In-plane Shape Anisotropy Research Articles

Write Error Rate in Bias-Magnetic-Field-Free Voltage-Induced Switching in a Conically Magnetized Free Layer

Write error rate (WER) in voltage-induced magnetization switching of a conically magnetized free layer with an elliptic cylinder shape is numerically calculated on the basis of the macrospin model. Simulations using the Langevin equation show that a WER lower than the order of ${10}^{\ensuremath{-}5}$, which enables practical WER with a single error-correction process, is theoretically feasible at zero-bias magnetic field and room temperature. We also show that WER at a given thermal stability factor and the volume of the free layer can be reduced by adopting the free layer with the larger in-plane shape anisotropy field and a moderate cone angle at zero-bias voltage.

Study on a new manner of the magnetization switching actuated by a unidirectional pulse current

A new writing scheme with a unidirectional pulse current is proposed for spin transfer torque (STT) based magnetic random-access memory (MRAM). To investigate the feasibility of the writing scheme, bilayered nano-pillars composed of a soft layer with small in-plane shape anisotropy and a hard layer with either large perpendicular anisotropy (PMA) or in-plane anisotropy (IMA) are designed and their switching behaviors are studied. It is found that in either type of bilayered nano-pillars, with the aid of the attached hard layer, the magnetization of the soft layer can be switched back and forth under a unidirectional pulse current. In an IMA/IMA nano-pillar, the magnetization of the free layer (FL) can achieve excellent alignment, which is in contrast to the IMA/PMA nano-pillar. By optimizing the dimensions and magnetic parameters of the IMA/IMA nano-pillar, a decently low switching current density (4.3 × 1011 A m−2) and ultrashort switching time (<1 ns) can be reached. Based on these results, the unidirectional writing scheme is practical if an IMA/IMA bilayer is used to replace the FL in a magnetic tunnel junction. Considering that a unidirectional writing scheme can enable the application of materials with high spin polarization such as half metals, and avoid the injection of writing current into junction using a special design, it may be very promising for STT-MRAM.

Bias-field-free high frequency microwave emission of spin-transfer nano-oscillator with magnetizations all in-plane

We reported microwave measurements on a nanoscale MgO-based magnetic tunnel junction having an elliptical shape with large aspect ratios to obtain enough in-plane shape anisotropy to ensure free layer magnetization along the long axis. Combined with the magnetization of a synthetic antiferromagnet pinned layer along the short axis, this results in the perpendicular configuration between the magnetizations of free and pinned layers. A steady high frequency oscillation up to 5 GHz was achieved in such devices at zero magnetic field. Meanwhile, a large frequency tunability of 0.11 Hz·cm2/mA (2.67 GHz/mA) was obtained. The micromagnetic simulations confirm the origin of the high oscillation frequency of our spin transfer nano-oscillators (STNOs). These results suggest the great possibility of improved integration and potential application of STNOs for developing the next-generation of on-chip oscillators.

Electric-field-driven Deterministic and Robust 120° Magnetic Rotation in a Concave Triangular Nanomagnet

Deterministic magnetic switching driven by electric fields rather than power-dissipating currents at the nanoscale is fundamentally challenging yet promising for applications to energy-efficient and high-density spintronic devices. Here, we demonstrate an electric-field-controlled deterministic, robust and repeatable $120{}^{o}$ rotation of ``Y''-like magnetic state in a patterned nanoscale multiferroic heterostructure consisting of a concave triangular nanomagnet deposited on $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$-${\mathrm{Pb}\mathrm{Ti}\mathrm{O}}_{3}$ film. Using phase-field simulations, we find that the rotation of ``Y''-like magnetic state is controlled by a co-action of strain-mediated electric-field-induced uniaxial magnetoelastic anisotropy, magnetic in-plane shape anisotropy of the concave-triangle-shaped nanomagnet, and an interfacial exchange-bias field from a juxtaposed antiferromagnetic layer. It is also shown that deterministic magnetic state switching can be accomplished by a pulsed strain, the duration of which can span from ten nanoseconds or longer down to a few nanoseconds, providing great design flexibility. We also discuss the dynamics of electric-field-driven switching of ``Y''-like magnetic state as well as the influence of side length, thickness, and shape variation (i.e., concave radius) of the nanomagnet on the critical strain for the switching. These results offer a technologically viable route to designing nanomagnet-based nonvolatile spin memories with high density and low power.

Voltage control of magnetic domain wall injection into strain-mediated multiferroic heterostructures.

Effective control of domain wall (DW) injection into magnetic nanowires is of great importance for future novel device applications in spintronics, and currently relies on magnetization switching by the local external magnetic field obtained from metal contact lines or a spin-transfer torque (STT) effect from spin-polarized current. However, the external field is an obstacle for realizing practical spintronic devices with all-electric operation, and high current density can occasionally damage the devices. In this work, voltage controlled in-plane magnetic DW injection into a magnetic nanowire in the strain-mediated multiferroic heterostructures is studied by means of fully coupled micromagnetic-mechanical Finite Element Method (FEM) simulations. We propose an engineered shaped nano-magnet on a piezoelectric thin film in which a 180° magnetization rotation in the DW injection region is accomplished with in-plane piezostrain and magnetic shape anisotropy, thereby, leading to a DW injection into the nanowire. In this architecture, we computationally demonstrate repeated creation of DWs by voltage-induced strains without using any magnetic fields. Our FEM simulation results demonstrated an ultralow area energy consumption per injection (∼52.48 mJ m-2), which is drastically lower than the traditional magnetic field and STT driven magnetization switching. A fast-overall injection time within ∼3.4 ns under continuous injection is also demonstrated. Further reduction of energy consumption and injection time can be achieved by optimization of the structure and material selections. The present design and computational analyses can provide an additional efficient method to realize low-power and high-speed spintronic and magnonic devices.

Two-dimensional ferromagnetic van der Waals CrCl3 monolayer with enhanced anisotropy and Curie temperature

Among the recently widely studied van der Waals layered magnets $\mathrm{Cr}{X}_{3}$ ($X=\mathrm{Cl}$, Br, I), $\mathrm{CrC}{\mathrm{l}}_{3}$ monolayer (ML) is particularly puzzling: it is shown by experiments to have only an in-plane magnetic easy axis and, furthermore, all previous first-principles calculation results contradict this. Through systematic first-principles calculations, we unveil that the in-plane shape anisotropy that dominates over the weak perpendicular magnetocrystalline anisotropy is responsible for the in-plane magnetic easy axis of $\mathrm{CrC}{\mathrm{l}}_{3}$ ML. To tune the in-plane ferromagnetism of $\mathrm{CrC}{\mathrm{l}}_{3}$ ML into the desirable perpendicular one, we propose substituting Cr with isovalent tungsten (W). We find that $\mathrm{CrWC}{\mathrm{l}}_{6}$ has a strong perpendicular magnetic anisotropy and a high Curie temperature up to 76 K. Our work not only gives insight into understanding the two-dimensional ferromagnetism of van der Waals MLs but also sheds new light on engineering their performances for nanodevices.

Sensitivity of the Power Spectra of Thermal Magnetization Fluctuations in Low Barrier Nanomagnets Proposed for Stochastic Computing to In-Plane Barrier Height Variations and Structural Defects

Nanomagnets with small in-plane shape anisotropy energy barriers on the order of the thermal energy have unstable magnetization that fluctuates randomly in time. They have recently emerged as promising hardware platforms for stochastic computing and machine learning because the random magnetization states can be harnessed for probabilistic bits. Here, we have studied how the statistics of the magnetization fluctuations (e.g., the power spectral density) is affected by (i) moderate variations in the barrier height of the nanomagnet (caused by small size variations) and (ii) the presence of structural defects — both localized and delocalized — in order to assess how robust the stochastic computing platform based on Low Barrier Nanomagnets (LBM) is. We found that the power spectral density is relatively insensitive to moderate barrier height change and also relatively insensitive to the presence of small localized defects. However, extended (delocalized) defects, such as thickness variations over a significant fraction of the nanomagnet, affect the power spectral density very noticeably. That means extended defects can significantly alter the fluctuation rate of the magnetization in low barrier nanomagnets. Since the fluctuation rate is crucial for stochastic computing applications, this has very serious implications for the latter. Thickness variations are difficult to avoid in real nanomagnets with in-plane anisotropy since they must be thin to keep the barrier height small and the substrate on which they are fabricated may have surface roughness comparable to the nanomagnet thickness. This raises questions about the viability of stochastic computing with low barrier nanomagnets possessing in-plane anisotropy. Our results establish that small variations in the shape (causing small variations in the barrier height), or small localized defects, are relatively innocuous and tolerable but extended defects are not. The latter must be avoided for stochastic computing applications.

Zero-field dynamics stabilized by in-plane shape anisotropy in MgO-based spin-torque oscillators

Here, we demonstrate numerically that shape anisotropy in MgO-based spin-torque nano-oscillators consisting of an out-of-plane magnetized free layer and an in-plane polarizer is necessary to stabilize out-of-plane magnetization precession without the need of external magnetic fields. As the in-plane anisotropy is increased, a gradual tilting of the magnetization towards the in-plane easy direction is introduced, favouring zero-field dynamics over static in-plane states. Above a critical value, zero-field dynamics are no longer observed. The optimum ratio of in-plane shape to out-of-plane uniaxial anisotropy, for which large angle out-of-plane zero-field dynamics occur within the widest current range, is reported.

Nanocaps: A numerical study of remanence, quasistatic and dynamic switching

Abstract Finite element micromagnetics are used to simulate remanence, hysteresis and dynamic switching in crescent shaped permalloy caps, a geometry that corresponds to either normal or oblique deposition of films on nanosphere arrays. Oblique deposition breaks the symmetry and favours onion states rather than vortices. It introduces in-plane shape anisotropy analogous to that of an elongated island and increases the in-plane coercivity. In isolated caps, the critical diameter above which the vortex state is the minimum energy state, is D = 123 nm for angles below θ = 20 deg. It increases with θ up to a vlaue of D = 157 nm at θ = 45 deg. Even for sizes for which the onion state is the lowest energy state, vortex states can be stabilized in isolated caps but the interparticle magnetostatic interactions tend to destabilize them driving the system to its ground state. The switching field of onion states can be reduced by 36% using microwave resonance at frequencies approaching the resonant (Kittel mode) frequencies.

Designer Shape Anisotropy on Transition-Metal-Dichalcogenide Nanosheets.

MoS2 and generally speaking, the wide family of transition-metal dichalcogenides represents a solid nanotechnology platform on which to engineer a wealth of new and outperforming applications involving 2D materials. An even richer flexibility can be gained by extrinsically inducing an in-plane shape anisotropy of the nanosheets. Here, the synthesis of anisotropic MoS2 nanosheets is proposed as a prototypical example in this respect starting from a highly conformal chemical vapor deposition on prepatterend substrates and aiming at the more general purpose of tailoring anisotropy of 2D nanosheets by design. This is envisioned to be a suitable configuration for strain engineering as far as strain can be spatially redistributed in morphologically different regions. With a similar approach, both the optical and electronic properties of the 2D transition-metal dichalcogenides can be tailored over macroscopic sample areas in a self-organized fashion, thus paving the way for new applications in the field of optical metasurfaces, light harvesting, and catalysis.

The competition between magnetocrystalline and shape anisotropy on the magnetic and magneto-transport properties of crystallographically aligned CuCr2Se4 thin films

Crystallographically aligned nanocrystalline films of the ferromagnetic spinel CuCr2Se4 were successfully synthesized and their structure and alignment were confirmed by X-ray diffraction and high-resolution transmission electron microscopy. The average size of the crystallites is about 200–250nm, and their (111) crystal planes are parallel to the film plane. A good match of the film’s electronic structure to that of bulk CuCr2Se4 is confirmed by transverse Kerr effect measurements. Four easy 〈111〉 axes are present in the films. One of these axes is oriented perpendicular and three others are oriented at an angle of 19.5° relative to the film plane. The magnetic properties of the films are determined by a competition between the out-of-plane magnetocrystalline anisotropy and the in-plane shape anisotropy. Magnetic measurements show that the dominating type of anisotropy switches from shape to magnetocrystalline anisotropy near 160K, which leads to a switch of the effective easy axis from inside the film plane at room temperature to perpendicular to the film plane as the temperature decreases. At last, a moderately large, negative value of the low-temperature magnetoresistance was observed for the first time in CuCr2Se4 films.

The investigation of ferromagnetic resonance linewidth in Ni80Fe20 films with submicron rectangular elements

Patterned magnetic films with nano-scaled dots exhibit some special magnetic properties. In this paper, we investigate the in-plane shape anisotropy and the magnetization dynamic damping in permalloy (Ni80Fe20) arrays of submicron rectangular elements using ferromagnetic resonance (FMR). The FMR linewidth exhibits a dependence on the element size, and mainly comes from the contribution of the intrinsic damping. Also the contribution of two-magnon scattering plays an important role and is reduced with increasing aspect ratio. The damping coefficient decreases from 0.0129 to 0.0118 with the element length increasing from 300 nm to 1200 nm, and the theoretical calculation suggests that the change of damping results from the longitudinal and transverse interlayer spin current due to the spatially inhomogeneous magnetization dynamics.

Domain wall dynamics of periodic magnetic domain patterns in Co2MnGe-Heusler microstripes

Highly symmetric periodic domain patterns were obtained in Co2MnGe-Heusler microstripes as a result of the competition between growth-induced in-plane magnetic anisotropy and shape anisotropy. Zero field magnetic configurations and magnetic field-induced domain wall (DW) motion were studied by magnetic force microscopy-image technique for two different cases: dominant uniaxial- and dominant cubic in-plane anisotropy. We implemented a magneto-optical Kerr effect susceptometer to investigate the DW dynamics of periodic domain structures by measuring the in-phase and out-of-phase components of the Kerr signal as a function of magnetic field frequency and amplitude. The DW dynamics for fields applied transversally to the long stripe axis was found to be dominated by viscous slide motion. We used the inherent symmetry/periodicity properties of the magnetic domain structure to fit the experimental results with a theoretical model allowing to extract the DW mobility for the case of transverse DWs (μTDW = 1.1 m s−1 Oe−1) as well as for vortex-like DWs (μVDW = 8.7 m s−1 Oe−1). Internal spin structure transformations may cause a reduction of DW mobility in TDWs as observed by OMMFF simulations.

Micromagnetic Simulation on the Interelement Coupling of High-Density Patterned Film

In this paper, the magnetic properties of an individual square permalloy (Ni80Fe20) nanoelement at the center of an array with both in-plane shape anisotropy and interelement interaction were investigated by the 3-D object oriented micromagnetic framework. Variation of the interelement coupling was studied by changing the element lateral size ( a ) and interelement spacing ( s ). Magnetic hysteresis loop and dependence of saturation field on s/a ( R ) of the individual element at the center of array indicate that dipolar interaction dominates the magnetic properties of array with small R ( R ≤ 1), whereas at R > 1, the interelement interaction can be ignored, and therefore, the shape anisotropy plays an important role in determining both the strength and the direction of magnetic moments. Moreover, for small R , the global easy axis is along the direction of element edge, and with increasing R , the easy axis appears to gradually turn to the diagonal direction. It is noteworthy that the corresponding conversion points of the easy axis on R decrease from 0.6 to 0.3 as increasing a from 10 to 20 nm, indicating the effect of interelement coupling is weaker in array with a larger element lateral size. The collective magnetic behavior of array is also investigated for comparison.

Effect of the intrinsic in-plane shape anisotropy on the oscillation characteristics of zero-field spin torque oscillator

The spin-torque oscillator, which can generate an AC voltage oscillation with the same frequency, have attracted considerable attention due to its potential applications in the frequency-tunable transmitters and receivers for wireless communication and the recording heads of high-density hard disk drives. However, from the energy-balance equation's point of view, in the absence of in-plane shape anisotropy of spin torque oscillator, the energy supplied by the spin torque is always larger than the energy dissipation due to the Gilbert damping, thus, a finite magnetic field applied perpendicular to the plane is required for a steady-state precession. This feature has limited its potential applications. In this paper, the influence of the intrinsic in-plane shape anisotropy on the magnetization dynamics of spin torque oscillator consisting of an in-plane polarizer and an out-of-plane free layer is studied numerically in terms of the Landau-Lifshitz-Gilbert-Slonczewski equation. It is demonstrated that the additional in-plane shape anisotropy plays a significant role in the energy balance between the energy accumulation due to the spin torque and the energy dissipation due to Gilbert damping, which can stabilize a steady-state precession. Therefore, a stable self-oscillation in the absence of the applied magnetic field can be excited by introducing additional in-plane shape anisotropy. In particular, a relatively large current region with zero-field self-oscillation, in which the corresponding microwave frequency is increased while the threshold current still maintains an almost constant value, can be obtained by introducing a relatively large intrinsic in-plane shape anisotropy. Our results suggest that a tunable spin transfer oscillator without an applied magnetic field can be realized by adjusting the intrinsic in-plane shape anisotropy, and it may be a promising configuration in the future wireless communications.

Full 180° magnetization reversal with electric fields.

Achieving 180° magnetization reversal with an electric field rather than a current or magnetic field is a fundamental challenge and represents a technological breakthrough towards new memory cell designs. Here we propose a mesoscale morphological engineering approach to accomplishing full 180° magnetization reversals with electric fields by utilizing both the in-plane piezostrains and magnetic shape anisotropy of a multiferroic heterostructure. Using phase-field simulations, we examined a patterned single-domain nanomagnet with four-fold magnetic axis on a ferroelectric layer with electric-field-induced uniaxial strains. We demonstrated that the uniaxial piezostrains, if non-collinear to the magnetic easy axis of the nanomagnet at certain angles, induce two successive, deterministic 90° magnetization rotations, thereby leading to full 180° magnetization reversals.

Polarization-insensitive optical gain characteristics of highly stacked InAs/GaAs quantum dots

The polarized optical gain characteristics of highly stacked InAs/GaAs quantum dots (QDs) with a thin spacer layer fabricated on an n+-GaAs (001) substrate were studied in the sub-threshold gain region. Using a 4.0-nm-thick spacer layer, we realized an electronically coupled QD superlattice structure along the stacking direction, which enabled the enhancement of the optical gain of the [001] transverse-magnetic (TM) polarization component. We systematically studied the polarized electroluminescence properties of laser devices containing 30 and 40 stacked InAs/GaAs QDs. The net modal gain was analyzed using the Hakki-Paoli method. Owing to the in-plane shape anisotropy of QDs, the polarization sensitivity of the gain depends on the waveguide direction. The gain showing polarization isotropy between the TM and transverse-electric polarization components is high for the [110] waveguide structure, which occurs for higher amounts of stacked QDs. Conversely, the isotropy of the [−110] waveguide is easily achieved even if the stacking is relatively low, although the gain is small.

Phase diagrams of MgO magnetic tunnel junctions including the perpendicular spin-transfer torque in different geometries

We calculate the switching voltages for MgO-based magnetic tunnel junctions taking into account both the in-plane and the fieldlike spin-torque terms. To this end, we analytically solve the Landau-Lifshitz-Gilbert equation for a generalized geometry. We assume that the in-plane spin-torque varies linearly with the applied voltage, while the fieldlike torque exhibits a quadratic voltage dependence. Specifically, we consider that the free layer has two generic, orthogonal anisotropy components, one of which is along the direction defined by the magnetization of the reference layer, which also serves as a polarizer. The resulting formalism is applied to three different, experimentally relevant geometries: tunnel junctions with both the free and the reference layers magnetized in the plane of the layers, junctions with fully perpendicular anisotropy, and perpendicular junctions with an additional in-plane easy axis, respectively. We find that for in-plane devices, the quadratic dependence of the fieldlike torque on the applied voltage can lead to back hopping, which remains possible if we insert an additional linear term for the bias dependence of the fieldlike spin-torque comparable to current experimental results. For perpendicular anisotropy junctions neither back hopping nor spin-transfer-driven steady-state precession are expected. An additional in-plane shape anisotropy component stabilizes canted states in tunnel junctions with perpendicular anisotropy for specific values of voltage and field. The results are consistent with numerical integration of the Landau-Lifshitz-Gilbert equation and in good agreement with recent experiments involving perpendicular magnetic anisotropy magnetic tunnel junctions.

Magnetic Properties of Fe/WRe (001) Multilayers

Following recent theoretical predictions on perpendicular uniaxial magnetocrystalline anisotropy in multilayers of 5 monolayers of Fe and 2 monolayers of W x Re100&#8211;x with tetragonally strained components, we have measured the magnetization and detailed atomic structure in a series of such samples with x = 20&#8211;80 at%. Although the achieved strain in the WRe layers is smaller than in the modelled case, we do observe a positive uniaxial magnetocrystalline anisotropy of around 0.6 MJ/m3 at 40 K, after accounting for the in-plane shape anisotropy. This causes the out-of-plane saturation field to be reduced considerably compared to a pure Fe thin film, while the saturation magnetization is maintained at a value which is enhanced by at least 30% from what would be expected from the multilayer composition alone. The coercivity is low, on the order of 6 kA/m in all samples.

Controlled nucleation of topological defects in the stripe domain patterns of lateral multilayers with perpendicular magnetic anisotropy

Magnetic lateral multilayers have been fabricated on weak perpendicular magnetic anisotropy amorphous Nd-Co films in order to perform a systematic study on the conditions for controlled nucleation of topological defects within their magnetic stripe domain pattern. A lateral thickness modulation of period $w$ is defined on the nanostructured samples that, in turn, induces a lateral modulation of both magnetic stripe domain periods $\lambda$ and average in-plane magnetization component $M_{inplane}$. Depending on lateral multilayer period and in-plane applied field, thin and thick regions switch independently during in-plane magnetization reversal and domain walls are created within the in-plane magnetization configuration coupled to variable angle grain boundaries and disclinations within the magnetic stripe domain patterns. This process is mainly driven by the competition between rotatable anisotropy (that couples the magnetic stripe pattern to in-plane magnetization) and in-plane shape anisotropy induced by the periodic thickness modulation. However, as the structural period $w$ becomes comparable to magnetic stripe period $\lambda$, the nucleation of topological defects at the interfaces between thin and thick regions is hindered by a size effect and stripe domains in the different thickness regions become strongly coupled.