Strain coupling optimization in magnetoelectric transducers

📝 Abstract

The mechanical behavior of magnetoelectric transducers consisting of piezoelectric-magnetostrictive bilayers has been modeled. The effect of the aspect ratio of the transducer as well as the influence of non-active surrounding layers has been modeled, including a passivation layer surrounding the active device, a clamping layer above the active device, and an interfacial layer that might be inserted between the magnetostrictive and the piezoelectric layers. Strategies to control and maximize the strain magnitude and orientation based on material selection and device design are proposed.

💡 Analysis

The mechanical behavior of magnetoelectric transducers consisting of piezoelectric-magnetostrictive bilayers has been modeled. The effect of the aspect ratio of the transducer as well as the influence of non-active surrounding layers has been modeled, including a passivation layer surrounding the active device, a clamping layer above the active device, and an interfacial layer that might be inserted between the magnetostrictive and the piezoelectric layers. Strategies to control and maximize the strain magnitude and orientation based on material selection and device design are proposed.

📄 Content

Strain coupling optimization in magnetoelectric transducers
D. Tierno a, b*, F. Ciubotaru a, R. Duflou a, M. Heyns a, b ,
I. P. Radu a, C. Adelmann a a Imec, Kapeldreef 75, 3001 Leuven, Belgium b KU Leuven, Departement Materiaalkunde (MTM), B-3001 Leuven, Belgium

Abstract The mechanical behavior of magnetoelectric transducers consisting of piezoelectric-magnetostrictive bilayers has been modeled. The effect of the aspect ratio of the transducer as well as the influence of non-active surrounding layers has been modeled, including a passivation layer surrounding the active device, a clamping layer above the active device, and an interfacial layer that might be inserted between the magnetostrictive and the piezoelectric layers. Strategies to control and maximize the strain magnitude and orientation based on material selection and device design are proposed. Keywords: magnetoelectric effect, strain, transducers, spin waves

1. Introduction Current semiconductor-based CMOS devices may reach their physical limits in the next decade. To be able to continue Moore’s law, to improve the device performance, and to further lower the power per operation, the replacement of CMOS circuits by novel circuits based on different physical effects may become necessary. In particular, logic circuits based on the interference of spin waves [1, 2] are a promising alternative to CMOS technology and are highly suitable to efficiently implement majority gates [1 - 4], in which the state of the output is determined by the majority of the input states. In such spin wave logic gates, the information is encoded in the phase of the waves and the output is determined by the interference of multiple spin waves propagating in a common waveguide. Spin-wave computing has the potential for low-power computation since no charge motion takes place. Furthermore, it allows the functional scaling of the circuit [1] which would relax the high density of on chip-elements required in the CMOS technology. To build logic circuits based on spin-wave majority gates that are competitive with CMOS-based technology, it is necessary to develop energy efficient transducers between spin-wave and electric domains so to cointegrate the two technologies in a single system. Key requirements of such transducers are high coupling efficiency, low operational power, and high bandwidth [1-3]. Microwave antennae have typically been used to generate spin waves using electric currents [4, 5] but are neither scalable nor energy efficient. By contrast, magnetoelectric transducers represent a scalable and low-power alternative [2, 3] consisting of a piezoelectric-magnetostrictive (PE-MS) bilayer in which the coupling between the electric and the spin domain occurs via strain: when an electric field is applied across the piezoelectric, strain is induced and transferred to the magnetostrictive film that in turn changes its magnetic anisotropy via the inverse magnetostrictive effect. The resulting change of the effective magnetic anisotropy field can exert a torque on the magnetization and, in case of an AC excitation, generate spin waves.
   Most of the research performed in this field has focused on the coupling mechanism of magnetoelectric bilayers. By contrast, little interest instead is shown for actual micro- or nanoscale devices. Materials with high piezoelectric and magnetostrictive coefficients are desirable for the PE-MS bilayer but strain transfer optimization within the bilayer in patterned transducers presents several integration challenges. To design efficient micro- and nanomechanical transducers width dimensions of few μm or less, many aspects need to be addressed such as the impact of the geometry of the patterned transducer as well as the mechanical properties of all materials in fully integrated magnetoelectric transducers.

 Corresponding author - Davide Tierno: davide.tierno@imec.be; Kapeldreef 75, 3001 Leuven - Belgium

The stress-strain relation is described but the Generalized Hooke’s law: εxx= σxx E -υ σyy E -υ σzz E (1) εyy= -υ σxx E + σyy E -υ σzz E (2) εzz= -υ σxx E -υ σyy E + σzz E (3)

with E the Young’s modulus of the material and υ the Poisson ratio. The magnetoelastic torque τ on the magnetization due to a strain field is given by [6]: τmel= ( 2B1mymz(εyy-εzz)+B2(mzmxεxy-mxmyεzx+(mz 2-my 2)εyz) 2B1mzmx(εzz-εxx)+ B2(mxmyεyz-mymzεxy+(mx 2-mz 2)εzx) 2B1mxmy(εxx-εyy)+B2(mymzεzx-mzmxεyz+(my 2-mx 2)εxy) ) (4) where mx,y,z = Mx,y,z/MS are the normalized components of the magnetization vector 𝑀 with respect the saturation magnetization 𝑀𝑆, 𝜀𝑖,𝑗 are the components of the strain tensor within the magnetostrictive layer, 𝐵1 and 𝐵2 are the magnetoelastic coupling constants, and τ is the exerted torque, H is the effective magnetic field associated with the magnetoelasticity and 𝜇0 the permeability of vacuum.
From Eq. 4 it is obvious th

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