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.

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.

Imaging of voltage-controlled switching of magnetization in highly magnetostrictive epitaxial Fe-Ga microstructures.

The magnetoelectric behavior of epitaxial Fe-Ga microstructures on top of a (001)-oriented PMN-PT piezoelectric substrate is imaged with magnetic X-ray microscopy. Additionally, the micron-scale strain distribution in PMN-PT is characterized by X-ray microdiffraction and examined with respect to the results of the Fe-Ga magnetoelectric switching. The magnetic reorientation of Fe-Ga is found to be strongly correlated with size, shape, and crystallographic orientation of the microstructures. In the case of square-shaped structures, size dictates the influence of the strain distribution on both the initialization of the ground state and on the magnetic reorientation during application of voltage. On the other hand, elliptical microstructures demonstrate completely different magnetic responses depending on the relative orientation of their long axis with respect to the crystallographic directions of the PMN-PT. This study demonstrates that engineering the behavior of highly magnetostrictive epitaxial microdevices is possible. It further elucidates that voltage-induced actuation can be largely tuned to achieve the desired type of magnetic switching ranging from vortex circulation reversal, domain wall motion, to a large rotation of magnetization. Because of the outstanding properties of the investigated material system, the reported findings are expected to be of great interest for the realization of next-generation energy-efficient magnetic memory and logic devices.

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.

Capturing magnetic bead-based arrays using perpendicular magnetic anisotropy.

Designing and implementing means of locally trapping magnetic beads and understanding the factors underlying the bead capture force are important steps toward advancing the capture-release process of magnetic particles for biological applications. In particular, capturing magnetically labeled cells using magnetic microstructures with perpendicular magnetic anisotropy (PMA) will enable an approach to cell manipulation for emerging lab-on-a-chip devices. Here, a Co (0.2 nm)/Ni (0.4 nm) multilayered structure was designed to exhibit strong PMA and large saturation magnetization (M s ). Finite element simulations were performed to assess the dependence of the capture force on the value of M s . The simulated force profile indicated the largest force at the perimeter of the disks. Arrays of Co/Ni disk structures of (4-7) µm diameter were fabricated and tested in a microchannel with suspended fluorescent magnetic beads. The magnetic beads were captured and localized to the edge of the disks as predicted by the simulations. This approach has been demonstrated to enable uniform assembly of magnetic beads without external fields and may provide a pathway toward precise cell manipulation methods.

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.