# Unraveling Hidden Order and Dynamics in a Heterogeneous Ferroelectric System Using Machine Learning
## P. Ganesh, Nikhil Sivadas (NTI,CNMS,ORNL) and Abhijeet Dhakane (Bredesen Center, University of Tennessee)
### **Challenge Science Domain: Material Science**
Ferroelectrics are materials that have spontaneous electric polarization – which characterizes a well-defined state of the material system, that can be switched by an applied external electric-field. Existence of a spontaneous polarization implies that the ferroelectric material shows a hysteretic response to the applied field, ideal for use as a memory function, in a ferroelectric random-access memory (FeRAM) device. Real materials are not pure – they have point-and extended-defects, buried-interfaces as well as domain-walls (i.e. spatial discontinuity in the local polarization vector). In the presence of heterogeneities, in addition to the global order-parameter (i.e overall spontaneous polarization of the material) there are additional manifestations on the local order-parameter (local polarization), that lead to ‘hidden’ order in the material. As an example, interfaces of different ferroelectric thin-films can show chiral polarization loops, whose formation, stability and motion are not only governed by material properties, but also topological properties. We find that the shape as well as the area of the hysteresis loops are strongly modified by such local order. Further, the dynamics of ferroelectric switching are also significantly modified in the presence of such hidden order in heterogeneous ferroelectrics. We are specifically interested in discovering such ‘hidden’ order from molecular dynamics simulations, and correlate them with the type of heterogeneities present in the simulation, and ascertain how this order influences not just the memory function, but also its ‘dynamics’ under externally applied field. Dynamic control of memory is the basis of ferroelectric based neuromorphic materials.
**Additional Information:**
**Datasets:**
We uploaded a two class of datasets a) system equilibrated at constant temperature (no electric field) b) system applied with a varying electric field.
Dataset (a) contains 4 sub datasets with varying concentration of defects
where $`V_u`$ is the volume of the unit cell, $`Z_{Ti}^*`$, $`Z_{Ba}^*`$, $`Z_{O}^*`$ are the charges of the Ti, Ba and O atoms obtained using the Electron Equilibration Method (EEM) approach in ReaxFF, and $`r_{Ti} (t)`$,$`r_{Ba,i} (t)`$,$`r_{O,i} (t)`$ are the positions of the Ti, Ba and O atoms of each unit cell at time $`t`$ [1].
<bold> Fig. (A) shows a unit cell of the BaTiO3 (top), following Ti atoms motion resulted in the UP and DOWN polarization, (red arrow) points out the UP and DOWN polarization in a sectional view of BaTiO3 at equilibrium state(bottom).[1] </bold>
<bold> Fig. (B) shows, hysteric response to the applied electric field, results ordered arrangement of BaTiO3 [2] </bold>
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Motion of Ti atoms shown in Fig. (A) determines the local polarization of the unit cell in a given system. System may possess an infinite number of orders in the equilibrium state with no applied electric field. With the help of dynamics data provided in SUBSET A we are interested to know the order parameter of the given system. Ordered dynamics of BaTiO3 system differed by application of directional electric field with non-zero magnitude value that results in the hysteresis loop as shown in the Fig. (B). Data in SUBSET B we provided a 4 sets of configuration each has applied a non-zero magnitude of electric field. Earlier studies used methods such as DMD (Dynamic mode decomposition) method [3], VAE (Variational autoencoders) and TICA (time-lagged independent component analysis)[4] to separate out the dynamics from sequential data.
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**The challenge questions are:**
1) Can we map the molecular dynamics onto a convolutional graph dynamical network[5]?
2) Can we then identify both ‘static’ polarization states (i.e. regions with polarization that doesn’t change with time) as well as ‘dynamic’ polarization states (i.e. regions with dynamic change in polarization)?
3) Is it possible to use above mentioned methods (DMD,TICA or VAE) to identify both ‘static’/'dynamic' polarization states?
**Notes**
1) ML algorithms to be implemented in one of the following languages: Python, C/C++, Julia.
2) Preference for ML framework : PyTorch/PytorchGeometric, Tensorflow
**References:**
1) Akbarian, D., Yilmaz, D.E., Cao, Y., Ganesh, P., Dabo, I., Munro, J., Van Ginhoven, R. and Van Duin, A.C., 2019. Understanding the influence of defects and surface chemistry on ferroelectric switching: a ReaxFF investigation of BaTiO 3. Physical Chemistry Chemical Physics, 21(33), pp.18240-18249.
3) Demo, N., Tezzele, M. and Rozza, G., 2018. PyDMD: Python dynamic mode decomposition. Journal of Open Source Software, 3(22), p.530.
4) Pérez-Hernández, G., Paul, F., Giorgino, T., De Fabritiis, G. and Noé, F., 2013. Identification of slow molecular order parameters for Markov model construction. The Journal of chemical physics, 139(1), p.07B604_1.
5) Xie, T. and Grossman, J.C., 2018. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Physical review letters, 120(14), p.145301.
