Concurrent inverse effects of magnetostriction and electrostric-tionin magnetoelectric layered structures

The structures comprising intermittently bonded (laminated or deposited) magnetostrictive and piezoelectric layers attract a keen interest in sensor applications since they exhibit strong strain-mediated magnetoelectric (ME) coupling [1]. The bonding compliance exerts hidden stresses on the structure's layers that cause changes in their properties at $no$ mechanical load. We termed such effects in the ME structures concurrent inverse effects of magnetostriction and electrostriction (IEME), similarly to inverse effect of magnetostriction in ferromagnetic magnetostrictive materials [2], where it means a change in the magnetic anisotropy, and so the magnetization curve under external stresses. We studied theoretically and experimentally IEME for a laterally wide bi/tri-layer ME structure. Our theory is based on minimization of the total energy including bare elastic [3], magnetic-anisotropy and magneto-elastic energies [4] under the strains matching and zeromean traction conditions at the layers interfaces and facets, respectively. Unlike the previous theories [4], [5], our theory involves also the shear strain and traction. We predicted IEME of the following types: (i) a latent-stress induced magnetic anisotropy unnoted previously [5], [6]; (ii) a decrease of the ME coupling coefficient [5] below the values obtained previously [5], [6], which may make a slipping correction factor [6] to be redundant; (iii) a decrease of the dielectric permittivity of the piezoelectric layer(s) larger than in the previous theories [5], [6]. Our materials were Alfa Aesar 99.95% purity polycrystalline Ni foil and APC-844 ceramic lead zinc titanate (PZT). Two 20x20mm ² area samples with 0.5 mm thick Ni and 0.83 mm thick laminates were used for the magnetostriction measurements, and a pair of 5x2 mm ² area samples with 0.25 mm thick Ni and 0.58 mm thick laminates, for the magnetization measurements. The magnetostriction was measured with Vishay Micro-Measurements two-axis SR-4 strain gauges. The room temperature magnetization curves were obtained with a Physical Properties Measurement System (PPMS) machine. The type (i) IEME is seen in Figs.1 and 2 which show the magnetization and strain curves of the above Ni layer and the Ni/PZT laminate, respectively. A notable decrease of the initial susceptibility and magnetic saturation lag in the laminate, compared to the bare Ni layer is observed in Fig.1 and similar effects for the magnetostriction in Fig.2. Except reduction of the ME coefficient $\alpha $, as compared to the Harshe et. results [5], we predicted a shift of the magnetic bias of the $\alpha $ maximum abou twice that predicted from differential magnetostriction of the standalon Ni layer $\sim 68$ Oe, see in Fig.2, as assumed in previous theories [5], [6]. Our theoretical results on all above noted IEME agree well with the expriment.