Nanoscale magnetic ratchets based on shape anisotropy.

Controlling magnetization using piezoelectric strain through the magnetoelectric effect offers several orders of magnitude reduction in energy consumption for spintronic applications. However strain is a uniaxial effect and, unlike directional magnetic field or spin-polarized current, cannot induce a full 180° reorientation of the magnetization vector when acting alone. We have engineered novel 'peanut' and 'cat-eye' shaped nanomagnets on piezoelectric substrates that undergo repeated deterministic 180° magnetization rotations in response to individual electric-field-induced strain pulses by breaking the uniaxial symmetry using shape anisotropy. This behavior can be likened to a magnetic ratchet, advancing magnetization clockwise with each piezostrain trigger. The results were validated using micromagnetics implemented in a multiphysics finite elements code to simulate the engineered spatial and temporal magnetic behavior. The engineering principles start from a target device function and proceed to the identification of shapes that produce the desired function. This approach opens a broad design space for next generation magnetoelectric spintronic devices.

Modeling of magnetoelastic nanostructures with a fully coupled mechanical-micromagnetic model.

Micromagnetic simulations of magnetoelastic nanostructures traditionally rely on either the Stoner-Wohlfarth model or the Landau-Lifshitz-Gilbert (LLG) model, assuming uniform strain (and/or assuming uniform magnetization). While the uniform strain assumption is reasonable when modeling magnetoelastic thin films, this constant strain approach becomes increasingly inaccurate for smaller in-plane nanoscale structures. This paper presents analytical work intended to significantly improve the simulation of finite structures by fully coupling the LLG model with elastodynamics, i.e., the partial differential equations are intrinsically coupled. The coupled equations developed in this manuscript, along with the Stoner-Wohlfarth model and the LLG (constant strain) model are compared to experimental data on nickel nanostructures. The nickel nanostructures are 100 × 300 × 35 nm single domain elements that are fabricated on a Si/SiO2 substrate; these nanostructures are mechanically strained when they experience an applied magnetic field, which is used to generate M vs H curves. Results reveal that this paper's fully-coupled approach corresponds the best with the experimental data on coercive field changes. This more sophisticated modeling technique is critical for guiding the design process of future nanoscale strain-mediated multiferroic elements, such as those needed in memory systems.

Voltage-induced strain clocking of nanomagnets with perpendicular magnetic anisotropies.

Nanomagnetic logic (NML) has attracted attention during the last two decades due to its promise of high energy efficiency combined with non-volatility. Data transmission in NML relies on Bennett clocking through dipole interaction between neighboring nanomagnetic bits. This paper uses a fully coupled finite element model to simulate Bennett clocking based on strain-mediated multiferroic system for Ni, CoFeB and Terfenol-D with perpendicular magnetic anisotropies. Simulation results demonstrate that Terfenol-D system has the highest energy efficiency, which is 2 orders of magnitude more efficient than Ni and CoFeB. However, the high efficiency is associated with switching incoherency due to its large magnetostriction coefficient. It is also suggested that the CoFeB clocking system has lower bit-density than in Ni or Terfenol-D systems due to its large dipole coupling. Moreover, we demonstrate that the precessional perpendicular switching and the Bennett clocking can be achieved using the same strain-mediated multiferroic architecture with different voltage pulsing. This study opens new possibilities to an all-spin in-memory computing system.

Bi-directional coupling in strain-mediated multiferroic heterostructures with magnetic domains and domain wall motion.

Strain-coupled multiferroic heterostructures provide a path to energy-efficient, voltage-controlled magnetic nanoscale devices, a region where current-based methods of magnetic control suffer from Ohmic dissipation. Growing interest in highly magnetoelastic materials, such as Terfenol-D, prompts a more accurate understanding of their magnetization behavior. To address this need, we simulate the strain-induced magnetization change with two modeling methods: the commonly used unidirectional model and the recently developed bidirectional model. Unidirectional models account for magnetoelastic effects only, while bidirectional models account for both magnetoelastic and magnetostrictive effects. We found unidirectional models are on par with bidirectional models when describing the magnetic behavior in weakly magnetoelastic materials (e.g., Nickel), but the two models deviate when highly magnetoelastic materials (e.g., Terfenol-D) are introduced. These results suggest that magnetostrictive feedback is critical for modeling highly magnetoelastic materials, as opposed to weaker magnetoelastic materials, where we observe only minor differences between the two methods' outputs. To our best knowledge, this work represents the first comparison of unidirectional and bidirectional modeling in composite multiferroic systems, demonstrating that back-coupling of magnetization to strain can inhibit formation and rotation of magnetic states, highlighting the need to revisit the assumption that unidirectional modeling always captures the necessary physics in strain-mediated multiferroics.

Magnetic microscopy and simulation of strain-mediated control of magnetization in Ni/PMN-PT nanostructures.

Strain-mediated thin film multiferroics comprising piezoelectric/ferromagnetic heterostructures enable the electrical manipulation of magnetization with much greater efficiency than other methods; however, the investigation of nanostructures fabricated from these materials is limited. Here we characterize ferromagnetic Ni nanostructures grown on a ferroelectric PMN-PT substrate using scanning electron microscopy with polarization analysis (SEMPA) and micromagnetic simulations. The magnetization of the Ni nanostructures can be controlled with a combination of sample geometry and applied electric field, which strains the ferroelectric substrate and changes the magnetization via magnetoelastic coupling. We evaluate two types of simulations of ferromagnetic nanostructures on strained ferroelectric substrates: conventional micromagnetic simulations including a simple uniaxial strain, and coupled micromagnetic-elastodynamic simulations. Both simulations qualitatively capture the response of the magnetization changes produced by the applied strain, with the coupled solution providing more accurate representation.

Electrically driven magnetic domain wall rotation in multiferroic heterostructures to manipulate suspended on-chip magnetic particles.

In this work, we experimentally demonstrate deterministic electrically driven, strain-mediated domain wall (DW) rotation in ferromagnetic Ni rings fabricated on piezoelectric [Pb(Mg1/3Nb2/3)O3]0.66-[PbTiO3]0.34 (PMN-PT) substrates. While simultaneously imaging the Ni rings with X-ray magnetic circular dichroism photoemission electron microscopy, an electric field is applied across the PMN-PT substrate that induces strain in the ring structures, driving DW rotation around the ring toward the dominant PMN-PT strain axis by the inverse magnetostriction effect. The DW rotation we observe is analytically predicted using a fully coupled micromagnetic/elastodynamic multiphysics simulation, which verifies that the experimental behavior is caused by the electrically generated strain in this multiferroic system. Finally, this DW rotation is used to capture and manipulate micrometer-scale magnetic beads in a fluidic environment to demonstrate a proof-of-concept energy-efficient pathway for multiferroic-based lab-on-a-chip applications.