 pleasure to introduce to you Edwin Forteng, he's professor, associate professor at recent polytechnic institute in New York. He is actually visiting scientist, a visiting professor at the University of Linx, even it is not physically here, unfortunately, for corona related issues. So Edwin has been working a long time now on nanoscale structure, fluctuation and dynamics. You took coupled and competing spin, orbital charge and lattice degrees of freedom and it uses coherent diffraction, also non purely coherent imaging methods and neutron scattering. He's been professor also at Los Alamos before taking this position in New York. So he's the first of people who will contribute actually. So this is not a lecture on coherence on principles is really an example of application of these methods that we learned off to a real, real life example, so a scientific example. Next talk on a similar topic. So application of coherence to nanostructures is going to be given next week from Alex Birling who is also in the audience with us. So next few seminars will be actually dedicated also to applications. So Edwin, please start. Awesome. Thank you very much, Dina for the, the very nice introduction. So I'll be talking to you about, I'm not going to go so much detail into, into coherent diffraction imaging, specifically a black CDI. I think Dima Dimitriji gave gave a very, very nice intro and series of codes and phasing algorithms that we use for CDI. I'm going to focus here on one of the applications of CDI, specifically BCDI to specially resolve topological defects in in ferroelectric nanocrystals and I'm going to try to give the motivation for, for why topological defects and what are topological defects within the, the context of, of ferroelectricity, globally multi ferroic materials for energy storage and, and, and processing and, and just like the, the, the, the model of our universities that why not change the world. I'm hoping that CDI and the advances that we're making in synchrotron and, and photon science would be uniquely suited to, to usher us into the next civilization age. That's a very big word I use with my students. I should, I want to acknowledge the, the, the funding agencies and just a few collaborators and some of the light sources that I am able to perform this work in, especially in Los Alamos National Laboratory where, was previously I was the, the Lance Professor of Neutron Scattering. I, I still have, when I feel a position with them and we use that collaboration to work on the state of the art samples and the Department of DoD for funding some of this research, of course, the Department of Energy and NSF, I should have also included them. And most of my experiments are done out here in the US in, in the East Coast with Ross and Wonsuk. Okay. So I, I want to start off with this to give a little bit of motivation. This is a paper from Nicola Spaulding and, and Ramesh, within least top 10 science and technological challenges. And I, I try to highlight some of the few, but most of them are, if not all, are inherently applicable to ferroelectrics and, and to multiferous globally, nano ferroelectrics and multiferous. So discovery of, of a new room temperature multiferous with robust coupling between magnetism and ferroelectricity. So basically, being able to have a material that shows the has the coexistence of the electric polarization and electric degree of freedom and magnetic degree of freedom, meaning in the presence of an external electric field, you can control the magnetic texture, not just domain and induce different stable, lower symmetrical form of magnetic textures, topological textures, or in the presence of an electric field, you can tune the also the magnetic texture. So this would be extremely interesting, especially at room temperature. There's a lot of a priority for this, but there are issues of, of leakage is and, and high remnant magnetic moment and stuffs like that. And if you go through this list from the scientific to the technological, you, you see two underlying principles there. We, we need roots are a purchasing, which we can actually nano fabricate process and control structures at the nano scale. And more specifically, how we can non destructly probe them in situ. For example, if you, if you want to design a nano scale of ferroelectric system that has a spontaneous polarization of about one to five micro Coulomb per centimeter square, the only way to non destructively test that would be to design these given types of ferroelectric capacity, for example, and put them in your beam and perform in situ in a perennial experiment. So we actually sit very comfortably, most of us using a synchrotron facilities and an X fields to actually address some of these issues. And if you want to, you want to focus specifically on random access memory, which we use in, in our computer storage. This is this is a slide from the Journal of Material Science and an electronic. This, for example, B-Smooth ferrite is one of the very popular multi ferric material. It has the coupling between the ferroelectric order parameter and the magnetic order parameter. The challenge is that the, the order and temperature, the multi ferric temperature is, is not at room temperature. So there's this push to design, develop room temperature multi ferric materials where you can control the other parameters and switch the properties at room temperature. So this system can be used as an FE RAM. It is ferroelectric. It has a, I'm going to define ferroelectricity. I'm going to get into that. It has a spontaneous polarization. So symmetry is broken, broken in the absence of an electric field. And so B-Smooth ferrite has this type of a hysteresis loop between the E and the P field. It it's used, it has very fast processing and small storage density. So it's, it's good enough. And then you have the magnetic ramps. This is a typical example. It has a low storage density and it has a slow processing. Most of this has to do the dynamical behavior of these, the other parameter, which for this case is the, is the magnetic dipole orientation. So it's the magnetic domain. And for this case is the ferroelectric dipole orientation, which is now ferroelectric domains. Then of course, you have the magnetoelectric RAM where you, you take advantage of the multi ferric property of the, of B-Smooth ferrite. But most of these systems to achieve them, we have to perform some sort of processing for example, doping. So we, we introduce a magnesium substitution of atoms into B-Smooth ferrite. And, and then there are a couple of challenges that comes from the structural perspective, the, the atomic radius of, of magnesium, it's not very, very comparable to iron. So it, that's why it acts, it's, it, it might actually occupy interstitial sites at some point. And it becomes a bit of a hindrance because it, it, it, it can not just alter the elastic properties of the crystal, but sometimes you can pin magnetic domains. Those are some of the challenges. So there's this push to have a chemically homogeneous. So a system that is chemically homogeneous, and you can control it with an electric and magnetic field while you are still getting the benefit of achieving high storage density and fast processing. And one of the routes towards this goal is to, is to look at other parameters in, in complex ferrites. And here I, I, I, I show a list of specific types of systems. And I am listing the other parameters and the conjugate fields. So the conjugate fields are the external stimuli in the conjugate space that you can, you can use to control the other parameter. And normally, to understand most of all these materials go through a given phase transition where the system changes from a higher symmetry disorder phase to a lower symmetry order phase. Now, this phase transition, normally when you have phase transition, if you look at various simplistic phase transition, for example, in water, water to ice, water to vapor, you do have phase boundaries. If you the phase boundaries have very, very interesting properties, the phase boundaries, for example, could, they are not usually in, in, in the, in the, in the other parameter space, they are not thin, they could be thick enough, they could behave as domain walls, if you're looking at the other parameter of, of ferroelectric polarization. So if you are in a ferroelectric phase, so you can, you can look at ferroelectricity from a global phase space, you have a highest symmetric cubic phase in which the, the crystal is, doesn't have ferroelectricity due to the invasion symmetrical nation. And if you cool it down into a ferroelectric phase, nor ferroelectricity itself has different ground states that have energetically stable enough, you have the auto-rombique, you have a monoclinic and, and you have tetragonal and stuff like that. Now within this phase, this phase is in the ferroelectric phase, you can have phase transformations and transition. Now these phase transitions, they are usually accompanied by nucleations of topological defects. So just like the particle physicist tells that when the, the big bang, you had the universe that expanded rapidly and then it started cooling and this cooling process, which is a phase transition was accompanied by the nucleation formations of topological defects. So basically textures of the other parameter that are topologically protected are able to form. So we can use a Landau, Landau's theory to understand how other parameters and conjugate field for our own application in technology, how we could use them to store higher density information and achieve faster processing. So I'm going to focus mostly on the ferroelectric case in here. I would double a little bit into the ferroelastic if I have enough time, then I would mention scenarios of the magnetoelectric case. So the most important thing here is that if you look at this is the Landau free energy, the free energy of the system, you can expand it as a polynomial. This was actually given by Landau, a long time ago. The other parameter here is I'll call it N. If you are expanding, if you're looking at the free energy of a ferroelectric system, you can expand this in the polynomial of the polarization. Now when it is cubic versus ferroelectric, I'm going to go into a little bit detail about that. But the interesting thing is that the free energy now becomes a multifunctional, it becomes a function of the polarization for this case and you can minimize the free energy with respect to the polarization. Now that minimization, it means that you're looking for stability, you're looking for stable equilibrium. What states are stable as you're lowering the symmetry of the system? So the ferroelectric order parameter, which is the spontaneous polarization, you traditionally, if you increase an electric field, if you increase the electric field in a ferroelectric crystal, you raise up the electric field. The microstructure, if you look at the microstructure, you are basically switching domains. So if the system is a thin film on a substrate, you have a couple of competing energies. You have the elastic energy that comes in from us as a result of interfacial mismatch. There's always interfacial mismatch under the light structure. So one of the terms in the free energy that we have to include is the elastic energy. Then the second term, by virtue of the fact that these ferroelectric materials are piezoelectric themselves, now piezoelectricity is the fact that an external electric field can strain a crystal or a strain can produce an electric field in a crystal. You now have a depolarization field. So the depolarization field is now counteracting with the elastic energy. And then what happens is that the film would break up into domains. So for the level of thin film on a substrate, you have these competing terms that allows the system to break up into domain to release this stress that is coming out from this competition. Now these domains are the other parameter for the polarization in a standard thin film state. And normally the sizes of the domain will scale as the square root of the thickness of the film. But there have been a lot of reports that shows that this can change. So there's a bit of history here for ferroelectric materials. It was discovered about close to 100 years ago, ferroelectricity in some salt materials. And then later on, we start looking at a high dielectric constant. High dielectric constant here is a very interesting property. It's a property that relates how much ferroelectric crystal or peer-to-peer electric material can withstand a field without a breakdown. Now this is very, very important in our energy application, especially when you want to go beyond memories into different types of capacitors. I'm going to talk about that. But the main technology for F-E-RAM ferroelectric atom axis memory, you have a motor layer structure. This is one scenario. You have a ferroelectric layer. And this layer you can, just like I said, you can have, because of the competing energy, it breaks up into striped domains with spontaneous polarization pointing up or down as a function of the symmetry of the central titanium ion. Now chemical ferroelectricity has to do with emptiness of the 3D orbital. So if you look at the chemical structure, the de-orbital of the titanium species, empty. So that's one of the chemical origin of ferroelectricity. So what we've done with a couple, with some colleagues of mine in Los Alamos, we started looking for routes in which we can enhance the energy storage, namely the energy density of these ferroelectric material. And our choice of doing this was to look at different symmetrical forms, symmetrical or different forms of topological defects, topological. So we looked at topology. So we looked at the topology of the polarization texture. So we borrowed this idea from particle physics that tells us that you have domain walls, you have dislocations, you have scenions, you have neurons, you have different forms of these creatures, these topological relics. So features that are created when symmetry is broken, it was created during the Big Bang. So we, and the interesting thing is that the energy landscape, the energy landscape that showed the cooling of this system is very, very typical to the type of free energy that we have for ferroelectric crystals. So one of the things that we did was that we combined a Landau theory, DFT, and a little bit of symmetry analysis and came up with a structure. So this, the rods are made up of, these are barium titanate rods. You can embed the barium titanate rod in a matrix. The matrix could be STO, strontium titanate, or it could be a polymer composite. And the interesting thing was that depending on the aspect ratio of the rods, we can, we can have scenarios in which a single nanowire could admit a vortex or an anti-vortex, we can have a multi-vortex state. Then under the presence of an electric field, we were able to show that the electric field by switching the chirality of the vortices, so the vortex right now is one of the topological arrangement of the dipolar moment forms a flux closure and you can you can switch the dipolar moment. You can also drive, dynamically drive the vortices. Now this actually was, we showed that it could give much more higher energy density. So the energy density is the integral of EDP is the electric field and P is the polarization. So it actually behooves us to say that if you have a system in which it can admit large electric field and also a very reasonable value of the polarization, basically the area under the EP graph, gives us a feeling of the energy and more especially if you are concerned with switching application, you should be able to control, tune the value of the remnant polarization. So these are some particular samples that we've actually, we are fabricating them. The challenge is to create this type of nano rod in matrices and then we all understand the issues of interfacial strain and then defects would play a role and then a whole bunch of complications would come in during processing which deviates a lot from theory. So this is one of the prototypical systems that we are actually working to study. Most importantly, we showed that you can control the aspect ratio and that controls the number of the multi-voltaic states that could be stabilized in the structure and more specifically the energy density of such a system for the case of the 57 nanometer nanoparticle or nanowire rather. The energy density actually was much more, it was way better than the current state of the art of this PVD type bearing titanator nanocapacitors. So basically the energy storage efficiency can be tuned by tuning the dimensionality of the nanowires. You're going to smaller dimensions reducing the radius, you are basically you're going to the limit at which you're only controlling the single polar voltage or multi-polar voltage. So this is actually there is some relationship here between the aspect ratio of the vortex core and the diameter of the vortex itself that would actually give you this high energy efficiency and then of course the goal would be to achieve 100% efficiency, that would be very very challenging because you would be limiting yourself to the sizes of ionic radius and stuff like that. So and we've made some model diffractions of this type of structures, we can reconstruct them. The challenge of course now is to actually fabricate them and study them. So I'm going to jump a little bit into gear to some systems that we've actually studied, experimental samples that has this where we can control the topology of the other parameter space. One option here is bearing titanate, it's a very old and fascinating ferroelectric material and the other parameter space we're interested in is the polarization and we're asking ourselves questions, can we come up with different routes in which magnetism could be induced in bearing titanate or bearing titanate as you see. It has no magnetic element and titanium ion, the empty 3D orbital does not chemically and symmetrically allow bearing titanate to have magnetism but we will be able to hopefully convince you folks at some point that by looking at dynamic properties of of the ferroelectric polarization texture meaning the protected topological features that are formed you can actually create some form of a dynamic magnetism or by engineering the phase boundaries or by engineering domain walls. Another system that would be interesting also is a hexa ferrite. Now this is a multi ferrite material, it has iron and you have a very interesting competing spin state. Here you have a multi ferrite behavior which comes from coupling between a phonon mode and the ground state of the magnetic structure that allows it to drive ferroelectricity. So this is a magnetic ferroelectric, you have prototypical hexamonger knights and stuff like that but most of those systems the the odd in temperature is extremely it's not close enough to room temperature. So what so what I'm doing what what my research what we're looking at with our collaborators is that we are we are looking into candidate ferroelectric materials, multi ferrite materials and we try to see under what criterion an electric field an external stress meaning or under what external conjugate field can we control and protect different forms of topological features. So the for example these are some creatures of relics that could be you could you could classify the topology this is a topological charge of of plus one this is as a plus one this is minus one this for example would be an anti-vortex this would be prototypical vortex and then you could also have a fractional topological structures now the interesting thing is that with these fractional topological systems if you can if you can create this system and then you control the the band gap you close up the band gap so think of a scenario in which you have a ferroelectric nanoparticle it's BTO it's insulating and the crystal has the coexistence of two phases you have a t-phase and you have an o-phase then you have a phase boundary an electric field can also mediate or temperature can mediate this transformation now across the phase boundary if you can we don't want to go doping because we don't want to change the ground state but if you could find ways of of controlling the electronic properties of the phase boundary for example by using oxygen pressure or you know that would alter the after the defects at the phase boundary would actually alter the uh the conductivity so there's been a lot of reports that shows conductive uh domain walls and phase boundaries in in this oxide now that means that if you look at the the band gap you have something which is almost semi-metallic or semi-conducting so you can have a phase boundary that could be engineered for instance and then the that phase boundary the texture of that phase boundary could form different types of topological features that would be an interesting electronic element that would be very very useful so i'm going to get a little bit into the ferroelectric order so this is what the the free the free the free energy against polarization looks like for a dielectric in non ferroelectric material is just this simple behavior so in here you this is a higher symmetry phase so there is no ferroelectric ordering there is a the the crystal the crystal structure is is symmetric and symmetric with respect to space so it is it's a cubic phase then this is a how the energy landscape looks like for a proper ferroelectric material you now have these two possible grounds that this would correspond to the polarization pointing up the polarization pointing down so either by cooling either by cooling this system you can now come up to a scenario where the crystal structure will become if it's very tightly tetragonally strained and then the central titanium ion would now be off-center then it could be the off-center titanium ion if you calculate the the net dipole that you know the distance of the titanium ion to the oxygen to the barium and then you divide that by the volume of the unit cell so you're going to get some value in in some microcoulomb per centimeter cube or something like that you can have two scenarios in which the ion is shifted up shifted down so this is the expected energy versus polarization landscape for polarization up down or down up so these are two states that the quantum physicists would say that if in a sense if you can look at the electronic landscape you could say might be a superposition of states if you want to look at that and for the case of an improper ferroelectricity it is slightly different from a ferroelectric in a ferroelectric the polarization is the other parameter meaning in your free energy expansion the polarization itself it's the if you minimize this with respect to p so you take the first derivative of this partial derivative with respect to p you equate it to zero you're going to be able to find out the values for this coefficient a and b for which you should have stable minimums and then you're going to have these two possible scenarios for the case of an improper ferroelectric the polarization is not the primary order parameter it's more of a secondary order parameter so actually you you do have also have a local mean you have two local mean you have local minimum but it is more due to the slaving of for the coupling of phonon mode with the structural distortion of the crystal and to look a little bit into that I try to put some curtains here this is an example of of a high symmetry uh phase for barium titanate so high symmetry that would be the cubic phase if you look at the unit cell of barium titanate you have a titanium that sits nicely in this octahedra this is oh oh six cage and then these are the barium atoms now the the locate the location of these with respect to this top plane with respect to this top plane this the symmetry is conserved but if you if this thing becomes diagonally strained or if you cool it down you move from this highest symmetry phase to the lowest symmetry phase you're gonna have you can have two scenarios in which the central titanium is shifted up or shifted down so now these and these these have the low symmetry grand state of the system and now the crystal has a spontaneous a built-in spontaneous polarization that comes from the minimization of the free energy and this is mostly the work that was done by by Landau the highest symmetry in the highest symmetric phase the crystal is the structure is cubic the ferroelectric or the electronics the the the crystal structure is cubic the electronic structure is para-electric in highest symmetry so even though the crystal has ions a snapshot over time symmetry is not broken p px and p-x you don't have that uh inversion symmetry and you could see the dipos as some statistical fluctuations are averaging over time that doesn't give a net ferroelectric polarization but if you cool it down be beyond this TC you now move into this ferroelectric phase and inversion symmetry would imply that you can switch from you can move from one ferroelectric well to the next and those are equivalent directions and uh the so the curie temperature is very very interesting we normally tune that using our temperature but we for device applications we want to use fuels we want to use uh conjugate fuels like electric field stress and uh or even magnetic field the challenge would be to ask what other parameter can be controlled by by these systems so i would stick a little bit here to bto now we are in the ground state the low symmetry stable ground state ferroelectric you can see that the ferroelectric uh phase itself the other parameter now which is the polarization the crystal structure has a this rhombohedral octahedral tetrahedral and then you have the high symmetry cubic phase now within this temperature range you can have this given phase transformation the interesting thing for us is that we are interested in the phase boundaries these phase boundaries or domain walls within the given phases so in in a t-phase for example you if the polarization texture if it's uh if you have 180 degrees domains you're gonna have striped domains pointing up pointing down within a given phase so within a given phase you're gonna have domain walls the main walls are usually very small small as a couple of unit cells and large up to a few nanometers 30 40 depending on the aspect ratio of the thickness of the film uh with respect to the interfacial structural strain but more interestingly if you move into nanoparticles and in nanowires where you're now eliminating this interfacial strain effect you have different other terms that comes in as a function of the type of facet that the crystal has things like the gradient energy the electrostatic energy different terms come into play that could actually allow us to come to to have much more stable and smaller or even larger sizes of domains so within every individual phase you have domain walls that accounts for each of the individual symmetry and then across the given phases you have phase boundaries so these are all elements that could be tuned and controlled for for data application the phase boundaries could be traditionally bigger uh what would uh ultimately affect the sizes of the phase boundary would have to do with the uh chemical potential between the two different phases so this this is just a few slides snapshots of of the texture of the polarization of the parameter in ferroelectric that has been observed by uh my different groups using uh scanning microscopy this uh this is the the group of Ramesh Ramesh and uh they actually used the lambda theory and uh and transmission electron microscopy to to map out the formations of of polar domain so you know in a multi-layer so they had a multi-layer of of lead titanate and strontium titanate and alternating dielectric ferroelectric dielectric ferroelectric layer and then these alternating stack of the the competition in the gradient elastic energy would allow the system to actually nucleate this stable topological structure but most of this when you do electron microscopy and and uh as we we are very familiar with it's uh very very difficult to be able to probe the volume it's difficult to uh to apply external fuels and look at things in situ and in operando and this is where exactly we come in with our coherent x-rays so one of the things that we are looking at is that we we want to look at uh particles wires or thin films in situ apply an electric field shoot through them with coherent x-rays satisfy a given graph condition and since the polarization scares linearly with the displacement field as given by the the uh the bond effective effective charge or even from symmetry we can reconstruct this this displacement field and use lambda theory to extract the coupling coefficient between elastic strain and the polarization which is the uh we which has some some which has some tensors actually and that helps us now to actually reconstruct the ferroelectric polarization but more interestingly we ask ourselves uh are they or do we have exciting uh quantum mechanical or nanoscale behavior that comes in when you have uh you have phase boundaries for example within uh you have a single nanoparticle that has a co-existing phase so you know there are phase boundaries and within each phase itself there domain walls can we use those phase boundaries and domain walls as uh logical elements do we now can we now move and say okay the particle it order nanoware itself it's the bulk and then the interface or the domain wall now becomes uh uh the non-bulk feature and then there we have some interesting experiments going on where we are actually we are we are we formed uh sintered ceramics we control grain sizes and we are applying strong magnetic fields in things like barium titanate and the the hope here is to to look if we can create edge effects edge effects like you have in topological insulators where you take an insulator and you apply a strong a one tesla magnetic field and then the edges become conductive because you have electrons that could hop at the edge so we're asking ourselves can similar scenarios be created with with nanocrystals and and grains where now the the phase boundaries now become uh candidate for for for edge so you would have a crystal which is nominally insulating but you can you can close up the the band gap and and create exciting states and then the dynamic the motion of those charges the topology of those charges could inherently help us address the issue for the presence of magnetic because you want to find a way to be able to read write and and control them so uh perovskites are very very interesting uh the structure seems to be simple but depending on the chemistry there is a large range of applications that you could get just by looking at different perovskites from from anti ferroelectric behavior even to a superconductive conductivity that has been observed in in a dope strontium titanate now so this is a dielectric and this also we've seen in reports of ferromagnetic properties in in in sr um o3 we say we want to go be so most of this is guided by by the land out theory which is just phenomenology we want to go beyond that and understand microscopic mechanism and relevant nanoscopic degrees of freedom that would help us correlate displacement to polarization and control polarization texture and the the tool of choice for us here is uh it's a coherent diffractive imaging specifically uh brah coherent diffractive imaging now the challenge is um depending on your type of stroke if you have a the geometry of your structure if you have a thin film or mortar layer you have to go into brah tachography that's where uh stefan iskiewicz is going to actually come in with Virginia to tell us more about those techniques i on the contrary limit myself to bcdi and try to engineer the technology of single particle single wire system because bcdi so far advanced a little bit better it's been around for a while and uh dimitri actually gave us uh sets of codes that are very very efficient and um very very um robust so just briefly about bcdi which uh we are all very comfortable with i i presume if you uh have a um some degree of uh coherent in your in your beam coherent x-rays and you have a full illumination of an object and then you uh align your sample and your detector to satisfy the brah peak and you collect your diffraction pattern in the far field of course you can also do it in in the phenomena regime it just depends on how you want to face the structure and what information you're you're looking at now without loss of generality if the diffraction pattern is over sampled uh to at least uh twice the nycos frequency you can reconstruct the object shape and the displacement within the crystal and if you can map at three at least three different collinear reflections you can you can extract a strain tensor and then you can apply electric field so um over sampling uh it's uh it's extremely important because we have this limited uh information that we have in free risk space because the phases are lost so over sampling actually uh it's one of the ingredients that you need to to solve for the phase problem it is uh it is a necessary uh condition but over sampling on its own is not sufficient uh some degree of coherency and uh of course you have to take care of the type of detector that you're using and a whole bunch of different technical stuff that we're interested in I'll just jump into one of the applications that was done by uh Dima Dimitri Kapov a couple of years ago we uh Dima was um we were able to build a ferroelectric capacitor so we mixed carbon nano particles with uh with barium titanate in an epoxy in a polymer matrix of December that is used in industry to create a ferroelectric capacitor we use those and we now hire a system in which we had a whole bunch of different particles we were able to apply electric fields and ensure that we could see a hysteresis loop that's opening up from the banana shape to a nice hysteresis loop with saturation then we repeated the same experiments uh in operandum now with coherent x-ray being coming in and then land out here which I've discussed was used to uh interpret some of the results so what we what we what we had was that we could apply this was for a particle of about 160 nanometers give or take we apply an electric we did not map out the entire hysteresis loop we moved from zero electric field and then we increased the field all the way to the maximum field where you have saturation and then now we release the field now to back to remnant the interest that we could reconstruct the shape of the particle and the projections of the displacement field one-on-one displacement on the particle and we can also extract the polarization the polarization scales with the displacement field but you need um electrostrictive constants you need those constants from land out here to be able to fit the polarization to uh so it's really a rescaling problem at the end of the day the most interesting thing was that at the the zero electric field and the remnant which is also zero so the the virgin state and the and the remnant state you could see changes in the polarization texture and then this is what we had in the maximum electric field and we accounted for this from Landau theory by saying that at at the zero field you had a single vortex core that was there's a single vortex that is formed in the nanowire so the uh we started different series of nanowire and the 160 the 160 diameter nanowire was the reasonable size that way you have just one vortex structure which is protected within the volume of the particle if you move to larger particles you can you can have you're going to have multi multi uh vortex states and at at this zero electric field the the crystal structure was it was a it was a mixture of tea of tetragonal and monoclinic phase and as you increase the field up to your maximum field it was predominantly M phase so this phase uh transformation uh was actually accompanied by the motion of this uh vortex core so the motion of the vortex core was mediated by the phase transformation and then once you remove the field it comes back to this uh global t plus M phase but interestingly enough the polarization texture has changed even though the uh maximum value of the polarization stays the same the texture is changing so you can you can control different types of topology the uh information that we got from cdi which wasn't available from surface scanning up to when we did the starting surface scanning tool like uh microelectron microscopy told us that an electric field could move for vortices and this was done through mostly you know polishing and imaging series of polishing and imaging techniques and then connect connecting the uh the uh the the core of the vortex to form a vortex stream and what we did here was inoperando in zero and more interestingly we saw that for this for this field range for up to a field of about 223 kilovolts per centimeter the vortex uh has a structure so what we have here is the core this are just two 2d slices and you see the core but uh the if you connect the vortex core with with good enough resolution you have a one dimensional nano rod now that one dimensional nano rod is actually it is the phase boundary it's really literally it's the phase boundary and this nano rod in its sense it can it just rotates the nano rod is protected electric field simply rotates it and we do have some current studies that we are trying to look at how the the rotation of this nano rod within the particle displaces titanium ions and and barium ions and we're trying to estimate the amount of magnetic signature that could be produced by by that that's one approach the second approach that we are looking at this polarization it's a conjugate field it's conjugate to the electric field so if you look at uh Maxwell's one of Maxwell's equation the curl of an electric field is minus there will be by dirty so we're trying to look at ways in which either a time dependent magnetic field should be able to switch the chirality so we just don't want to translate it using a static field but we want to switch the chirality from pointing this away to pointing this away if you could control the switching uh so far we think it could be switches in a terahertz uh frequency so if you go or even gigahertz if you can control this switching that's a very very interesting application where you can read and write using a time dependent magnetic field for example and you could also produce magnetism from a crystal just by the dynamic we do have also some studies that we're trying to look at this in in microwave frequencies and this this are some of the experimental parameters and this is just the raw the raw data the most important thing like actually Dimitri mentioned in his talk it's you need pretty good you need state-of-the-art detectors you need to ensure that you can isolate individual crystals you need to be able to take into account the things like beam pressure radiation pressure you need to ensure that your electric field once you your your effect of your electric field is moving normal to the debaichera rings not along the debaichera ring so if we if you see stops happening these are ways it would probably be radiation pressure you're just moving the crystal around or you're just moving from one crystal to the next so these were extremely time consuming experiments that Dimitri did for over a couple of weeks and even though we had these particles in epoxy and in a polymer matrix that we're supposed to be really tightly held together the radiation pressure was sufficient enough to actually move some of these some of these particles so so this was a it was a little bit a twist of the hand to be able to stabilize these particles and this is just the the preparation procedure we the capacitor was about two by two by one millimeter cube we had epoxy polymer matrix with 40 percent carbon on the particle end and what Dimitri was doing is that he was increasing he was following roots that are done in industrial and commercial devices by mick by playing with this the fracture of of carbon nanoparticles to that of the baron titanate while he's looking at the hysteresis loop to ensure that the loop is is opening up to regions in which you start have ferroelectric switching and and the model that he came with to interpret what we're seeing he suggested that it has to do with the fact that the carbon he being Dimitri that the carbon nanoparticle should be able to form nice enough contact on close to individual particles for it to be able to so this is a this an example of a of a nanoparticle which we call active where you we we have good carbon contacts next to the end the presence of the voltage or electric field can actually switch them you could see the symmetry is broken we're creating this satellite meaning that the domain walls around the vortices are moving and this was a particle that the field just didn't do anything which is so breathing modes a little bit of changing in the intensity counts and and stuff like that and we also we have the Landau theory that would help us interpret what we're seeing what comes into the Landau free energy which is different from the case of a thin film is that you you have the elastic and energy density term that comes in you have the gradient energy the gradient energy has to it takes into account the the types of facets that you can have different facets in your in the particle and every individual first facet has a given a plane of density so the density of atoms and again planes different so the energies would be different and there's the gradient energy and then of course there's the electrostatic energy that comes in because these are these these differences in in atomic packing and hence displacement would create some inbuilt electrostatic field so taking all of this into consideration and then minimizing the Landau free energy term this is what you need to show the stability of vortices so basically a competition between these four terms would allow the formation of topological vortices and I've already shown this slide before but the most important thing I wanted to show here is that this term the so-called electrostrictive coefficients for example you you need to calculate the these terms have to be calculated from Landau theory and then you can extract the strain from multiple reflections and that would help you get projections of the displacement field for this case we looked at the one one one we looked at the one zero zero and we look at the one one o and then one of the most important features from this experiment is the fact that the uh you have a new other parameter which is the torridor moment so the torridor moment and this is the XR polarization so if you take a particle and you increase you apply an electric field your particle your Landau theory is guaranteed to stabilize the presence of a vortex or you make a hetero structures like I mentioned the others are doing what happens is that now depending on the external electric field that you are able to apply or hetero structure here would be the strain you have a couple of you have this region from zero field to about 250 ish where you have a very strong XR polarization but this region over here the torridor moment of one meaning that you have a curve torridor moment of zero means that you have no curve they're just dipolar structures so you can control electric field strength you can apply from zero to 100 and back to zero or from you can move from 250 to 300 and back to 250 depending on what type of topological structure you want to protect if you go if you go beyond this region you are going to unwind you're going to rotate the curve the the vortex structure out of the plane and you might actually cause the system you might actually have a complete phase transformation so t and n phase could become all all homogeneously t with some small fractions of n or things like that so basically you have a nice tool here where you can control topological structures by virtue of the size of the particle and hence the terms in your land or free energy parameter you can optimize a number of vertices to aspect ratio or size of particle and more specifically various forms of phase transformation can is what it's need it's needed to nucleate or to allow the motion of these protected vortices so a small conclusion just on this part of of the talk is that the the vortex core is a stable one-dimensional rod and this rod is topologically protected for giving electric fields and it can be transformed it can also be erased and rewritten using an electric field and this dynamical motion of the vort of the 1d rod is hysteresis it has a history it remembers even though the texture is different the the the maximum polarization is stays the same in case there there are no questions how am i doing on time well it is three o'clock now okay okay cool so if you feel like it's a good moment to take a break maybe we can take some questions yeah sure how long are you planning to continue we can take some break and i could i have about 10 15 more minutes i will talk on now a second order parameter which is now the ferroelastic but i'm open to questions and okay so maybe this is a this is a good moment because many some people may have a maybe some limited slot come on don't be shy please unmute yourself or raise your hand okay i see carlos please all right hi thank you for the question so i mean it's more or less like some doubts on what when you mentioned for example that you use these carbon particles to make like a proper connection did you did you able to see those particles or you just know that you have something because you have the proper response from your electric field yeah so we i mean we we can see those particles using traditional x-ray techniques i mean carbon has a very small cross-section atomic number with neutrons you could see them of course but we are the measure of our a success metric for us was the hysteresis loop when the loop is able to open so the the the idea of the connection of the carbon nanoparticle to the oxide nanoparticle for us to have conductivity it's a one it's one possible explanation it could but there could be possibly something else things we cannot see them so yeah okay yeah okay and i have another question just kind of curious you mentioned radiation pressure that i think i mean you basically saw your particles moving right yeah do you think it it could be anything related to some kind of radiation damage so that you may be also uh changing or of course i don't know if what you mean by radiation pressure but some kind somehow changing the epoxy the surrounding of the particle due to radiation damage yeah that's actually that was a very um that was a possibility that we consider we actually have a paper i could tell you to you where we uh we uh we just did radiation but we use radiation pressure to on on nickel nanowire to bend nickel nanowires and to to move around uh palladium nanocubes and we're able to estimate the radiation pressure it's uh it was somewhere for that was for for rosses beam 934 idc at at 9 kev with a two by two micron beam we had radiation pressure of about it was 10 atom newton sort of the force was 10 atom newton and and this uh when you are doing this at at at the back it is uh it is it is not it's not sufficient to when the momentum transfer is so when you are normal to the back where you to the scattering planes and your q vector is normal to those planes it you do have radiation pressure which basically pushes on the lattice for that plane but it's 10 out of newton it is quite small and yeah you could have other proper other other things that are happening around but that ferroelectric polarization that is accounted for from that projection of the lattice um would not be ultimately affected at least that's what we think but this is something which i think would be extremely useful to study especially if you're looking at at highlight perovskite where the environment plays a very very important role but yes that's something to to consider okay thank you very much thank you carlos ana uh thank you thank you for the talk uh so my question i mean i apologize for my ignorance doing this question but so i understand that praxe di is uh sensitive to displacement fields okay so if you have a vortex in the displacement film it's because you have some sort of point effect in your crystal right like in the atomic lattice now what you are interested in that i think is in topological defects in the polarization right so this is not exactly the same i think and then the question is how does this relate so if you see a vortex in the in the in the displacement field does does this mean automatically that it is also a vortex in the polarization or no no not this is really sorry actually yeah so they um that's that it's not an ignorant it's a it's a very good question so um so you could have a couple of things so if you uh you could have a ferroelastic that's actually where i wanted to go to next and you could have a ferroelectric so the the standard signature of let's say striped domain is uh this largest distortion so across the across the domain wall you have this uh uh you you you see this singularity in your in your phase map and then if you unwrap the phase on everything and this singularity is to maintain it means it's traditional means if it's one you have a 180 degrees at the main wall so you can always estimate the types of the main wall uh from these now uh the vortex is created when you have uh when you have a flux closure so if you so if you have uh let me let me see if i can go back to just a second i think i have a slide for that yeah yeah so um when you have a a flux closure so for example if you look at this state and this state for example this could just be a 180 degrees uh domain wall so if you have two domain walls that intersect for example and then you would uh it creates some sort of a flux closure so this will be mirror to this this will be mirror to this for example and the in the structural signature you in the displacement field you're gonna you're gonna be able to see phase uh reasonable phase jump that is uh uh it's it's it's similar to these changes in the lattice uh and you're gonna this way versus this way so the the interesting point here is that you can have this type of features even when the phase doesn't change from minus pi to pi you can have a fraction that changes from minus pi by two to plus pi by two we we normally account to those as to be fairly elastic domains so we we we go on a couple of things we go on the fact that the polarization from the bond effective charge approximation is linearly proportional to the displacement so now the displacement of course you have displacements of of irons and electronic displacement if you go into the picture but from the bond effective charge if you have the polarization field you if you have the displacement field you can extra you can also extract the polarization from that uh bond effective charge now the topological features in the polarization texture that we are looking at you can see them in the polarization but it doesn't it wouldn't necessarily exist in the displacement field or you're you're right about about that cdi directly gives us uh reconstructs the displacement and the only way for us to get the polarization is that you need to be able to come up with the uh with the electricity with this q tensor from uh from uh from land out theory now that q tensor on its own right now if you if you map out uh individual projections of the tensor you would see regions in which the tensor itself amid singularities or not and that multiplied by that reconstructed displacement field would would for a given iso surface would show you the polarization yeah so it would be very neat if we could find a unique way of being sensitive to the polarization itself directly and i i think i think the tool one tool towards this would be to combine um polarized x-ray resonance polarized x-ray and even even twisted light so if you are uh traditional um traditional if you have resonance scattering you essentially you have dichroism you're sensitive to dichroism but uh x-rays are not sensitive to quadrupole moment which is what you're trying to do to our current x-ray scattering we scatter with dipolar charges quadrupole moment in the ferrule in the electric electric field we're not sensitive to and the only way to be sensitive to quadrupole moment would be to have a beam that carries topological charge itself that's the way we'll be uniquely sensitive to to this uh to true polarization texture so what we're doing here is that we are reconstructing displacement field and then we are we are modeling uh coefficients of that correlates the polarization on the displacement then we use that to map out the polarization so it's not a true mapping of polarization per se because we are only sensitive to the displacement field yeah okay okay thank you yeah thank you it's it's a pretty good it's a it's a pretty good question yeah uh are there people with burning questions i don't know if there is anybody among you what does similar type of research hi hi adwin and uh just curious about the the paper the the paper you and Dimitri on the nation of communication paper you find a vortex in the between nanoparticle and how often are they exist in the between nanoparticle in your sample how often yeah how often you find a vortex in your particle uh yeah so we we we don't find them we don't find a vortex in every particle so that's that's the first thing um and then uh we for we we started we started we looked at a whole bunch of different individual particles and maybe out of 10 or 20 particles we see a vortex in one or two then we started uh dima started asking but they should be aware in which you have to know because we're just going by how this symmetry is broken in in displacement in diffraction to know if there's a vortex and then making a model to see if that model diffraction looks like the the experimental one but dima did a couple of interesting things to stabilize vortices where he he came up with a very very nice technique of uh he he he was quenching the particle so if you if you heat up the part if you take your barium titanin nanopowder and then you you sinter it into a ceramic and then you you heat it up above for above the uh the curie temperature so for barium titanin you go above 200 300 degrees c and then you then now he quenches it you so he he goes a different way we were able to have a larger fractions of particles that vortices were were stabilized so that's kind of what what we did to to stabilize more vortices so we think what is happening there is that doing quake if you quench the system if you heat it up and quench quench it you are nucleating different forms of of higher symmetry phases into lower symmetry ground states so one other thing that we saw which I haven't discussed we saw particles that you had the formations of this so-called polar nano region so you have a particle in which in the particle you have small potholes of cubic cubic phase things you know but if you control your cooling rate just in in the ferroelectric phase you can you can you can nucleate better o or r or t different types of domain um uh and vortices so that was the way of actually ensuring that we can stabilize and have more vortices or or stable or stable vortex in the particle that's what we'll do right now yeah and for the quenching are you quenching in the air or quenching in the vacuum oh we're quenching in vacuum in vacuum yeah if you quenching in air we we actually the quenches that we have having air we if the system forms a core shell particle as what comes out you have you have a core that is cubic and then yeah move for electricity and then you have a shell so but that sounds like a very interesting system because it still has you can still have some vortices in them but they're not uh they're not stable enough I mean the the core you mean the the model proposed by the Japanese like yeah yeah exactly yeah the model yeah yeah so that's a very yeah I I think that they they found this koshe just a possibility right they never they never see it yeah yeah actually yeah they haven't so I saw the paper and then I I was actually thinking of talking to them so we can actually uh measure that and use the I mean we've actually measured it use their theory the theory and the argument to understand what exactly we are seeing in uh in a core shell model of a particle because you have a interesting behavior of the elastic constant you have a region in which you have the gradient elastic constant and then so it's it's a it's a very it's a rich interesting system that shows different it shows most tribe like domain but the texture is uh it's uh interesting yeah yeah and the picture be very diffuse right because you have a cubic core core cubic shell and titan core so you have like the intensity in both in both part and also have some intensity in between so yeah yeah actually yeah so I think what would be interesting would be uh some sort of like relax our properties of that kind of a system you'll be nice to uh to study relax our properties of that kind of a system yeah that's it thank you thank you uh I mean I have a question for you which is a little bit more more general you touched upon very lightly on the quality of the beam and the you know the the the intensity of the coherent beam that you were using and seeing that this series of seminars is actually uh nesting a little bit also within the scientific case for bright sources I was wondering for this type of research what is the added value of an increased coherent flux that that's the first question for example does resolution matter you were mentioning simulation on on less than 100 nanometer particles or nanowires and then you are showing results on more than 100 nanometer so it's next step we're into smaller particles but also uh is it coherent enough or beam lines should what what else what are other experimental challenges that beam lines have to consider you know what is the extra equipment if there if there is any need for it for a successful experiment of this type yeah so so thanks Dean actually it's a very very important and interesting question uh the coherence for us was uh I think it is uh very very important because the resolution that we had from this reconstruction was somewhere around 18 between 18 to 20 nanometers and we are resolving a 1d rod that is about 30 nanometers so we don't we barely have enough pixels left to be able to understand the nature of the vortex wall uh so that's if you want to look into deeper physics if uh if topological structures themselves like domain walls or phase boundaries could be used as as functional elements you will need to we need to go down to to bear resolutions like 5 nanometer as uh as uh Andrew had in one of his science papers so so so then coherence becomes extremely important for us to uh to get better resolution and I I'm I'm actually I'm working on we're trying to make some models in which we we it's modeling forward problem where we we use land out to create a uh a nice looking 3d image where you can see the uh the domain walls and you can see it ahead to head or tail to tail domain wall telling you they are charged and stuff like that and then you simulate the forward scouting problem and then you try to see to uh to go backward for that to understand what are the requirements on the flocks what are the requirements on the coherence and what types of uh pixels and the detector do I need a sample distance to resolve this so resolution is it's really really important for us that's one thing then um one of the challenges that we uh we had which is also now it is this issue of radiation pressure you sometimes you find a pretty good particle you are excited about it you set it up do set your rocking scan you go for coffee or something you come back the particle is gone and then you you're searching for the particle again maybe the next five ten minutes you you cannot find you can find the particle it's you don't have you don't know what's happening if it's it's beam damage or it's just radiation pressure so so there are lots of avenues that would like to explore better especially issues of radiation pressure on on on on on polarization that's one thing and then in the sample environment applying electric fields is also very challenging because on your guinometer I mean you have you have uh you have electrodes coming into your sample you have very limited degree of freedom so sometimes uh there were a couple of days that we could only go to one more one reflection we just couldn't rotate everything around so so it's uh there are a couple of things that would hope that the the the beam line over time we can we can develop better to aid this type of experiment like having better ways of applying electric electric field and more importantly if we could synchronize synchronizing the electric field with the with the with the power structure of the of the synchrotron is would be something which would be uh fundamentally interesting for us especially if we want to move to to to to time-dependent e-field so if you want to apply a very rapidly oscillating field just like not as rapid as you because rapidly you would just use terahertz you use lasers and stuff like that but we want to do time-dependent e-field where we can control the power shape the power structure and power duration if you can synchronize those train of policies with uh with the time structure of the synchrotron that would be extremely interesting because you can do time-dependent switching of chirality and you can track down the things out there they are moving so those are some of the uh technical requirements that i i feel for now would be very very interesting more importantly things within this here would be to have magnetic fields so i just came up from an NSF review panel where Cornell University so the Czechs was funded to have a high magnetic field beam line so so now the experiments that we have we've done experiments on magnetostriction and and and where we apply we use DC magnetic fields so to to look at giant magnetostriction in nanowire so it would also be very interesting if we can have stabilized type of dipolar to quadri-polar hexapolar magnetic fields that could be applied in the sample environment so sample environment is very very useful for us external perturbation of e-field magnetic field it just and then uh synchronizing it to the power structure if it's possible if you want to look at that if you want to look at oscillating fields it would be it would open very very new avenues and this would link directly to coherence and to the structure so that's that's kind of that's my feeling so technically a better resolution it would be nice to have more resolution we've been trying to actually get beam time at the x field but it's been it's been very very challenging and you know how it is so it would be where we use a pump probe experiment where we use a fast optical terahertz lasers the idea here is that the rapidly varying electric field of these lasers should be able to to resonate these topological charges so if you can resonate them it's it becomes a max-worth problem you could you're hoping that some magnetic field would be created and that pushes you back to it I think of doing neutron experiments in which you have a laser oscillating charges and then you're doing some sort of polarizing neutron spectrometry or small angle or neutrons scattering to try to see what the magnetic texture looks like or or just what symmetry of forming so there are some interesting things that I would be excited to see magnetic fields at you know beam lines that especially black beam lines that have a magnetic sample environment and a flexible electric sample environment and an optical