@misc{DornischSchradeWolfetal., author = {Dornisch, Wolfgang and Schrade, David and Wolf, Jana and M{\"u}ller, Ralf}, title = {Numerical methods for the modeling of the magnetization vector in multiferroic heterostructures}, series = {Proceedings in Applied Mathematics and Mechanics, Special Issue: 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017)}, volume = {17}, journal = {Proceedings in Applied Mathematics and Mechanics, Special Issue: 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Weimar 2017)}, number = {1}, publisher = {WILEY-VCH Verlag GmbH \& Co. KGaA}, address = {Weinheim}, issn = {1617-7061}, doi = {10.1002/pamm.201710221}, pages = {503 -- 504}, abstract = {Multiferroic heterostructures are commonly used to obtain electro-magnetic coupling effects. Thereby, the ferroelectric layer is used to control the magnetization in the ferromagnetic layer. The coupling between the layers is obtained by the mechanical coupling between the layers, which have well-defined interfaces. Within this contribution we use phase field models to define the polarization and magnetization in the ferroelectric and ferromagnetic layers, respectively. A coupling between polarization/magnetization and strains in each layer in combination with coherent deformations at the interface yields an electromagnetic coupling within the entire heterostructure. Numerical formulations for the interpolation of the polarization vector are well-defined in the literature. However, the establishment of a consistent numerical formulation for the ferromagnetic layer, where the length of the magnetization vector has to be constant, remains a difficult task. We propose a new numerical approach for the consistent treatment of the ferromagnetic layer and provide numerical simulations which illustrate the electromagnetic coupling effect.}, language = {en} }