Ferroelectric Ferromagnet Multiferroic on the Basis of EuTiO3 Nanowires

11 Ferroelectric Ferromagnet Multiferroic on the Basis of EuTiO3 Nanowires 

New multiferroic on the base of quantum paraelectric EuTiOs thin films has been discussed briefly previously in the Sect. 4.2.2. While the idea [10] to induce new multiferroic properties by elastic strain seems to be very attractive, its realization could meet some difficulties in epitaxial films, since relatively high misfit strains ( l-3 %) between the film and substrate relaxes due to e.g. the appearance of misfit dislocations. It is extremely difficult to synthesize a strongly strained epitaxial film without rather special, complex and thus high cost deposition processes. It has been demonstrated [10] that strain relaxation to the values lower than 1 % eliminates ferroelectric ferromagnetic (FE + FM) phase appearance in EuTiOs thin film. 

However, in nanowires and nanorods (Fig. 4.41a), the intrinsic surface stress exists spontaneously due to the surface curvature and typically does not relax. Surface stress is inversely proportional to the wire radius and directly proportional to the surface stress tensor (similar to Laplace surface tension). The intrinsic surface stress should depend both on the growth conditions and the surface termination morphology [136, 137]. Although surface tension appears even for the case of non-reconstructed geometrical surfaces due to the surface curvature [137], surface reconstruction should affect the surface tension value or even be responsible for the appearance of surface stresses [138,139]. 

Considering very long cylindrical EuTiOs nanowires with polarization and external electric field (if any) directed along the cylinder z-axis, one could neglect the depolarization field if the wire length h is much higher than its radius R, i.e.. 

Integration in Eq. (4.85c) is performed over the system volume V and surface S. In Eq. (4.85c) = (0,0, E() is the external electric field. The coefficient yp and the gradient term g are positive. In accordance with Barrett law (that has to be applied 

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