Landau-Khalatnikov simulation for magnetoelectric coupling in CoFe2O4–BaTiO3 composites
Graphical abstract
Introduction
Multiferroics show multiple ferroic orders in the systems of single-phase compounds or multi-phase composites [1,2]. Multiferroics have been paid much attention due to fundamental scientific and various applications interests. Magnetoelectric (ME) coupling is known to be weak in the single-phase compounds but strong couplings were observed in composite systems. The coupling behaviors in thin films and bulk ceramics of piezoelectric and magneto-strictive materials composite systems with various geometries have been studied intensively. Well-known ferroelectric and piezoelectric perovskite BaTiO3 (BT) and strong magneto-strictive ferrite CoFe2O4 (CF) is the most promising combination for ME coupling application between ferroelectric polarization (P) and ferromagnetic magnetization (M) through piezoelectric and magneto-strictive properties [3].
Magnetic-field dependent ME coupling and its P change have not been investigated systematically. Magnetic field (H) driven ME coupling coefficient is defined as , which is usually measured in mV/cm⸱Oe experimentally. And 10 mV/cm⸱Oe is estimated to be 1 ps/m in SI unit with an assumption that dielectric constant of the material is 100. As increasing magnetic field, H, rapid increase of under low H and slow decrease after maximum value were observed usually, of which behavior was tried to be understood based on non-linear properties of ME coupling [4]. And some complicate hysteretic behaviors of magnetization, and were observed as in CF-BT bulk composites. But these experimental behaviors of have not been analyzed well theoretically. In this work, was simulated based on phenomenological Landau-Khalatnikov (LK) equations and compared with experimental results.
Section snippets
Simulation
LK simulations have been used to study various ferroelectric [[5], [6], [7], [8], [9]] or magnetic properties [[10], [11], [12], [13]] such as switching with a few parameters phenomenologically. New physical properties difficult to obtain experimentally can be simulated. Gibbs free energy density functionals are expressed with even terms of order parameters – P in ferroelectrics and M in ferromagnets. For ME coupling, a new term with both of P and M can be introduced as described with coupling
Results and discussion
Fig. 1(a) shows the reported experimental of 0.4CF-0.6BT composite [3]. With initial increase of H, increased and decreased slowly (denoted as orange squares and ①). Some hysteretic behaviors were observed in decreasing H (denoted as blue diamonds and ②) and in second increasing H (denoted as red filled circles and ③). The data of 0.4CF-0.6BT composite [3] are shown as symbols in Fig. 1(b), and solid lines are simulated results calculated based on parameters listed in Table 1
Conclusion
The Landau-Khalatnikov (LK) simulation was used to study magnetoelectric (ME) coupling phenomena in composite system of magneto-strictive and piezoelectric materials, CoFe2O4–BaTiO3 (CF-BT). By adding ME coupling term between polarization, and magnetization, of in thermodynamic free energy density functional for LK simulation with ME coupling parameter , the hysteretic ME coupling coefficients, in CF-BT composite system were well simulated and small changes of magnetic-field (
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research was supported by Changwon National University, South Korea in 2019–2020.
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