Coupled phase field simulations of ferroelectric and ferromagnetic layers in multiferroic heterostructures

  • Wolfgang DornischEmail author
  • David Schrade
  • Bai-Xiang Xu
  • Marc-André Keip
  • Ralf Müller


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.


Multiferroic heterostructure Phase field method Ferroelectric material Ferromagnetic material Finite element method Rotation interpolation 



W. Dornisch and D. Schrade were partially supported by the German Research Foundation (DFG) within the Research Group FOR 1509, Grant Number MU 1370/8-2. The research of B.-X. Xu was partially supported by DFG within FOR 1509, Grant Number XU 121/4-2. The research of M.-A. Keip was partially supported by DFG within FOR 1509, Grant Number KE 1849/2-2. This support is gratefully acknowledged.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lehrstuhl für Technische MechanikTechnische Universität KaiserslauternKaiserslauternGermany
  2. 2.Mechanics of Functional MaterialsTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Institute of Applied Mechanics (CE)University of StuttgartStuttgartGermany

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