Strong enhancement of direct magnetoelectric effect in strained ferroelectric-ferromagnetic thin-film heterostructures

The direct magnetoelectric (ME) effect resulting from the polarization changes induced in a ferroelectric film by the application of a magnetic field to a ferromagnetic substrate is described using the nonlinear thermodynamic theory. It is shown that the ME response strongly depends on the initial strain state of the film. The ME polarization coefficient of the heterostructures involving Terfenol-D substrates and compressively strained lead zirconate titanate (PZT) films, which stabilize in the out-of-plane polarization state, is found to be comparable to that of bulk PZT/Terfenol-D laminate composites. At the same time, the ME voltage coefficient reaches a giant value of 50 V/(cm Oe), which greatly exceeds the maximum observed static ME coefficients of bulk composites. This remarkable feature is explained by a favorable combination of considerable strain sensitivity of polarization and a low electric permittivity in compressively strained PZT films. The theory also predicts a further dramatic increase of ME coefficients at the strain-induced transitions between different ferroelectric phases.Comment: 7 pages, 3 figure

Thermodynamic theory of epitaxial ferroelectric thin films with dense domain structures

A Landau-Ginsburg-Devonshire-type nonlinear phenomenological theory is presented, which enables the thermodynamic description of dense laminar polydomain states in epitaxial ferroelectric thin films. The theory explicitly takes into account the mechanical substrate effect on the polarizations and lattice strains in dissimilar elastic domains (twins). Numerical calculations are performed for PbTiO3 and BaTiO3 films grown on (001)-oriented cubic substrates. The "misfit strain-temperature" phase diagrams are developed for these films, showing stability ranges of various possible polydomain and single-domain states. Three types of polarization instabilities are revealed for polydomain epitaxial ferroelectric films, which may lead to the formation of new polydomain states forbidden in bulk crystals. The total dielectric and piezoelectric small-signal responses of polydomain films are calculated, resulting from both the volume and domain-wall contributions. For BaTiO3 films, strong dielectric anomalies are predicted at room temperature near special values of the misfit strain.Comment: 19 pages, 8 figure

Soft modes of collective domain-wall vibrations in epitaxial ferroelectric thin films

Mechanical restoring forces acting on ferroelastic domain walls displaced from the equilibrium positions in epitaxial films are calculated for various modes of their cooperative translational oscillations. For vibrations of the domain-wall superlattice with the wave vectors corresponding to the center and boundaries of the first Brillouin zone, the soft modes are singled out that are distinguished by a minimum magnitude of the restoring force. It is shown that, in polydomain ferroelectric thin films, the soft modes of wall vibrations may create enormously large contribution to the film permittivity.Comment: 6 pages, 3 figure

Spin-orbit torque control of spin waves in a ferromagnetic waveguide

Spin-orbit torque (SOT) created by a spin current injected into a ferromagnet by an adjacent heavy metal represents an efficient tool for the excitation and manipulation of spin waves. Here we report the micromagnetic simulations describing the influence of SOT on the propagation of spin waves in the $\mathrm{W}/\mathrm{CoFeB}/\mathrm{MgO}$ nanostructure having voltage-controlled magnetic anisotropy (VCMA). The simulations show that two spin waves travelling in the opposite directions can be generated in the center of the $\mathrm{CoFeB}$ waveguide via the modulation of VCMA induced by a microwave voltage locally applied to the $\mathrm{MgO}$ nanolayer. The amplitudes of these waves exponentially decrease with the propagation distance with similar decay lengths of about 2.5 $\mu$m. In the presence of a direct electric current injected into the $\mathrm{W}$ film beneath the waveguide center, the decay lengths of two spin waves change in the opposite way owing to different directions of the electric currents flowing in the underlying halves of the $\mathrm{W}$ layer. Remarkably, above the critical current density $J_\mathrm{W} \approx 2 \times 10^{10}$ A m$^{-2}$, SOT provides the amplification of the spin wave propagating in one half of the waveguide and strongly accelerates the attenuation of the wave travelling in the other half. As a result, a long-distance spin-wave propagation takes place in a half of the $\mathrm{CoFeB}$ waveguide only. Furthermore, by reversing the polarity of the dc voltage applied to the heavy-metal layer one can change the propagation area and switch the travel direction of the spin wave in the ferromagnetic waveguide. Thus, the $\mathrm{W}/\mathrm{CoFeB}/\mathrm{MgO}$ nanostructure can be employed as an electrically controlled magnonic device converting the electrical input signal into a spin signal, which can be transmitted to one of two outputs of the device.Comment: 7 pages, 6 figure