Abdon Sepulveda

Electrical control of a single magnetoelastic domain structure on a clamped piezoelectric thin film—analysis

This paper presents an analytical model coupling Landau-Lifshitz-Gilbert micromagnetics with elastodynamics and electrostatics to model the response of a single domain magnetoelastic nano-element attached to a piezoelectric thin film (500 nm). The thin film piezoelectric is mounted on a Si substrate, globally clamping the film from in-plane extension or contraction. Local strain transfer to the magnetoelastic element is achieved using patterned electrodes. The system of equations is reduced to eight coupled partial differential equations as a function of voltage (V), magnetic potential ϕ, magnetic moments (m), and displacements (u), i.e., fully coupled material. The weak forms of the partial differential equations are solved using a finite element formulation. The problem of a Ni single domain structure (i.e., 150 nm × 120 nm × 10 nm) on a thin film (500 nm) piezoelectric transducer (PZT)-5H attached to an infinite substrate is studied. Discretization in the single domain structure is on the order of the ...

Generation of localized strain in a thin film piezoelectric to control individual magnetoelectric heterostructures

Experimental results demonstrate the ability of a surface electrode pattern to produce sufficient in-plane strain in a PbZr0.52Ti0.48O3 (PZT) thin film clamped by a Si substrate to control magnetism in a 1000 nm diameter Ni ring. The electrode pattern and the Ni ring/PZT thin film heterostructure were designed using a finite element based micromagnetics code. The magnetoelectric heterostructures were fabricated on the PZT film using e-beam lithography and characterized using magnetic force microscopy. Application of voltage to the electrodes moved one of the “onion” state domain walls. This method enables the development of complex architectures incorporating strain-mediated multiferroic devices.

Strain-mediated 180° perpendicular magnetization switching of a single domain multiferroic structure

Analytical results for a voltage induced 180° perpendicular magnetization switching in a single magnetic nanoelement are presented. This 180° switching is achieved by combining perpendicular magnetic anisotropy due to surface effects with a temporally short voltage induced strain pulse. The angular momentum of the magnetic moment results in its precession in response to an in-plane effective magnetic field induced by strain, causing it to overshoot the 90° reorientation to an in-plane equilibrium position. Removal of the strain at the peak overshoot results in a 180° magnetization switch. This process is simulated using a micromagnetic dynamic approach implemented in a finite element framework that includes shape anisotropy and perpendicular magnetic anisotropy contributions to the energy functional in addition to the exchange and magnetoelastic energy terms. Control of the energy landscape to enable the 180° switching was accomplished by controlling the film thickness, and the strain pulse amplitude and duration. A film thickness near the critical thickness for in-plane to out-of-plane equilibrium magnetization direction was used to reduce the energy barrier to switching and thus reduce the necessary strain to levels that can be achieved in ferroelectric thin films clamped by a substrate.

Voltage induced mechanical/spin wave propagation over long distances

We simulated the generation and propagation of spin waves (SWs) using two excitation methods, namely, magnetic field and voltage induced strain. A fully coupled non-linear magnetoelastic model, combining Landau–Lifshitz-Gilbert with elastodynamic equations, is used to study the propagation characteristics of SWs in magnetoelastic materials. Simulation results show that for excitation frequencies above ferromagnetic resonance (FMR), SWs excited by voltage induced strain propagate over longer distances compared to SWs excited by magnetic field. In addition, strain mediated SWs exhibit loss characteristics, which are relatively independent of the magnetic losses (Gilbert damping). Moreover, it is also shown that strain induced SWs can also be excited at frequencies below FMR.

Strain-mediated 180° switching in CoFeB and Terfenol-D nanodots with perpendicular magnetic anisotropy

A micromagnetic and elastodynamic finite element model is used to compare the 180° out-of-plane magnetic switching behavior of CoFeB and Terfenol-D nanodots with perpendicular magnetic easy axes. The systems simulated here consist of 50 nm diameter nanodots on top of a 100 nm-thick PZT (Pby[ZrxTi1-x]O3) thin film, which is attached to a Si substrate. This allows voltage pulses to induce strain-mediated magnetic switching in a magnetic field free environment. Coherent and incoherent switching behaviors are observed in both CoFeB and Terfenol nanodots, with incoherent flipping associated with larger or faster applied switching voltages. The energy to flip a Terfenol-D memory element is an ultralow 22 aJ, which is 3–4 orders more efficient than spin-transfer-torque. Consecutive switching is also demonstrated by applying sequential 2.8 V voltage pulses to a CoFeB nanodot system with switching times as low as 0.2 ns.

A preference aggregation rule approach for structural optimization

In this paper, preference aggregation rules are used to define overall design evaluation measures in optimal design problems. A methodology for the efficient solution of the corresponding design optimization problems is presented. Each design criterion as well as the constraints imposed on the design variables and problem parameters are characterized by preference functions. The nondifferentiable nature of the optimization problems which arise in this formulation is coped with using a first-order algorithm combined with approximation concepts. High-quality approximations for the system response functions are constructed using the concepts of intermediate response quantities and intermediate variables. These approximations are used to replace the original problem by a sequence of approximate problems. Example problems are presented to study the performance of the proposed optimization technique as well as the methodology based on approximation concepts.

The repulsion algorithm, a new multistart method for global optimization

This paper proposes a new multistart algorithm to find the global minimum of constrained problems. This algorithm, which in this paper is called the repulsion algorithm, efficiently selects initial design points for local searches. A Bayesian approach provides the stopping rules. The method uses information from the previous sampling points and the corresponding sequences generated by local searches to select new initial points. This approach increases the probability of finding all local minima with fewer local searches. Numerical example problems show that compared with traditional multistart methods, the repulsion algorithm reduces significantly the number of local searches required to find the global minimum.

Strain-mediated deterministic control of 360° domain wall motion in magnetoelastic nanorings

This study provides numerical simulations for deterministic 360° magnetization rotation of the transverse domain walls in a nickel nano-ring (outer diameter: 500 nm, inner diameter: 300 nm, and thickness: 10 nm) on a lead zirconate titanate (Pb[ZrxTi1-x]O3 0 < x < 1) (PZT) thin film (500 nm) deposited onto a Si substrate with surface patterned electrodes. Two alternative electrode architectures are studied, namely, a 4-electrode and a 6-electrode configuration. The 4-electrode configuration relies on magnetization dynamics to produce an overshoot coupled with proper timing control of the voltage applied to achieve 360° magnetization rotation. In contrast, the 6-electrode configuration only requires sequential voltage application to successive pairs of electrodes and thus can be operated at quasi-static speeds and does not rely on magnetization dynamics to achieve 360° magnetization rotation. These analytical models provide support for developing new devices such as nanoscale multiferroic driven electromag...

Global optimization using accurate approximations in design synthesis

The design variable space of a design synthesis problem may contain multiple local optima. In the approximation concepts approach to design synthesis, the design objective and constraint functions are approximated in order to reduce the overall cost. If the approximations accurately capture the actural behavior of the objective function and constraints, then the approximate design variable space may also contain local optima. In this work, a multistart optimization algorithm is used to search for the global optimum of the actual design using just a few design cycles. Example problems are presented to illustrate the methodology set forth.

Influence of Nonuniform Micron-Scale Strain Distributions on the Electrical Reorientation of Magnetic Microstructures in a Composite Multiferroic Heterostructure

Composite multiferroic systems, consisting of a piezoelectric substrate coupled with a ferromagnetic thin film, are of great interest from a technological point of view because they offer a path toward the development of ultralow power magnetoelectric devices. The key aspect of those systems is the possibility to control magnetization via an electric field, relying on the magneto-elastic coupling at the interface between the piezoelectric and the ferromagnetic components. Accordingly, a direct measurement of both the electrically induced magnetic behavior and of the piezo-strain driving such behavior is crucial for better understanding and further developing these materials systems. In this work, we measure and characterize the micron-scale strain and magnetic response, as a function of an applied electric field, in a composite multiferroic system composed of 1 and 2 μm squares of Ni fabricated on a prepoled [Pb(Mg1/3Nb2/3)O3]0.69-[PbTiO3]0.31 (PMN-PT) single crystal substrate by X-ray microdiffraction and X-ray photoemission electron microscopy, respectively. These two complementary measurements of the same area on the sample indicate the presence of a nonuniform strain which strongly influences the reorientation of the magnetic state within identical Ni microstructures along the surface of the sample. Micromagnetic simulations confirm these experimental observations. This study emphasizes the critical importance of surface and interface engineering on the micron-scale in composite multiferroic structures and introduces a robust method to characterize future devices on these length scales.