Magnetization Of Nanomagnets Research Articles

Macrospin study on magnetization reversal in synthetic antiferromagnetically coupled composite of perpendicularly magnetized nanomagnets

Macrospin study on magnetization reversal in synthetic antiferromagnetically coupled composite of perpendicularly magnetized nanomagnets

Synthetic exchange coupled composite for widening an in-plane ballistic switching region

This study proposes synthetic exchange coupled composites to control ballistic switching effectively. We performed macrospin simulations for the ballistic switching of in-plane magnetized nanomagnets with varying antiferromagnetic coupling constant. It was discovered that there exists an optimal value of the antiferromagnetic coupling constant at which the ballistic switching region can be widened to 3.3 times of that of the single hard nanomagnet, where the antiferromagnetic coupling field torque significantly counteracts the demagnetizing field torque of the hard nanomagnet. The ballistic switching region is also effectively widened due to the volume-averaging of saturation magnetizations; that is, the cancelation of demagnetizing fields at the large antiferromagnetic coupling beyond the optimal value.

Switching field distribution of ultradense arrays of single-crystalline magnetic nanowires

Ultradense arrays of magnetic nanoelements present considerable interest for extending areal densities in magnetic recording media, provided that they display high switching fields and corresponding low standard deviations. Here, we report the switching field distribution of bottom–up synthesized single-crystalline vertical Co nanowires self-organized in 2D hexagonal superlattices. The combined shape and Co hexagonal compact magnetocrystalline anisotropies in individual nanowires of diameter as small as 6 nm define a robust perpendicular magnetic anisotropy despite important interactions in superlattices of 10 × 1012 NWs/in2. Using quantitative analysis of temperature-dependent first-order reversal curves, we capture the switching field distribution in this dipolar-coupled perpendicularly magnetized nanomagnets. First, the interwire dipolar interactions are treated separately and show a dominant mean field character with temperature independent amplitudes that scale with the nanowire packing fraction. Then, the intrinsic switching field distribution, namely, independent of interwire interactions, is determined as a function of temperature in the 5–300 K range. The mean value and deviation are both found to be driven by the intrawire dipolar interaction and the temperature-dependent uniaxial magnetocrystalline anisotropy, but of smaller amplitudes than those expected from bulk behavior. With coercive fields ranging between 0.3 and 0.8 T, the switching field deviations relative to coercivity reach 20%, which is a moderate value regarding pitch arrays as small as 8 nm.

FORC signatures and switching-field distributions of dipolar coupled nanowire-based hysterons

Analysis of first-order reversal curves (FORCs) is a powerful tool to probe irreversible switching events in nanomagnet assemblies. As in essence switching events are related to the intrinsic properties of the constituents and their interactions, the resulting FORC diagrams contain much information that can be cross-linked and complex to deconvolute. In order to quantify the relevant parameters that drive the FORC diagrams of arrays of perpendicularly magnetized nanomagnets, we present step-by-step simulations of assemblies of hysterons to determine the specific signatures related to different known inputs. While we explored the consequences of dipolar interactions using either mean field or magnetostatic approaches, we completed by taking the hysteron switching field distribution (SFD) as either normal or lognormal. We demonstrated that the transition between FORC diagrams composed of an isolated interaction field distribution (IFD) and a wishbone shape operates via the SFD deviation, σHsw, in the presence of a weakly dispersed interaction field. In the presence of a magnetostatic interaction field, the IFD profile is peaked and a coercive field distribution (CFD) sums to the IFD as σHsw increases. A transition between IFD + CFD and wishbone shapes is clearly demonstrated as a function of the interaction field deviation σHint. In addition, we demonstrate that whatever the considered cases, σHswcan be quantitatively extracted from the FORC diagrams within an error inferior to 10%. These findings are of interest for dipolar coupled perpendicularly magnetized nanomagnets, as in assemblies of magnetic nanowires and nanopillars, as well as bit patterned media.

Reduction of the switching current in perpendicularly magnetized nanomagnets using an antiferromagnetic coupling structure

This paper reports a current-induced magnetization switching with a nanosecond-scale pulse current in a nanomagnet using a perpendicularly magnetized synthetic antiferromagnetic coupling (p-AFC) structure. The results indicate that the magnetization switching current in the p-AFC structure is less than that in the single-nanomagnet structure with perpendicular anisotropy when the differences in thickness and saturation magnetization between the upper and lower layers of the p-AFC structure are small and the Gilbert damping constant is also small. The results also show that the p-AFC structure can reduce the switching current when the pulse duration is short and its structure is effective for a high-speed switching. The results of this study shall be useful in the design of spin-transfer torque random access memory.

Cache Memory Design With Magnetic Skyrmions in a Long Nanotrack

Magnetic skyrmion (MS), a vortexlike region with reversed magnetization in nanomagnets, has recently emerged as an exciting development in the field of spintronics. It has a number of beneficial features, including remarkably high stability, ultralow depinning current density, and extremely compact size. Due to these benefits, skyrmions have generated great interest in the design of spintronic memory. In this paper, we evaluate the use of skyrmion-based memory as a last-level cache for general-purpose processors. In the skyrmion-based memory structure, data can be densely packed as multiple bits in a long magnetic nanotrack. Write operations are performed by injecting a spin-polarized current in the nanotrack. Since multiple skyrmions (each representing a bit) are packed into a single nanotrack, they need to be accessed by shifting them along the nanotrack with a charge current passing through a spin-Hall metal (SHM). We identify the following key challenges associated with MS-based cache design: 1) the high-current requirements for skyrmion nucleation limit the density benefits offered by these structures, since the transistor supplying write currents is the limiting factor that determines the bit-cell area; 2) the proposed nanotrack structure results in significant performance overheads due to the latency arising from the shift operations; 3) the skyrmions move toward the edge of the nanotrack during shift operations owing to the Magnus force. Hence, an additional idle operation time is required to relax skyrmions back through the repulsive force from the edge; and 4) to avoid annihilation of skyrmions from the edge, the duration and the current density of the shift operation have to be well controlled. To overcome these challenges, a multi-bit skyrmion cell with appropriate peripheral circuit is proposed, considering the heterogeneity in the read/write characteristics. The density benefits are explored by performing the layout of different multi-bit cells. We perform a systematic device-circuit-architecture co-design to evaluate the feasibility of our proposal. Our experiments demonstrate the potential of, and the challenges involved in, using skyrmion-based memory as last-level caches.

Reversal Time of Jump-Noise Dynamics for Large Nucleation

The jump-noise is a phenomenological stochastic process used to model the thermal fluctuation of magnetization in nanomagnets. In this work, the large nucleation regime of jump-noise dynamics is studied, and its reversal time is characterized from Monte Carlo simulations and analysis. Results show that the reversal time of jump-noise dynamics for large nucleation is asymptotically equal to the time constant associated with a single jump-noise scattering event from the energy minimum in the energy landscape of the magnetization. The reversal time for large nucleation depends linearly on the height of the energy barrier for large barriers. The significance of the large nucleation regime of jump-noise dynamics to phenomenologically explain the magnetoelectric switching of antiferromagnetic order parameter is also prospected.

Hybrid Magnetodynamical Modes in a Single Magnetostrictive Nanomagnet on a Piezoelectric Substrate Arising from Magnetoelastic Modulation of Precessional Dynamics.

Magnetoelastic (or "straintronic") switching has emerged as an extremely energy-efficient mechanism for switching the magnetization of magnetostrictive nanomagnets in magnetic memory and logic, and non-Boolean circuits. Here, we investigate the ultrafast magnetodynamics associated with straintronic switching in a single quasielliptical magnetostrictive Co nanomagnet deposited on a piezoelectric Pb(Mg1/3Nb2/3)O3-PbTiO3 substrate using time-resolved magneto-optical Kerr effect (TR-MOKE) measurements. The pulsed laser pump beam in the TR-MOKE plays a dual role: it causes precession of the nanomagnet's magnetization about an applied bias magnetic field and it also generates surface acoustic waves in the piezoelectric substrate that produce periodic strains in the magnetostrictive nanomagnet and modulate the precessional dynamics. This modulation gives rise to intriguing hybrid magnetodynamical modes in the nanomagnet, with a rich spin-wave texture. The characteristic frequencies of these modes are 5-15 GHz, indicating that strain can affect magnetization in a magnetostrictive nanomagnet in time scales much smaller than 1 ns (∼100 ps). This can enable ∼10 GHz range magnetoelastic nano-oscillators that are actuated by strain instead of a spin-polarized current, as well as ultrafast magnetoelectric generation of spin waves for magnonic logic circuits, holograms, etc.

Magnetization-induced dynamics of a Josephson junction coupled to a nanomagnet

We study the superconducting current of a Josephson junction (JJ) coupled to an external nanomagnet driven by a time dependent magnetic field both without and in the presence of an external AC drive. We provide an analytic, albeit perturbative, solution for the Landau-Lifshitz (LL) equations governing the coupled JJ-nanomagnet system in the presence of a magnetic field with arbitrary time-dependence oriented along the easy axis of the nanomagnet's magnetization and in the limit of weak dimensionless coupling $\epsilon_0$ between the JJ and the nanomagnet. We show the existence of Shapiro-like steps in the I-V characteristics of the JJ subjected to a voltage bias for a constant or periodically varying magnetic field and explore the effect of rotation of the magnetic field and the presence of an external AC drive on these steps. We support our analytic results with exact numerical solution of the LL equations. We also extend our results to dissipative nanomagnets by providing a perturbative solution to the Landau-Lifshitz-Gilbert (LLG) equations for weak dissipation. We study the fate of magnetization-induced Shapiro steps in the presence of dissipation both from our analytical results and via numerical solution of the coupled LLG equations. We discuss experiments which can test our theory.

Heteroclinic tangle phenomena in nanomagnets subject to time-harmonic excitations

Magnetization dynamics in uniformly magnetized nanomagnets excited by time-harmonic (AC) external fields or spin-polarized injected currents is considered. The analysis is focused on the behaviour of the AC-excited dynamics near saddle equilibria. It turns out that this dynamics has a chaotic character at moderately low power level. This chaotic and fractal nature is due to the phenomenon of heteroclinic tangle which is produced by the combined effect of AC-excitations and saddle type dynamics. By using the perturbation technique based on Melnikov function, analytical formulas for the threshold AC excitation amplitudes necessary to create the heteroclinic tangle are derived. Both the cases of AC applied fields and AC spin-polarized injected currents are treated. Then, by means of numerical simulations, we show how heteroclinic tangle is accompanied by the erosion of the safe basin around the stable regimes.

Noise-induced bifurcations in magnetization dynamics of uniaxial nanomagnets

Stochastic magnetization dynamics in uniformly magnetized nanomagnets is considered. The system is assumed to have rotational symmetry as the anisotropy axis, the applied field, and the spin polarization are all aligned along an axis of symmetry. By appropriate integration of the Fokker-Planck equation associated to the problem, the stochastic differential equation governing the evolution of the angle between the magnetization orientation and the symmetry axis is derived. The drift terms present in this equation contain a noise-induced drift term, which, in combination with drift terms of deterministic origin, can be written as the derivative of an effective potential. Superparamagnetic-like transitions are studied in connections with the bifurcations of the effective potential as temperature and excitation conditions are varied.

Experimental Realization of a Nanomagnet Full Adder Using Slanted-Edge Magnets

We present the experimental realization of a full adder circuit using Nanomagnet Logic (NML). The circuit relies heavily on the properties of asymmetric slant magnets that allow robust operation and reduced footprint. We demonstrate stand-alone NML majority gates and wires, and interconnect these components into an NML full adder that functions properly for all 8 input combinations. To our knowledge, this is the first working implementation of an NML full adder from in-plane magnetized nanomagnets, and one of the very few existing non-electrical, room temperature nanoscale computing units.

Four-state nanomagnetic logic using multiferroics

The authors theoretically demonstrate the implementation of a low-power 4-state universal logic gate (NOR) using a linear array of three dipole-coupled magnetostrictive-piezoelectric multiferroic nanomagnets (e.g. Ni/PZT) with biaxial magnetocrystalline anisotropy. The two peripheral nanomagnets in the array encode the 4-state input bits in their magnetization orientations and the central nanomagnet's magnetization orientation represents the output bit. Numerical simulations are performed to confirm that the 4-state output bit is the Boolean NOR function of the two 4-state inputs bits when the array reaches its ground state. A voltage pulse alternating between −0.2 and +0.2 V, applied to the piezoelectric layer of the central nanomagnet, generates alternating tensile and compressive stress in its magnetostrictive layer. This drives the array to the correct ground state where dipole interaction between the magnets ensures that the output is the NOR function of the input. For the system considered, the gate operation is executed while dissipating only ∼33 000 kT (0.138 fJ) of energy.

Proposal for an all-spin logic device with built-in memory

The possible use of spin rather than charge as a state variable in devices for processing and storing information has been widely discussed, because it could allow low-power operation and might also have applications in quantum computing. However, spin-based experiments and proposals for logic applications typically use spin only as an internal variable, the terminal quantities for each individual logic gate still being charge-based. This requires repeated spin-to-charge conversion, using extra hardware that offsets any possible advantage. Here we propose a spintronic device that uses spin at every stage of its operation. Input and output information are represented by the magnetization of nanomagnets that communicate through spin-coherent channels. Based on simulations with an experimentally benchmarked model, we argue that the device is both feasible and shows the five essential characteristics for logic applications: concatenability, nonlinearity, feedback elimination, gain and a complete set of Boolean operations.

Reducing the critical current for spin-transfer switching of perpendicularly magnetized nanomagnets

We describe nanopillar spin valves with perpendicular anisotropy designed to reduce the critical current needed for spin transfer magnetization reversal while maintaining thermal stability. By adjusting the perpendicular anisotropy and volume of the free element consisting of a [Co/Ni] multilayer, we observe that the critical current scales with the height of the anisotropy energy barrier and we achieve critical currents as low as 120 μA in quasistatic room-temperature measurements of a 45 nm diameter device. The field-current phase diagram of such a device is presented.

Attempt frequency of magnetization in nanomagnets with thin-film geometry

Solving the stochastic Landau-Lifshitz-Gilbert equation numerically, we investigate the effect of the potential landscape on the attempt frequency of magnetization in nanomagnets with the thin-film geometry. Numerical estimates of the attempt frequency are analyzed in comparison with theoretical predictions from the Fokker-Planck equation for the N\'eel-Brown model. It is found that for a nanomagnet with the thin-film geometry, theoretically predicted values for the universal case are in excellent agreement with numerical estimates.

Current-induced magnetization dynamics in nanomagnets

An overview is given of the various approaches that have been proposed for the interpretation of spin-transfer-driven magnetization dynamics. Models of critical currents and critical fields for switching as well as for the onset of magnetization oscillations are discussed, together with methods for the construction of field-current stability diagrams. Finally, the role of thermal fluctuations is analyzed. Particular emphasis is given to the study of uniformly magnetized nanomagnets, which represents an essential step before moving to the numerical computation of more complex micromagnetic configurations.

Transient dynamics leading to self-oscillations in nanomagnets driven by spin-polarized currents

Magnetization dynamics in uniformly magnetized nanomagnets subject to spin-polarized currents is studied by Landau-Lifshitz-Gilbert (LLG) equation with a spin-transfer torque term. This kind of magnetic system may exhibit stationary states and self-oscillatory regimes. By using the fact that spin-transfer torque and Gilbert damping are small perturbations of the conservative LLG dynamics, the analysis of self-oscillations is carried out by an appropriate perturbation technique. Averaging technique is then used to derive an approximated model for the energy dynamics which enables one to study the transient leading to self-oscillatory regimes. The accuracy of the proposed analytical technique is tested by comparison with numerical solutions of the LLG equation.

Effect of Spin Chirality on Magnetization in Triangular Rings

Role of spin chirality on magnetization process of triangular spin rings has been studied. A half step magnetization, unexpected for isothermal process, is observed at the level crossing between the doubly degenerated S = 1/2 states and the excited S = 3/2 state. The present result substantiates adiabatic change of magnetization in nano-magnets.

S mixing and quantum tunneling of the magnetization in molecular nanomagnets.

The role of S mixing in the quantum tunneling of the magnetization in nanomagnets has been investigated. We show that the effect on the tunneling frequency is huge and that the discrepancy (more than 3 orders of magnitude in the tunneling frequency) between spectroscopic and relaxation measurements in Fe(8) can be resolved if S mixing is taken into account.