### **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.
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 ‘hidden’ 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.
We provided the files with local polarization for a length of time for all datasets:
Local polarization $`P_u`$ of each unit cell (shown in figure below) was calculated using:
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].
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 using a reactive force field (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> Figure B shows the hysteric response of BaTiO3 to an applied electric field. It is not clear how domain wall dynamics differ for different field-values, and control the shape of this loop [2] </bold>
<bold> Figure B shows the hysteric response of BaTiO3 to an applied electric field. It is not clear how domain wall dynamics differ for different heterogeneities, and control the shape of this loop [2] </bold>
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The relative atomic motion of Ti-atom as shown in fig. (A) determines the unit cell's local polarization for a given system. Orange and blue regions are two different symmetric ‘domains’ – domain with Pup and Pdown respectively, with a domain-wall between them. Under an electric-field, say one pointing up, the domain wall move so as to increase the fraction of UP domains. At a particular electric-field, all domains (or almost all) will be converted to a single UP domain. Reversal of the electric-field will result in an increase in the DOWN domain fraction, and the total polarization point up will reduce in magnitude. Interestingly, a plot of the total polarization of the box, when as a function of the electric-field, does not show perfect reversible motion – one sees a so-called hysteresis loop, as shown in fig. (B) – where a change in the total polarization depends on which state it started from, and in which direction is the field applied. This motion (i.e. kinetics and dynamics) of domain walls under fields can be different when defects are present. While in a static snapshot, as shown above, one only sees two domains, different parts of the same domain could show different dynamics or kinetics. We want to identify how many different such ‘dynamical’ states (or domains) exist in our MD simulation when it is in equilibrium? How these dynamical states participate in field-induced switching ? How presence of different defect types change the number of these dynamical states?
Identifying dynamics states, and learning their equation-of-motion, can be performed by combining Koopman’s operator theory of dynamical systems [3] or methods like DMD (Dynamic mode decomposition) method [4], VAE (Variational autoencoders), and TICA (Time-lagged independent component analysis)[5]. This can separate the 'static' states from the 'dynamical' states from sequential data.
The relative atomic motion of Ti-atom as shown in fig. (A) determines the unit cell's local polarization for a given system. Orange and blue regions are two different symmetric ‘domains’ – domain with Pup and Pdown respectively, with a domain-wall between them. Under an electric-field, say one pointing up, the domain-wall moves so as to increase the fraction of UP domains. At a particular electric-field, all domains (or almost all) will be converted to a single UP domain. Reversal of the electric-field will result in an increase in the DOWN domain fraction, and the total polarization pointing up will reduce in magnitude till the macroscopic polarization is flipped. Interestingly, a plot of the total polarization of the box, when as a function of the electric-field, does not show perfect reversible motion – one sees a so-called hysteresis loop, as shown in fig. (B) – where a change in the total polarization depends on which state it started from, and in which direction the field was applied. This motion (i.e., kinetics and dynamics) of domain walls under fields can be different heterogeneities, such as defects, are present. While in a static snapshot of the local polarization at an instant in time, as shown in fig. (A) above, one only sees two domains, different parts of the same domain could show different dynamics as well as kinetics. We want to identify how many different such ‘dynamical’ states (i.e., regions with different dynamics) exist in our MD simulation when it is in equilibrium? How do these dynamical states evolve under an applied electric-field? How are these dynamical states modified in the presence of heterogeneities thereby leading to a change in the hysteretic response?
The current state-of-the-art methods to extract dynamical information from molecular dynamics simulations combine Koopman’s operator theory of dynamical systems [3] or methods such as dynamic mode decomposition (DMD) [4] with Variational autoencoders (VAEs) and Time-lagged independent component analysis (TICA)[5]. We are interested in extending the current state-of-the-art approaches to identify dynamical states in hysteretic solids.
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**Datasets:**
@@ -67,10 +66,9 @@ Second line onwards, first three columns (column wise) are cartesian co-ordinate
**The challenge questions are:**
1) Can we map the molecular dynamics onto a convolutional graph dynamical network?
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?
1) How to extract and represent dynamical states from a molecular dynamics simulation using graph-based methods?
2) How do these dynamical states evolve under an applied electric-field?
3) How are these dynamical states modified in the presence of heterogeneities thereby leading to a change in the hysteretic response?
**Notes**
1) ML algorithms to be implemented in one of the following languages: Python, C/C++, Julia.
