 Thank you very much, Dina, for the opportunity to speak to you all today and for the invitation. I'm just sharing my screen now, I guess you can see it, okay. Okay, so yeah, happy new year everybody. And again, a massive thank you for the invitation. I'm really happy to be able to talk to you about our work on, let's say coherent actually imaging, but for the application for 3D magnetism that we've done over the last few years. And today, specifically, so I'm not going to be going into too much of the details, you know, of the coherent defective imaging techniques, but it's much more of a, sort of a few examples of how they can be applied to be, or they can be incredibly useful to by being applied to specific magnetic systems. So you'll see at the top of the screen that I have three affiliations here. So as I'm, as Dina said, I'm currently at the University of Cambridge doing with my fellowship. But some of the work that I'm going to show to you today was also partly done during my time at the Palshire Institute and ETH Zurich where I did my PhD in a postdoc. So before we get into the details of 3D magnetism and how we can look at them with coherent X-rays, I thought I'd first start off with perhaps the most important part of the talk, which is a massive thank you and acknowledgement to the huge number of people who were involved in the work that I'm going to show you to today, without whom it really would not have been possible. So this ranges from the group of Laura Hyderman at the Palshire Institute and ETH Zurich, though that the Swiss light source specifically at the CSEX beamline and also at the Pollux beamline. And more recently my collaborators in Glasgow and Cambridge and of course the funding, which is always very important. So now on to the topic of magnetism. I thought it'd start with a quick introduction or motivation of why magnetic systems are particularly interesting. And I think the reason that I like to think of it myself is that with magnetism we have a wide range of very rich and interesting physics, but we also have direct possibilities for applications. And this is kind of can be thought of in a number of ways. And there's three main examples that I'd like to tell you about today. First of all, I mean, so the reason why we have so much physics and so many applications is because we can actually use the magnetic materials and tailor their properties in a number of ways. So for example, we have the case that the micro and nano structure of the magnetic material very much influences its behavior, leading to possibilities to create new types of physics in pattern systems, but also being very important for for example permanent magnets and the micro structure is a key to achieving very, you know, efficient energy generation. We also have the formation of topological structures in magnetic systems and I'm sure you're all very aware of the magnetic scourmillon which is has received a lot of interest and a lot of research in the last couple of decades. And of course it's not been long. It wasn't long until there was applications based on scourmillons proposed, such as new possibilities for data storage. And it's also possible to tailor the magnetization and with, let's say external effects, such as here, both with the spin, so we can tailor the spin with for example charge so with the spin tronic so applying currents, but also with other, other, let's say, parameters such as heat or indeed strain. And in this way, as you can imagine, this has already led to a number of applications, including data storage, memory and also sensing devices. So we've hopefully shown you in this slide that magnetism has a lot to offer. And the specific part of magnetism that I am interested in is, let's say going to a higher dimension. Now, when we think about all of what I've shown you today and what we use when we look at magnets, you know, and in everyday life and also in everyday research. The one thing that most of them have in common is that our understanding but also the systems themselves are quite limited to our generally consist of two dimensional or planar systems. So how about going to the third dimension. So we can already see from the schematic that when we go to 3D we have a huge number of new possibilities for geometries. And we actually find in magnetism that there's a, you know, a huge number of advancements in the actual sort of magnetic properties and the magnetic behavior. And a few examples of why this is so interesting. So perhaps the most well known example of a 3D magnetic device is that of the racetrack memory, which was first proposed over a decade ago now. And the idea is here that we take a magnetic nanowire and we wrap it up into a 3D architecture, allowing for very high density data storage in the end. It's not only, let's say, density, though, that the three dimensionality can give us an advantage in. We also have the possibility for new sort of dynamics in the magnetization with very, very fast to main wall dynamics that indeed have been recognized or realized in the last few years experimentally. We have the possibility for really complex energy landscapes and new efforts, going into new regimes of physics and patterned magnetic structures. And of course in topology, so when it comes to topological structures and are very well known magnetic skirmion. And when we go to the bulk, so bulk or three dimensional systems, we can get these skirmion tubes and actually topological transformations within the bulk. And perhaps the most recent example of a 3D topological structure that people are very interested in is that of the magnetic hopfion. And this is kind of the one dimension up from a skirmion and not been experimentally observed yet, but people are very much, you know, on the lookout for them and hoping to observe them in the in the coming years. So, now that we have, hopefully I've shown to you that going to three dimensions in magnetism is a very, that's the interest and exciting direction to go in. However, if we want to explore these things experimentally, we need a new methods. And there are two main regimes of, let's say method development that are needed for 3D magnetism. First of all, the fabrication so realizing these 3D systems, but also characterizing them. So in the fabrication, the fabrication side, there's been a lot of advances in the last few years, and essentially 3D printing techniques of magnetic materials, both with kind of coating 3D scaffolds with magnetic materials, but also directly printing magnetic materials themselves. And as you can see from these examples, we've now got a huge amount of freedom and flexibility in realizing three dimensional magnetic nanostructures. So the next question is the fabrication we've made huge progress in or the communities make huge progress in the next challenge that we needed to advance in was going to 3D characterization and really being able to image three dimensional, you know, magnetization vector fields. And of course, in the last few years, there's been a number of work done with essentially different props. And in order to determine what, let's see, what probe you need, you need to think about your sample and what kind of, let's say the pros and cons of these different systems. So, for example, there's been a 3D imaging of magnetic systems with electrons. Here with electrons we have very high spatial resolutions on the order of nanometers of sub, yeah, on the order of sub 10 nanometers, let's say. But we of course were limited to really thin films on the order of, you know, a couple of hundred nanometers at most. And then we have the opposite extreme where there's been examples of the imaging of 3D magnetic fields in with neutrons. And then here we're looking at much larger length scales. So here, you know, field of view or sample size of even millimeters up to centimeters in size. But again, your spatial resolution is therefore a bit lowers on the order of 10s to hundreds of micrometers. And finally, we have x-rays. So, and this is what I'm going to be talking to you about today. And x-rays are particularly interesting for 3D systems because they bridge the gap between, let's say, electrons and neutrons, I like to think. We can retain the high spatial resolution of electrons, but by using higher energy x-rays, so hard x-rays, we can actually penetrate larger amounts of material up to micrometers in size. So today in the in this talk, I'm going to be talking to you about our work on 3D characterization of magnetic systems with x-rays and specifically coherent x-rays. So when we think about 3D imaging, essentially what we're talking about are the techniques where the idea is that we measure two dimensional projections, so transmission projections of our sample of our structure at many different orientations with respect to your x-ray beam. Now, that's your standard tomography that you get in your of the electronic contrast, you get this the same thing, you know, in hospitals and stuff for your CT scan. So what happens when we go to magnetic tomography? Well, there's a few ingredients that we need in order to realize this technique. First of all, 2D imaging of the magnetization, so these projections of the magnetization for this we need a highly sensitive technique and this is where coherent refractive imaging techniques feed in. So we need to combine these with new types of, you know, setups to essentially work out what combination of projections we need to probe the magnetization fully. And thirdly, we also need reconstruction algorithms to recover the 3D vector field in the end. So first of all, 2D magnetic imaging. And this is, as I mentioned already, this is where coherent refractive imaging techniques, let's see, take their place within, you know, the work that I'm going to talk to you about today. So when we're talking about the imaging of magnetic systems with x-rays, the contrast mechanism that we mainly make use of is the x-ray magnetic circular dichrosis. The idea here is that the orbital angular momentum of our light can couple to the spin angular momentum of our magnetization, a little bit of an oversimplification. But through this mechanism, we gain, let's say we're able to probe the component of the magnetization prior love to the x-ray beam. And what is particularly important to note is that the energy, also the absorption edge at which you're working at, because it's a resonant technique, really determines the strength of the magnetic signal that we're going to probe. Specifically, the vast majority of magnetic imaging, so that has been done in the last few years, has been mainly done with soft x-rays. And this is due to the fact that we have very, very strong X and CD signals in the soft x-ray regime, even up to 100% of the total absorption of the material. However, as I mentioned before, one of the advantages of x-rays that for looking at 3D magnetic systems is that we can go to these higher energy x-rays in order to probe thicker amounts of material. The main, let's say, drawback of hard x-rays is that we have a very weak signal because we're indirectly probing the magnetic electrons of our material. And for this we need a very sensitive and high spatial resolution technique in order to probe the magnetization. In order to, let's say, address this challenge, we turn to coherent imaging. Specifically, we make use of dichroic dichography, where we measure dichographic images of our sample with C plus and C minus polarizations, and we make use of the amplitude part of the complex transmission function in order to get both a quantitative of, let's say, our transmission, but also a very high spatial resolution. And you'll see in this first demonstration of hard x-ray dichroic dichography, we were able to get a spatial resolution of sub 50 nanometers, bringing the hard extra magnetic imaging, or the spatial resolution that we can achieve about 50 times higher than had previously been achieved. And we have our, let's say, our basic ingredient, which is high resolution, high sensitivity to a dimensional magnetic image. The next question is what combination of these images do we need. And what we first of all need to think about there is what are we actually probing. So I mentioned with the XNCD that we're sensitive to the component parallel to the magnetization parallel to the x-rays. And specifically if our x-rays are coming along Z, we're sensitive to the Z component, meaning that if we rotate our sample in the standard tomographic axis, then we are sensitive to the magnetization in the plane. However, we're not sensitive to the component parallel to the rotation axis. And in order to get around this, we actually measure two different tomographic measurements, one with the sample vertical and one with the sample tilted. And then we have the, with this sample holder here, that allows us to probe all three components of the magnetization. Now that we have our 2D images measured, let's say, around these two tomographic axes, we can then turn to a reconstruction algorithm that we've developed in the house in order to recover the three-dimensional magnetic vector fields. So without having gone over this kind of first introduction into the technique, I can introduce you to the first demonstration of this technique where we looked at the gadolinium cobalt pillar, cut from a nugget with a focused ion beam. And the key thing to note here is that it's five micrometers in diameter, which means that with the other techniques that I've talked about before, it would not be possible to look inside. So actually imaging is really the only technique that we can use to look at the magnetization within this structure. So we can, first of all, use a 2D look at the magnetic configuration in two dimensions to get an idea of what's going on. We see, let's say, quite a strong evidence of the weakness of our magnetic signal because with a single polarization, it's very much dominated by the electronic contrast. So when we take the difference between the two circular polarizations, we get these bright and dark patches which correspond to the magnetization point in parallel and anti-parallel to the X-ray beam, showing that the sample is magnetic, but also that there's quite an intriguing or complex internal magnetic structure. So we measure such XMCD images for over, or single polarization images for over 1,000 different orientations of the sample with respect to the X-ray beam. So we use our reconstruction algorithm to reconstruct the internal configuration with 100 nanometers spatial resolution. And as you can see here in this video, can I want to emphasize that this is a static configuration, we're just showing it in a relatively dynamic way. And we have a relatively smoothly varying magnetization, but there's a number of twists and turns in the structure of which are particularly interesting. So we can have a first insight into what's going on inside by looking at a horizontal slice where we've plotted the in-plane magnetization with the streamlines and the color corresponds to the component perpendicular to the screen. And what we can immediately see is that we have a number of topological structures within this system. And this is relatively, let's see here, familiar, maybe of weather forecasts and everything. And this is due to the fact that these topological structures, of course, are not only seen in magnets, but are seen in many different types of systems. We see vortices where the magnetization curls around a central point. And we also see anti-vortices, which are the topological opposite of a vortex. They're more saddle-like structure. And again, these vortices and anti-vortices kind of form what is known as a cross-tie wall that spans the diameter of our micro pillar. But of course, this is a very 2D way to look at our data. So we can go on and look at the volume instead to work out what's going on in three dimensions. Specifically, we look at a sub-volume which surrounds the central vortex. And when we look at what happens to the vortex within this sub-volume, we can notice a few different things. So first of all, we can notice the color, which corresponds to the vertical component of the magnetization. On the left, generally, everything's pointing up. On the right, everything's pointing down. And in between, we have this white surface, which corresponds to the magnetic domain wall. We see actually that the core of the vortex crosses the magnetic domain wall at two points within the sub-volume. And when it crosses the main wall, it changes its topology actually, so it changes its polarization with the direction of the core. Meaning that we expect the presence of singularities of the magnetization. And indeed, when we plot the magnetization in the vicinity of these crossing points, we see what looks very much like a circulating block point, what is known. So a magnetic singularity with a circulating structure in the plane and pointing up and down above and below. And at the other point, we see a more twisted structure that we believe to be an anti-block point. So just as we had the vortex and the anti-vortex, here we have a block point and an anti-block point. And this was the first time that the surroundings of these structures were observed, even though they were predicted back in the 1960s by Feldkiller. Meaning that this is a very nice demonstration of the new insights that we can get with these 3D magnetic imaging techniques. And of course, we've got these new results. Perhaps what everyone may be thinking is, can we really trust them? How do we know that these are really, let's say, true? So of course, we wanted to validate our measurement and we did this by looking or simulating magnetic tomography on three-dimensional micro-magnetic simulations, which had a number of features that were quite similar to what we saw in the experiment. Vortices and block point and anti-block point, so these magnetization singularities. So essentially by simulating magnetic tomography with all the same, let's say, parameters as we had in the experiment, we were able to determine that we're able to get a very accurate reconstruction of these features. And in general have, let's say overall, a pretty accurate reconstruction of the magnetization vector with the vast majority of the individual pixels being, you know, the error of less than 2% in the magnitude, but also a very small error in terms of the direction, giving us a lot of confidence in that what we see in the experiment is really something real. So this was the first kind of demonstration of our technique, but the challenge is not over yet. And indeed, what we are soon finding or what we see with them, we have these huge datasets, and I'm sure many of you in the audience are very familiar with big datasets, but here what we have, the challenge that we have is that we have these millions of pixels, each with three components of the magnetization. And the question is how can we reliably and sort of efficiently identify the relevant structures within these systems. This was a main challenge, how can we delve into these big datasets and identify, let's say the interesting magnetic structures. So in order to do to address the challenge, we've developed a new type of data analysis for our magnetic configurations. And specifically by implementing a calculation, which is that of the magnetic forticity. So I put this equation up on the slide for those of you who are interested, but essentially what the magnetic forticity is, is a quantity that is related to the topology of our system. So we think of our magnetic scourmions, and the topological index that quantifies the topology is known as the scourmion number. Essentially what the magnetic forticity is, is the flux of the scourmion number density. Now what this means is that for topological structures within our system, we would have a non zero magnetic forticity vector. So for example for vortices we would have a vorticity vector pointing parallel to the core of a vortex. And for anti vortices which have the opposite topological charge we would have the magnetic vorticity vector pointing anti parallel to the vortex, again, emphasizing that this is a mathematical parameter that really is related to the topology of our configuration. So we can use this now to essentially identify the relevant parts or the relevant features within our very large data sets. By first of all plotting the regions of high vorticity within our magnetic pillar, where you see immediately that we have this kind of complex network of loops and tubes, which correspond to the cores of our vortices and anti vortices. But it's not only, let's say the presence of topological structures that we can identify with this vorticity vector. We can also look for regions of abruptly changing topology, as we saw before, this would lead to the presence or imply the presence of singularities of the magnetization. So indeed by plotting the divergence of this vorticity vector, we are able to locate singularities or block points and very, very easily compared to, you know, looking for crossing points of different structures here with a single calculation, we're able to identify the presence of over 50 block points and within again millions of pixels. This is a very nice demonstration of how, let's say being a bit clever or creative with our types of data analysis can really help in identifying the relevant structures that are hidden within the bulk of our system. This again, so it's not, not only is perhaps a very overused phrase in this talk, but not only can we use this quantity to identify the location of our structures, but we can also use it to interpret or to understand a little bit more, but some features that we've actually observed. One of the features that I want to talk to you very quickly about is some loops that we've observed in the magnetization. These loops are formed of, again, cores of vortices and anti-vortices where you can see in this cross section, this is a vortex here and an anti-vortex here. And what is very interesting with these structures is that they are about 400 nanometers in diameter and they are very much, you know, a loops, they're very much a kind of contained three-dimensional structure. So we were kind of interested and intrigued by wondering what these are, but it wasn't until we plotted the magnetic vorticity around these structures that we realized that they have a circulating magnetic vorticity, meaning that these are actually magnetic vortex rings. And they're directly analogous to hydrodynamic vortex rings that we're very familiar with with smoke rings or bubble rings and fluids. In more than one way, not only in the fact that they have a circulating vorticity vector, but also the fact that they are predicted to be only stable in a dynamic configuration. So they're not actually predicted to be stable in a static configuration. However, of course, we have observed them statically here in our sample. So the next question was, well, can we understand why these structures are stable? We went on to look if we could see more of these structures within the bulk of our pillar. And indeed we saw a few of them, as you can see here, each with their own circulating vorticity. And we're able to determine, let's see, by looking in more detail and trying to understand that it's actually some kind of static interaction that's responsible for the stability of these structures. So again, without this 3D magnetic imaging technique, we would not have been able to observe these structures. But also this has given us a lot more understanding of the physics behind three dimensional magnetic configurations. So hopefully with these couple of examples, I've shown you that magnetic tomography has already given us a lot of insight into 3D magnetic systems. But of course, let's see, a couple of years ago, we achieved magnetic tomography. We didn't want to stop there. We knew that there was a number of different, let's say, advances in experimental capabilities that we still wanted to see, or a number of directions that we still wanted to kind of make advances along. So we have three main, let's say, regimes in which we would like to improve our capabilities. First of all was going to more flexible experimental geometries to be able to look at, let's say, a wider variety of samples. Secondly was going to the fourth dimension. So we knew that a lot of the most interesting physics of 3D magnetic systems would actually involve their dynamic behavior. So of course going to higher spatial resolution, so could we push down the lens skills that we were actually able to image the magnetization on. So first of all, the more flexible experimental geometries. The first question may be, why do we need more flexible experimental geometries and why is tomography not a one size fits all technique. Well, the point with tomography is that we have tomography is a non-destructive imaging technique for 3D imaging. And it is particularly well suited for cylindrical samples. However, when we have a non-cylindrical sample, so a flatter extended sample as you see with the silicon nitric membrane here. At certain direct, so certain orientations of the sample when we rotate it, we actually block the beam, meaning that we have a loss of information at certain angles, and therefore lose or introduce some artifacts into our reconstruction. Now an alternative imaging technique that gets around this problem is laminography. We're here as opposed to tomography where it's very much, let's see, characterised by the rotation axis being perpendicular to the X-ray beam. With the laminography, we have actually our rotation axis tilted towards the beam at a non perpendicular angle, meaning that for different orientations of the sample with respect to the beam, we actually have a consistent amount of material, meaning that we can look at flat extended systems. And of course, before we could go on to immediately 3D magnetic laminography, what we needed to do was actually upgrade our reconstruction algorithm. So what we've done is we've essentially upgraded it, meaning that all projections measured at all different sample orientations are just combined in a single step, and that the tomographic geometry is no longer assumed in our reconstruction algorithm. Now this has actually led to substantial increases in construction. And with the recent implementation of GPU code, it has meant that it's a lot faster as well. So it's really helped a lot in terms of the flexibility and the speed of our reconstructions. And if anyone's interested in making use of this, it's available on open access online, and of course, if anyone wants to collaborate, then you're more than welcome to get in touch or ask questions. So we have our reconstruction algorithm. The next thing we needed was a setup, and we're lucky for us. The high-resolution tachographic laminography was being pioneered at the C-Sax beamline at the Swiss light source at the same time. So in here what I'm showing you is a video from Mirko, where they looked at an integrated circuit with, again, tachographic laminography. And as you can see, it's very impressive. They go from really these large scales with these large extended samples, and they can zoom in and look at the nanostructure of the circuits with the sub-20 nanometer spatial resolution. So it's a really highly effective, let's say, stable setup for laminography image. So we then go on to make use of this setup for magnetic laminography. And again, another advantage of laminography for magnetic imaging is that this time, because we now have our rotation axis at a sort of non-right angle to the x-rays, we actually probe all three components of the magnetization with one rotation axis, meaning that we only need one data set to one rotation, or projections around one rotation axis to actually recover all three components of the magnetization. And we've confirmed this with simulations of magnetic laminography. So the sample that we're looking at here is a 1.2 micrometer thick gadolinium cobalt film into which we've patterned a disk of five micrometers diameter. And again, we take a dichroic dichography to have a look at the 2D projections of the magnetic structure. As you can see, again, the sample is magnetic, which is great. And we have a very clear magnetic signal where we do see some change in the magnetic structure through the thickness of the disk. We measure 144 of these XMCD images around 360 degrees and for laminography. And we then use our reconstruction algorithm to reconstruct the internal magnetic configuration where we're able to observe that we have the change in the magnetic anisotropy through the thickness of the film, which leads to this transition between a single domain state at the top and a double vortex domain mode state at the bottom, showing that we have a very good reconstruction or very high resolution, effective reconstruction of our 3D magnetic structure that is again mounted on these extended sample holders. So this takes me on to the second point on our to-do list, which is going to the fourth dimension. And it's actually with this laminography or the development of magnetic laminography was a key step in making this possible. Specifically, because we now are able to probe flat extended samples, such as silicon hydride membranes with laminography, we're able to pattern contacts onto the surface of our sample. And in this way we perform essentially a pump probe measurement where we pass an AC current through our strip line, which is frequency and phase matched to the time structure of the synchrotron, so 500 megahertz. And essentially what we do is we measure a laminography data set for many different time delays of the excitation with respect to the X-rays. So we are able to obtain four-dimensional magnetic information. So what we can first of all do is we can have a look to see what this means. So what does 4D data mean when it comes to the magnetization? Well, we can first of all look at the lower half of our sample where we have vortex domain walls. And we see here what I'm showing you is a difference image between a reference state. So we can see that the vortex domain walls are actually oscillating from one side to the next of this white reference position. And indeed when we track the position of the vortex domain walls, we see indeed that we have a kind of breathing mode of the central domain, which all makes sense from a magnetic point of view. It's a really nice demonstration of the fact that within the bulk of our system, we're able to track the position of topological structures essentially. So domain walls in this case with high accuracy. But it's not only the tracking of structures that we can do. We can also perform Fourier analysis of our 4D data, or isolate or pick out the parts of our systems that correspond to the rotation of the magnetization at 500 megahertz. So we can see the frequency at which we're exciting our sample. And in this way we can identify coherent rotation modes of the magnetization that we see are very closely linked to the 3D magnetic structure with them. Let's see the rotation or the modes limited to kind of edge modes in the upper half of the sample, but of course very much in the vicinity of these vortex domain walls in the lower half. And we have this work featured on the cover of Nature Nano earlier last year. So now that we've developed magnetic laminography, and we've taken first steps to actually imaging 3D magnetization dynamics, and the last point on our list was of course going to higher spatial resolutions. And as I'm sure many of you in the audience are very aware, for coherent active imaging techniques, we have a very exciting time that could say in the next few years when it comes to pushing the spatial resolution of our techniques. So when we think about smaller length scales we of course know that we need higher spatial resolution or higher signal to noise ratio essentially in our data. So there's two main ways that we can do this. Firstly is going to higher coherent flux. So with the next day in the next few years we expect, or there's already let's say, many upgrades, either in planning or actually in progress at the moment. So that will provide orders of magnitude more coherent flux. And of course we've got the already the next generation of synchrotrons as well such as Max4 in Sweden and Sirius in Brazil. And with these let's say three orders of magnitude more flux for these techniques, we can expect to really push our spatial resolution down to very interesting length scales for the magnetization. Let's say approaching what's known as the magnetic exchange length. So on the order of 20 nanometers or even sub 20 nanometers where our understanding of the magnetic structures and how they manifest themselves is starting, you know, it becomes a little bit more limited. Now at the moment we don't yet have access to data sets that we can make use of this higher coherent flux. So we've gone in another direction in the last couple of years. And that is going to increase our signal to noise ratio by going to stronger signals in the first place and this is with soft dexterities. And where again, as I mentioned at the top of my talk, we have a much higher XMTD signal, where it's going to be up to 100% of the absorption of our magnetic material. So in the last couple of minutes of my talk, I'll give a quick intro into what we've been doing on the soft dexterities point of view with 3D magnetic imaging. We've not been using a coherent imaging technique, unfortunately, but we've been, we have been able to implement laminography at the Pollux beamline, this with slight source, which meets the use of scanning transmission X-ray microscopy. And as you can imagine, when the soft dexterity regime, everything's a bit tighter, everything's obviously in vacuum as well, but Katarina Witte, a postdoc at PSI, did a really great job of implementing this rotation stage with the, as you can see, the optics and the detector everything in place. And this allowed us to do our first sort of demonstration of 3D magnetic imaging with laminography at the Pollux beamline, who were able to map out the 3D magnetic structure of a target scourmillon. So you see essentially the blue and the red correspond to the magnetization pointing up and down and we have these ring like structures. So, what this shows us is that now by making use of the, let's say, higher sensitivity or the higher XMT signals of soft dexterities, we can now probe magnetic nanostructures and potentially, let's say in the next few years, go on to probing three dimensional magnetic nanostructures. And I think this is also an area where making use of coherent diffractive imaging techniques such as soft lecture typography will really help as well to push down these spatial resolutions to very interesting land scales. So, with that, I'd like to conclude. What I've shown you today is our work on applying coherent diffractive imaging techniques to three dimensional magnetic systems, specifically with our development of magnetic tomography where we're able to, for the first time observe these three dimensional or the 3D structure surrounding magnetic singularities. We've been able to through new types of data analysis, observe vortex rings in the magnetization. And with the development of magnetic lamina more recently, we've been able to map out the magnetization dynamics in 3D. And also, let's say take first steps towards higher spatial resolutions and soft dexterities. So, we're looking forward in the next few years. And we're really looking forward to taking advantage of the higher flux at, or the higher coherent flux at the upgrades and the next generation sinkers will make a huge difference to the quality of the data and the spatial development scales that we can look at the magnetization on. And with that we'll be aiming to look at both the statics and dynamics of 3D magnetic systems, and also going on the hunt for let's say new types of topological magnetic structures. So, in the last second, I'd just like to mention that next year I'll be starting my own group at Max Planck Institute in Dresden in Germany. So I do have PhD positions available. So if anyone knows of anybody who's looking for a PhD, please feel free to put them in contact with me. So thank you very much. And I'd be more than happy to answer any questions that you have. Thank you so much, Claire, for this beautiful impressive talk. I think really this brings coherent applications to a new level. So it's very beautiful to see this. I opened the session for questions. There is already one couple, a couple of them from Ian Robinson. Please Ian, unmute yourself and ask the question. And for everybody else, either you can write them in the chat, or you can raise your hand and I will. I think in my experience it's more effective if you unmute yourself and then we start the discussion. It's nicer. Please Ian. Yes, well, thank you again Claire. Very beautiful work and very impressive to new results from just published last year that's really good. We've got three questions but I won't feed all of them to you right now. Maybe come back later on some of the other ones. But the most curious question is, what is the theoretical reason why the magnetic vortex rings are not expected to be stable? Because to me they're the same as dislocations in a normal crystal and those, okay they're perturbations but there's no particular reason why they should not be stable. And I'm wondering why a magnetic vortex ring would not be stable. So the reason for that, and this is something that we've realised, so the reason why they were not predicted to be stable was that in the theory work that was done in the 1990s predicting the presence of these structures, they mainly they essentially only take into account the exchange due to the fact that these are analytical models and the magnetostatic interaction which is a long range interaction is particularly difficult to incorporate. Now what they saw was that essentially what you need is a nonlinear interaction or effect in order to stabilise these structures. So what people have generally in the last few years have been sort of thinking is that therefore you need chiral interactions such as a gelatin scheme area interaction in order to have stable 3D sort of configurations such as these vortex rings or indeed these hot beyond structures. Now what we've seen in our data is of course that they are stable and we believe that this is due to the magnetostatic interaction that is not often taken into account is of course a nonlinear interaction or a nonlinear effect especially. And in our case this seems to be the reason why we see these structures. So without the DM interaction you still think they would not be stable because again I'm curious. So we don't have any DMI in our systems and that's why we were quite surprised actually to see such structures. These are topologically trivial structures. I didn't go into detail about that but they are not a hot beyond their topologically trivial. But it's really the combination of the exchange and magnetostatics that is leading to their stability and this was quite a surprise I think for the community. If I can continue into my second question I'll skip the third one. I was wondering because of the DMI you would expect that you would see an asymmetry between clockwise and counterclockwise versions of these things but you said there is no DMI here so I guess the answer is you see equal numbers of each chirality is that right? So yeah it's essentially because we don't see any preferred chirality. And I think in our system we have no DMI and that would be a direction we're particularly interested in pursuing is looking at systems that hopefully we can stabilize these structures or somehow stabilize them and therefore look for topologically non-trivial systems. So I believe that although of course we don't need the DMI in order to stabilize these structures probably for higher order textures the DMI would help a lot. So let's hope. Thanks. Yeah there is a question from Ash Thripati and he says maybe I misunderstood but the results you showed are absorption contrast. Did you go on the resonance or to a part of the resonant edge where you could see only phase or is this interested or not? Yeah I can show you a slide that, so yeah you're absolutely right that we are using the absorption contrast of our, sorry. So yeah we're using the absorption contrast and the reason for that is so when we go to, of course with ticography we have access to the full complex transmission function. We have access to both the phase part and the absorption part of the XMCD signal. So you can see in this earlier work when we were first developing 2D magnetic imaging with ticography, you see this quite clearly that we have this absorption in red which we have this peak at the absorption edge. But of course we also have this kind of phase contrast where we actually flip the contrast of the signal, let's say above and below. Now what we found for our essentially for high spatial resolution imaging of magnetic structures is that the absorption contrast essentially gives us higher signal to noise ratio and higher spatial resolution. So that's the reason why we choose to use this absorption contrast part of our magnetic, let's say projections. Now for this, of course, maybe seems a bit strange that we're throwing away part of our information. When we're measuring at the maximum absorption or maximum absorption contrast or the energy that corresponds to the maximum absorption contrast, we have almost zero magnetic signal in the face and that's the reason why we can't use a combination of both. But for example when we come to, let's say thicker systems that would be very highly absorbing and we're already looking at some systems where we're really at the limit of getting even harder x-rays through our samples. That's where the phase may be an advantage where we can measure slightly below the absorption edge and get a relatively high signal to noise ratio in our images. So it's a bit of a compromise in terms and what we've been really looking forward or looking for is optimizing the image quality rather than choosing a particular part. I hope that helps answer the question. Actually, the question following this, is it clear why we have a better resolution with the absorption rather than in phase? So we have looked into this and as far, a few years ago actually, as far as I remember the main reason is just the, let's say, imaginary part of the scattering factor is just a bit stronger in this case. So when it comes to these kind of resonant effects with the magnetization we do just have, we have a stronger, stronger scattering. But yeah, I can definitely look into that again and possibly come up with a better answer if you're interested in more details. Here's another question from me, Lee, concerning the slice of circular left and right data from magnetic tomography, how did you get this? Do you reconstruct the data with circular right and circular left? So that's a very good point. So when it comes to, let's see, when it comes to tomography, you can see or perhaps it makes sense here. For tomography, we have the case that C plus and C minus, no, zero and 180 degrees are essentially the same orientation. So what we actually do to avoid, so we're creating our circular right using a faceplate and to avoid moving the faceplate during the measurement, we essentially just measure with one circular polarization, but measure around 360 degrees. And this way we effectively get XMCD images around 300 or 180 degrees. Now for laminography, where we have this alternative geometry, we have the case that let's say zero and 360 degrees. No, zero and 180 degrees, sorry, are no longer equivalent. So we actually measure C plus and C minus around 360 degrees. Please, don't be shy and mute yourself and raise your hand. Hi Dina, hi Claire. I may have a very quick one if I do not take time from anybody else. So in your 3D system, I think you can assume that your incoming beam is constant, the property of your incoming beam is constant all along the 3D object that you are, it's not like in optics for instance where if you have a very the incoming field would be transformed and distorted as all along the beam path through the samples, right? Yeah, yeah, yeah, you're absolutely right. We just, we assume essentially, yeah, so we assume parallel illumination and we assume that it's constant. It doesn't change. Yes, that's cool. That's very nice. Thank you. Any other questions? I am sure. I have a sort of a general question because I work with some, I think probably work with some things that may be comparable in like the tomographic department with also with CSACs data with small angle x-ray scattering. I'm just a bit curious, like when you run your reconstruction algorithms on like these big data sets, what sort of time scales are we talking about for like whatever you consider a normal size data set or could you give me some examples of the computation resources and time? Yeah, so of course as you know this very much relies on or depends on the size of the data set, so which is directly related to the volume that we're looking at. The first thing I can say is that when we went to the, let's say the upgrade of our reconstruction algorithm, we went to the GPU, this made a huge difference. So it dropped down our computation times from the order of, you know, hours, 10 hours even down to, you know, 10 minutes. So it's made a complete difference or a huge difference, which really means that we can kind of run reconstructions on the go at the beam line, which makes a big difference. Now for the, to give a couple of examples for the Laminography data set, which for this is a relatively small volume, it's, you know, just over a micrometer thick and a five micrometers in diameter. This takes probably about, I just have a few minutes to reconstruct the internal reconstruction or the internal configuration. More recently we were looking at a much larger system, which was like about 10 micrometers thick and really looking at about 20 micrometers in diameter of the area that we were reconstructing. And this was then taking again hours. So it is quite a computation heavy. Yeah, no, no, I have a similar situation here. So I was just curious. But it's definitely, yeah, it's, it's no more manageable, but I think there's a lot that we can do to. Yeah, as long as it's not like months or weeks. Exactly. Especially once you realize you've done something wrong and you need to repeat it. But yeah, it's, it's manageable. Definitely we're going to look into trying to improve these things. Any more questions from the audience. I will, I have a one, a silly one, so maybe that helps everybody else to bring up some more interesting question. We have a sense why you had this, you have a limitation on the accuracy for the determination of magnetic momentum and direction. Do you have a sense, what is this, what is this due to, what is this limitation is experimental. Yeah, exactly. So, so first thing I would say is the numbers that I showed in this slide so this 2% and 2% in the magnitude and I think it was like 15 degrees in the, in the, in the direction. When we use the new type of reconstruction algorithm where we combine all of the projections in one single step, this gets brought down really decreases a lot. So the main source of error is it is actually a fundamental one. Essentially, it comes from the fundamental thing that's that is to do with the X-ray magnetic circular dichroism so we're sent to do the component of the magnetization parallel to the X-ray beam. What this means is that, imagine if you had to have a hedgehog structure so a highly divergent structure, where we have something you know, things to things pointing in or two things pointing out the net magnetic mass that we get from that is zero. So, and, and of course you wouldn't be able to tell the difference in a projection between you and all in or an all out hedgehog, essentially. So, and indeed that's what we see we've done quite a lot of them, looking into what the limitations are and we essentially get our errors are very much correlated with the presence of divergent structures such as block points or textures in the magnetization. But saying that although there is this kind of fundamental limitation we see that it's still actually works surprisingly well so we'll get higher errors in the vicinity of really the center of these, for example the singularities. But the, and therefore, but that, when we get the error, it's mostly manifests in a decrease of the magnitude of the magnetization so the direction of the magnetization is surprisingly still reconstructed with a very high degree of accuracy. So that is a fundamental thing and we're actually looking at combining this, and let's say this, this type of contrast with other types of contrast to try and get around this, this limitation. So Richard Sunberg as requested. The result's really amazing. Sorry if I missed it. If you've already discussed it about the time resolved images, where you're doing the AC pumping. How often are you taking a tomograph or a lamina geography image there. Could you tell me a little bit about how many positions you're doing how many rotation angles for the time result. Essentially what we did, so we were exciting the sample at 500 megahertz. We were very exciting actually with the or stood field of our strip lines and not directly with the current, and we measured eight, eight time steps or snapshots. And this is every 250 pico seconds. And for each of those snapshots we took 144 or 288 projections so 144 different orientations of the sample, you know, around this 360 degrees. So it's a lot of a lot of data but due to the smaller volume of the, of the sample that we were looking at so this disk which is a bit smaller than the big micro pillar, we were able to squeeze this into the constraints of a beam time. And this is one of the, well, actually we got extra we got we were lucky enough to be given some in house beam time, as well as our, this the official beam time which allowed us to really measure this data. And I think this is one of the main restrictions at the moment is the time it takes to measure these, these data sets so this is something that's also with the increase in coherent flux is going to make a massive difference with feasibility. So that was more of a, if I understand it was more of a stroboscopic measurement it wasn't like single shots you were doing. No, no. The limitation with this that it has to be stroboscopic because we need to measure many different orientations and even for tomography we need to measure many different projections and for a single time stop so I don't think that the single shot technique would be. Would work. Would work. Yeah. Thanks. Thank you. So I see that there is no other people who are asking questions. I actually have one Claire and more generic kids, you know, you were mentioning the development of new sources at the increase of coherent flux, and you know there is a dramatic increase of coherent flux actually in the for obvious reasons. But then the 3d it's maybe not really compatible with it with a soft x-rays but then you're interested in nano structure so where do you see that actually increase dramatic increase or coherent flux in the soft. So actually you can actually help you in your research, considering the difficulty and considering that when you go to such a small structures, then maybe other techniques can be a bit more efficient. Yeah, yeah. So I think it's a really good. It's a really good point. So we have been doing as I showed we had, we have been doing some some soft x-rays or 3d magnetic imaging. And they are okay we're working at the politics in mind where it's a bending magnet so we're very much limited by the flux but the one of the difficulties difficulties that we've been having is that we have highly so when you go to these 3d structures and you have a lot of electronic contrast because it's really quite highly absorbing an increase in flux in any cases really we're really desperate for photons at this case. In terms of the dichography and soft x-rays I think if we want to really go down to interesting then skills and by that I mean even reaching towards sub 10 nanometers spatial resolution which would be really important for these 3d magnetic I think that dichography is the way to go and really rather than perhaps and stick some more or TXM and stuff and I think that's where these increases in coherent flux will allow us to go to higher spatial resolution to really push the magnetic imaging sub 10 nanometers, but also a little bit related to the previous question. And I think it will really help with the throughput of measurements so if we want to do time resolved or quasi static measurements you know where we where we change some parameters such as magnetic field or temperature and stuff and and really be able to measure 3d data sets for for multiple different configurations, you know in the time constraints of a beam time I think this is also that like the pure essentially the time taken for a measurement will really benefit from the from the increase in flux. So I do think that soft x-rays are are going to be equally as as useful when it comes to the upgrades as hard x-rays. I've seen the audience there are many beamline scientists we have a request. Yeah, and so I think having I mean having the the option to measure these. So essentially to measure with high high spatial resolution but also with the combination of for example Laminography or the thermal technology if we have that possibility and we have the reconstruction algorithms so if anyone is interested in, let's say trying out magnetic 3d magnetic imaging at the beamline and I've been more than happy to talk about speaking to people and getting things up and running and hopefully getting more people interested in the technique. Thank you so much Claire. Thank you very much.