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

Zhuyun Xiao,Abdon Sepulveda,Robert N Candler,Cheng-Yen Liang,Gregory P Carman,Jeffrey Bokor,Cai Chen,Roberto Lo Conte

doi:10.1038/s41598-018-23020-2

Abstract

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.

Highlights

Controlled magnetization motion, including domain-wall (DW) and domain state rotation, in miniaturized multiferroic heterostructures creates the possibility of new types of devices in a range of applications, including memory[1], logic devices[2,3] and nanoscale sensors4/actuators[5]
In the aforementioned multiferroic heterostructures (Fig. 1a), will the strain in the piezoelectric substrate influence the magnetic anisotropy in the magnetic film owing to the inverse magnetostrictive effect (Villari effect)[34], and the change in magnetization in the film will in turn feedback to the piezoelectric material via the magnetostrictive effect
No oscillations in the magnetic state are observed from the unidirectional model

Summary

Modeling Setup

Once the field is removed, the magnetization falls into a magnetically-relaxed state due to minimization of the total energy[19,36], including demagnetization energy (shape anisotropy energy) and exchange energy For a ring, this step generates the nucleation of two DWs in diametrically opposite position. An electric field is applied through the thickness of the PMN-PT [011] substrate, which is in a pre-poled ferroelectric state, with polarization pointing up (or down) In such strain-mediated multiferroic approach, a voltage applied to the PMN-PT substrate induces anisotropic strain in the magnetoelastic structures. For a Ni ring on PMN-PT (see Fig. 1b), DWs tend to rotate toward the compressive strain direction [100] due to the negative saturation magnetostriction of Ni. different from the Terfenol-D ring system setup, for the piezoelectric substrate underneath Ni ring, compressive strain is induced along 45°.

Computational Details

Results and Discussions

Conclusions

Author Contributions

Additional Information