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 exchange length (8.5 nm), providing spatial and temporal information on the local mechanical and magnetic fields. A -0.5 V potential is applied to a pair of surface electrodes, producing out-of-plane deformation and in turn straining the magnetoelastic single domain nanostructure in-plane. This strain is sufficient to reorient a single domain structure representative of an idealized memory element.