain texture in polycrystalline barium titanate by polarized Raman microprobe spectroscopy

A quantitative determination of domain distribution in polycrystalline barium titanate (BaTiO3, henceforth BT) ceramics has been pursued with the aid of a microprobe polarized Raman spectrometer. The crystallographic texture and domain orientation distribution of BT ceramics, which switched upon applying stress according to ferroelasticity principles, were determined from the relative intensity of selected phonon modes, taking into consideration a theoretical analysis of the angular dependence of phonon mode intensity for the tetragonal BT phase. Furthermore, the angular dependence of Raman intensity measured in polycrystalline BT depended on the statistical distribution of domain angles in the laser microprobe, which was explicitly taken into account in this work for obtaining a quantitative analysis of domain orientation for in-plane textured BT polycrystalline materials.

Advantages of CNT–MFM probes in observation of domain walls of soft magnetic materials

The advantage of the CoFe-coated carbon nanotube (CNT) probes in a magnetic force microscope (MFM) is verified on in-plane magnetized soft magnetic materials. CoFe-coated CNT, standard and low-moment MFM probes were used to observe closure domains in square and rectangular Permalloy elements. The perturbative effect of the CNT–MFM probe was far less than that of a standard MFM probe. Domain walls were clearly observed as a pair of dark and bright lines which was in agreement with the micromagnetic simulations. The vortex core was also clearly observed using the CNT–MFM probes.

Focus on Analytical Instruments

Focus on Analytical Instruments

Designation of Mode Mix in Orthotropic Composite Delamination Problems

In interfacial fracture modeling of composite delamination, mode mix is typically specified in terms of energy release rates. Other near-tip quantities can be used to designate mode mix, however. This paper considers the designation of mode mix in terms of energy release rates, stress intensity factors, stresses ahead of the crack tip and crack face displacements and the consequences of using different near-crack-tip quantities to designate mode mix in analyzing composite delamination. The problem addressed is two-dimensional debonding between plies or ply groups modeled as in-plane orthotropic materials; however, the conclusions discussed apply to general composite delamination problems. It is shown that use of different quantities to designate mode mix can give significantly different results in matching composite applications to mixed-mode toughness tests. For cases where measured interfacial toughness increases with increasing mode II deformation, it is demonstrated that use of a mode mix designation based on energy release rates could be non-conservative. Based on these findings, it is suggested that practitioners consider the differences in failure load predictions that would result if different near-tip quantities were used to relate composite applications to measured toughnesses. To this end, methods for converting mode mix designations in terms of energy release rates into designations in terms of other fracture quantities are outlined and applied.

Elastic bodies reinforced with inextensible surfaces

The constraint of in-plane rigidity is examined within the general framework of the theory of internally constrained materials. It is shown that, for in-plane rigid materials, local strain and active stress are both defined by vectorial quantities. Representation formulae for the elastic response mapping are established in the cases of transverse isotropy and maximal symmetry, compatible with the constraint manifold. The equilibrium problem for an elastic body reinforced with parallel inextensible planes is also considered. In particular, universal solutions for bodies with maximal material symmetry are determined within the class of deformations which leave rigid every reinforcing plane.

Separation of crack extension modes in orthotropic delamination models

In modeling a crack along a distinct interface between dissimilar elastic materials, the ratio of mode I to mode II stress intensity factors or energy release rates is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. Although methods have been developed for comparing mode mixes for isotropic interfacial fracture problems, this behavior currently limits the applicability of interfacial fracture mechanics in predicting delamination in layered materials without isotropic symmetry. The virtual crack closure technique (VCCT) is a method used to extract mode I and mode II energy release rate components from numerical fracture solutions. Energy release rate components extracted from an oscillatory solution using the VCCT are not unique due to their dependence on the virtual crack extension length, Δ. In this work, a method is presented for using the VCCT to extract Δ-independent energy release rate quantities for the case of an interface crack between two in-plane orthotropic materials. The method does not involve altering the analysis to eliminate its oscillatory behavior and it is similar to existing methods for extracting a mode mix from isotropic interfacial fracture models. Knowledge of near-tip fields is used to determine the explicit Δ dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on Δ. A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that Δ-independent energy release rate quantities result. The modified technique has potential as a consistent method for extracting a mode mix from numerical solutions. The Δ-independent energy release rate quantities extracted using this technique can also aid numerical modelers, serving as guides for testing the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.