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+title: "What Can DP Do too? | Simulating Ferroelectric Topological Structures with Deep Learning Potentials"
+date: 2025-01-13
+categories:
+- DeePMD-kit
+---
+
+Recently, the research group led by Shi Liu from the Department of Physics, School of Science, Westlake University, based on their previous work "Modular development of deep potential" (ModDP) [1], utilized the deep potential of the solid solution Pb<sub>x</sub> Sr<sub>1 - x</sub> TiO<sub>3</sub> to simulate the full - composition superlattices of the (PbTiO<sub>3</sub>)<sub>10</sub>/(Pb<sub>x</sub> Sr<sub>1 - x</sub> TiO<sub>3</sub>)<sub>10</sub> system within the range of 0 &le; x &le; 1. This revealed a rich phase diagram derived from topological structures. In this study, the researchers took the typical system of (PbTiO<sub>3</sub>)<sub>10</sub>/(Pb<sub>x</sub> Sr<sub>1 - x</sub> TiO<sub>3</sub>)<sub>10</sub> as a starting point to simulate the special phase transition of vortex domains in the superlattice during the heating process, namely, the ferroelectric - like - antiferroelectric - like - paraelectric phase transition. Moreover, the ferroelectric - like phase and the antiferroelectric - like phase can be respectively regulated under an external electric field, thus achieving two different types of electric hysteresis loops. By introducing Pb doping into the  layer, the researchers also found that due to the weakening of the depolarization field, a topological phase transition from the vortex state to the skyrmion state can be induced. The relevant research results, titled "Topological phase transitions in perovskite superlattices driven by temperature, electric field, and doping", were published in Physical Review B [2]. Doctoral student Jiyuan Yang is the first author.
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+
+## Research Background
+
+Topological structures in ferroelectric superlattices, as the electrical counterparts of magnetic topological structures, often form due to the competition among electrostatic energy, gradient energy, elastic energy, etc. Currently, ferroelectric topological structures such as vortices, skyrmions, polarization waves, flux - closure domains, and merons have been experimentally discovered. These structures are expected to play a role in realizing high - density ferroelectric memories. In terms of theoretical research methods, first - principles calculations and phase - field simulations have played important roles in understanding and designing these ferroelectric topological structures, while the molecular dynamics method based on all - atom force fields has been rarely used. This is mainly due to the lack of high - precision and high - efficiency force fields. This situation is expected to change with the impetus of deep potentials, which can enrich our research methods for such topological structures and enable large - scale molecular dynamics simulations with first - principles accuracy.
+
+## Research Results
+
+Taking the (PbTiO<sub>3</sub>)<sub>10</sub>/(Pb<sub>x</sub> Sr<sub>1 - x</sub> TiO<sub>3</sub>)<sub>10</sub> superlattice as an example, this system has been experimentally verified to be in a vortex state [3]. Most existing experiments are carried out at a temperature of 300K, but the research on its phase transition behavior with temperature changes is still insufficient. To explore this in depth, the research team constructed a superlattice model containing 80,000 atoms and successfully reproduced the high - density vortex domain structure through molecular dynamics simulations. During the heating process, the researchers found that this system exhibited a unique phase transition sequence: ferroelectric - like state → antiferroelectric - like state → paraelectric state (as shown in Figure 1). This phase transition path is different from the "ferroelectric - paraelectric" transition of traditional ferroelectric systems and the common "antiferroelectric - ferroelectric" transition of antiferroelectric systems. This special phase transition behavior stems from the mutual transformation of positive and negative domains in the topological structure and is a physical phenomenon unique to ferroelectric topological systems.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/DeePMD_13_01_2025_app/pic1.png pic_center width="60%" height="60%" /></center>
+
+*Figure 1. Heating phase transition in the simulated (PbTiO<sub>3</sub>)<sub>10</sub>/(Pb<sub>x</sub> Sr<sub>1 - x</sub> TiO<sub>3</sub>)<sub>10</sub> superlattice*
+
+During the temperature increase, the researchers observed that the positions of the vortex centers underwent systematic changes, evolving from the initial "Z" - shaped configuration close to the boundary into a regular straight line (as shown in Figure 2). To quantitatively describe this process, the researchers introduced an order parameter ξ, which is the distance from the vortex center to the center of the PbTiO<sub>3</sub> layer. In - depth analysis revealed that the change of this order parameter with temperature conforms to the characteristic law of the Landau first - order phase transition. Through time - domain Fourier analysis of the order parameter ξ, the researchers discovered a significant characteristic peak at a frequency of 0.1 THz. This result is highly consistent with the characteristic frequency of the "vortexon" observed in experiments [4], strongly confirming the reliability of the force field model used in this study.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/DeePMD_13_01_2025_app/pic2.png pic_center width="60%" height="60%" /></center>
+
+*Figure 2. Phase transition principle and dynamics of the order parameter ξ*
+
+By applying electric fields to the ferroelectric - like state and the antiferroelectric - like state respectively, the researchers found that the ferroelectric - like regions exhibited the usual ferroelectric hysteresis loops, while the antiferroelectric - like regions exhibited an S - shaped hysteresis loop (see Figure 3), and their local structures showed a transition from the vortex state to the polarization wave state. This type of hysteresis loop has potential applications in both energy storage of ferroelectrics and high dielectric responses.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/DeePMD_13_01_2025_app/pic3.png pic_center width="60%" height="60%" /></center>
+
+*Figure 3. S-shaped electric hysteresis loop in the antiferroelectric region*
+
+The research team successfully regulated the depolarization field by doping Pb ions into the SrTiO<sub>3</sub> layer, thus providing a new approach to manipulate the topological structures in the superlattice. Specifically, in the (PbTiO<sub>3</sub>)<sub>10</sub>/(Pb<sub>0.4</sub> Sr<sub>0.6</sub> TiO<sub>3</sub>)<sub>10</sub> superlattice, the original vortex state evolved into a skyrmion state with a larger size (as shown in Figure 4). Compared with traditional skyrmions, this new topological structure exhibits a unique extended boundary characteristic. This characteristic mainly stems from the weak ferroelectric properties of the Pb<sub>0.4</sub> Sr<sub>0.6</sub> TiO<sub>3</sub> layer. It is worth noting that this new type of skyrmion state not only has unique structural features but also exhibits excellent dielectric response properties.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/DeePMD_13_01_2025_app/pic4.jpeg pic_center width="60%" height="60%" /></center>
+
+*Figure 4. (a)-(b) Enlarged skyrmions and (c) standard skyrmions*
+
+## Summary
+The simulation of the complex system of (PbTiO<sub>3</sub>)<sub>10</sub>/(Pb<sub>x</sub> Sr<sub>1 - x</sub> TiO<sub>3</sub>)<sub>10</sub> superlattice verifies the effectiveness of the modular development of deep potential (ModDP) method. It not only provides new simulation means but also reveals new physical properties that do not exist in conventional ferroelectrics, such as topological phase transitions and high dielectric responses.
+
+## References
+
+[1] Jun Wu, Jiyuan Yang, Lin Ma, Lei Zhang, Shi Liu, Modular development of deep potential for complex solid solutions, Physical Review B 107, 144102 (2023).
+
+[2] Jiyuan Yang, Shi Liu, Topological phase transitions in perovskite superlattices driven by temperature, electric field, and doping, Physical Review B 110, 214112 (2024).
+
+[3] A. K. Yadav, Observation of polar vortices in oxide superlattices, Nature (London) 530, 198 (2016).
+
+[4] Qiang Li, V. A. Stoica, M. Pasciak, Yiming Zhu, Yutong Yuan, Tian Yang, M. R. McCarter, S. Das, A. K. Yadav, S. Park et al., Subterahertz collective dynamics of polar vortices, Nature (London) 592, 376 (2021).