Landau-Khalatnikov simulation for magnetoelectric coupling in CoFe2O4–BaTiO3 composites

doi:10.1016/j.cap.2020.12.008

Current Applied Physics

Volume 23, March 2021, Pages 15-18

https://doi.org/10.1016/j.cap.2020.12.008 Get rights and content

Highlights

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The Landau-Khalatnikov simulation was used to study magnetoelectric coupling in a composite system of CoFe₂O₄ and BaTiO₃.
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By adding ME coupling term of $γ P^{2} M^{2}$ , the hysteretic ME coupling coefficients $α_{M E} (H)$ were well simulated.
•
The maximum values of are proportional to in the broad ranges of more than 7 orders of magnitude.

Abstract

The Landau-Khalatnikov (LK) simulation was used to study magnetoelectric (ME) coupling phenomena in a composite system of magneto-strictive CoFe₂O₄ (CF) and piezoelectric BaTiO₃ (BT) materials, CF-BT. By adding ME coupling term with coupling parameter $γ$ , between polarization, $P$ and magnetization, $M$ of $γ P^{2} M^{2}$ in thermodynamic free energy density functional for LK simulation, the hysteretic ME coupling coefficients, $α_{M E} (H)$ in CF-BT composite systems were well simulated and small changes of magnetic-field ( $H$ ) dependent polarization, $P (H)$ were calculated. The maximum values of $α_{M E}$ are proportional to $γ$ in the broad ranges of more than 7 orders of magnitude.

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 $α_{M E} (H)$ is defined as $α_{M E} = d P / d H$ , 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 $α_{M E} (H)$ 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, $M (H)$ and $α_{M E} (H)$ were observed as in CF-BT bulk composites. But these experimental behaviors of $α_{M E} (H)$ have not been analyzed well theoretically. In this work, $α_{M E} (H)$ 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 $α_{M E} (H)$ of 0.4CF-0.6BT composite [3]. With initial increase of H, $α_{M E} (H)$ 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 $M (H)$ 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, $P$ and magnetization, $M$ of $γ P^{2} M^{2}$ in thermodynamic free energy density functional for LK simulation with ME coupling parameter $γ$ , the hysteretic ME coupling coefficients, $α_{M E} (H)$ in CF-BT composite system were well simulated and small changes of magnetic-field ( $H$

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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Landau-Khalatnikov simulation for magnetoelectric coupling in CoFe2O4–BaTiO3 composites

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Simulation

Results and discussion

Conclusion

Declaration of competing interest

Acknowledgements

Thin Solid Films

Curr. Appl. Phys.

Curr. Appl. Phys.

Acta Mater.

Nat. Mater.

Phys. Today

J. Mater. Chem. C

Landau-Khalatnikov simulation for magnetoelectric coupling in CoFe₂O₄–BaTiO₃ composites