@misc{DornischSchradeXuetal., author = {Dornisch, Wolfgang and Schrade, David and Xu, Bai-Xiang and Keip, Marc-Andr{\´e} and M{\"u}ller, Ralf}, title = {Coupled phase field simulations of ferroelectric and ferromagnetic layers in multiferroic heterostructures}, series = {Archive of Applied Mechanics}, volume = {89}, journal = {Archive of Applied Mechanics}, number = {6}, issn = {0939-1533}, doi = {10.1007/s00419-018-1480-9}, pages = {1031 -- 1056}, abstract = {The combination of materials with either pronounced ferroelectric or ferromagnetic effect characterizes multiferroic heterostructures, whereby the different materials can be arranged in layers, columns or inclusions. The magnetization can be controlled by the application of electrical fields through a purely mechanical coupling at the interfaces between the different materials. Thus, a magneto-electric coupling effect is obtained. Within a continuum mechanics formulation, a phase field is used to describe the polarization and the magnetization in the ferroelectric and ferromagnetic layers, respectively. The coupling between polarization/magnetization and strains within the layers, in combination with the mechanical coupling at the sharp layer interfaces, yields the magneto-electric coupling within the heterostructure. The continuum formulations for both layers are discretized in order to make the differential equations amenable to a numerical solution with the finite element method. A state-of-the-art approach is used for the ferroelectric layer. The material behavior of the ferromagnetic layer is described by a continuum formulation from the literature, which is discretized using a newly proposed approach for the consistent interpolation of the magnetization vector. Four numerical examples are presented which show the applicability of the newly proposed approach for the ferromagnetic layer as well as the possibility to simulate magneto-electric coupling in multiferroic heterostructures.}, language = {en} } @misc{DornischSchradeXuetal., author = {Dornisch, Wolfgang and Schrade, David and Xu, Bai-Xiang and M{\"u}ller, Ralf}, title = {Coupling of phase field models for ferroelectric and ferromagnetic layers in multiferroic heterostructures}, series = {VII International Conference on Coupled Problems in Science and Engineering (Coupled Problems 2017)}, journal = {VII International Conference on Coupled Problems in Science and Engineering (Coupled Problems 2017)}, publisher = {CIMNE}, address = {Barcelona}, pages = {1}, abstract = {Heterostructures of ferroelectric and ferromagnetic layers are commonly used to obtain electromagnetic effects. The elastic coupling between the layers is widely acknowledged as the main mechanism responsible for the electro-magneto interaction. Within this contribution we study the coupling of ferroelectric and ferromagnetic layers with well-defined interfaces. The intention is to simulate the switching of the magnetization with the help of electric fields, which has been studied experimentally in [1]. Each layer is simulated by using mechanically coupled phase field modeling, whereby the approaches presented in [2] and [3] will be used. The strains in each layer depend on the direction of the polarization/magnetization. A mismatch of these strains will be compensated by local deformations at the interface as the coupling results from the coherent deformation at the interface. This leads to the possibility to alter the magnetization direction by changing the electric polarization and vice verse. Numerical simulations will illustrate the evolution of the ferroic microstructures with a focus on the strain coupling and the resulting interactions between layers.}, language = {en} }