5
Correlated Oxides
The first speaker on the workshop’s second day, Ramamoorthy Ramesh from the University of California, Berkeley, went beyond the van der Waals materials that had been the focus of much of the workshop’s first day and spoke about correlated oxides, with a particular focus on the behavior of the superlattices created by stacking thin layers of different oxides together. The goal, he said, was to examine how work in correlated oxides might point the way to materials similar in spirit to the structures made from graphene and other van der Waals materials that had been described earlier.
FCGT: A POLAR MAGNETIC METAL
Before speaking about correlated oxides, though, Ramesh began with what he called an “exotic example” of a van der Waals–bonded transition metal dichalcogenide (TMD): the compound Fe5–xCoxGeTe2, or FCGT for short. With no cobalt doping (x = 0), the material, Fe5GeTe2, is a ferromagnet, and it has the ABC crystalline structure shown on the left-hand side of Figure 5-1. When some of the iron atoms are replaced by cobalt, the planes in the crystal start to slide, and the structure changes to AA stacking. And when exactly 50 percent of the iron atoms are replaced by cobalt, yet another structure emerges, he said. “It goes from sliding about these tellurium planes into a rotation” to form an AA' structure. The ABC and AA structures are both inversion centric, but the AA' is a non-centrosymmetric Wurtzite crystal structure. Thus, a rather dramatic conclusion is that one can, through chemical tuning, make the crystal undergo a structural phase transition to create a polar magnetic metal.
Ramesh then described a number of interesting aspects about these materials, beginning with a closer look at what happens when the shift from the AA to the AA' structure takes place. Showing some atomic-scale images of the materials taken with a scanning transmission electron microscope (STEM) that revealed the positions of the different atoms, he pointed out that the flipped orientation of the lines of iron/cobalt atoms from one layer to the next in the AA' structure ends up producing a chevron pattern, with the iron/cobalt lines zigzagging from one layer to the next, while in the AA structure the atomic lines all pointed at the same angle from layer to layer. Then he pointed out a more subtle difference between the two phases: Counting the number of iron/cobalt atoms stacked between each of the lines of tellurium atoms, one discovers that while there are seven stacked atoms in the AA phase, there are only six in the AA' phase. “You can clearly see that already gives you an indication how the symmetry is being broken. It goes from having inversion symmetry for the AA phase to breaking inversion symmetry.” In particular, it is the removal of the “extra” iron layer that breaks the inversion symmetry.
SOURCE: Ramamoorthy Ramesh, University of California, Berkeley, presentation to the workshop, May 19, 2021; reprinted with permission from H. Zhang, Y.-T. Shao, R. Chen, et al., 2022, “A Room Temperature Polar Magnetic Metal,” Physical Review Materials 6:044403, https://doi.org/10.1103/PhysRevMaterials.6.044403, © 2022 by the American Physical Society.
One obvious question to ask about the material, Ramesh said, is why this symmetry breaking should happen right at 50 percent cobalt. This is something that he and his group are still trying to understand he said. One group is working to model the system and understand it from a theoretical perspective, but the calculations are complex, and no clear answers have yet emerged.
Another interesting aspect of the material, he said, is the presence of spin textures, or skyrmions, under the right conditions. When a thin sample of the AA' structure is examined straight on, with no tilt and no magnetic field, the sample looks uniform, with no contrast. When it is tilted at about 18 degrees, however, domain contrast starts to appear, and then when a small magnetic field is applied, skyrmions start to appear. There has been debate as to whether they are Bloch-type skyrmions or Neel-type skyrmions, Ramesh said, but the tilting behavior implies that very likely they are Neel-type skyrmions. The skyrmions can be observed directly with magnetic force microscopy, and they appear in a regular hexagonal array with a spacing of around 115 nm. “What this is telling you,” he said, “is that because the system broke inversion symmetry, you can now sustain a skyrmion lattice in the system. That’s a first.” By contrast, the AA phase has no skyrmions in it, he said. It is magnetic, but no skyrmions are observed under any conditions.
The material’s properties open up a number of possibilities for applications, Ramesh said. For example, showing several graphs of the material’s spin-torque ferromagnetic resonance (ST-FMR), he said that he had had discussions with people in the intelligence community about a new type of logic and memory device that used a magnetoelectric material to convert charge to spin, do logic operations in spin space, and then go back from spin to charge using the inverse spin Hall effect. The FCGT material might be very useful in such a device, he said. It has good ST-FMR properties, and its spin–orbit torque efficiency is reasonable—0.6 to 0.7, as compared with about 0.1 for platinum—but the efficiency will need to be much higher for practical applications. It should be possible to significantly increase the spin–orbit torque efficiency of the FCGT system, he said, and it is an intense topic of research worldwide.
In short, he said, the cobalt-doped, iron–germanium–telluride material is a very interesting material. They are polar magnetic metals, and there are many possibilities for moiré structures. If one examines a sample of the AA' structure, which in its ideal form has a perfect chevron design with the iron-cobalt stacks in alternating layers zigging one way and then zagging the other way in the next layer, it becomes apparent that a typical sample does not have this ideal pattern. Instead, there may be two or three layers in a row that zig in the same direction before the next layer zags. These stacking defects arise because the energy difference between the two phases—AA and AA'—is not very large. Moiré patterns can also be explored to bring together such polar magnets into contact with ferroelectric layers to
create magnetoelectrics and multiferroics, materials that have both a spontaneous polarization and a spontaneous magnetic moment.
One question then, is how one can manipulate the structure in the desired way when the energy landscape is very shallow. So one question his group is examining is whether these systems can be grown block by block using molecular beam epitaxy or ultrahigh vacuum sputtering. Can the symmetry be controlled? Can it be flipped back and forth via simple chemical doping at that site? Can the angle arbitrarily be changed from 0 to 180 degrees? Right now the materials either have a 0° angle, which is the AA phase or a 180° angle, which is the AA' phase, Ramesh noted; how about other angles in between? How about random sequences of the AA and AA' stacking? Can you control the chemistry of each layer at will? What does one need to do to couple the chemical species—in this case cobalt or iron—to specific layers in the structure? All of these issues are open questions, he said.
FROM TRANSITION METAL DICHALCOGENIDES TO COMPLEX OXIDES
Having discussed the Fe5–xCoxGeTe2 system, Ramesh turned to the issue of how one might approach creating structures with complex oxides that are akin to the two-dimensional structures with graphene and transition metal dichalcogenides (TMDs) that had been discussed earlier in the workshop. He began with an overview of complex oxides that he said was intended mainly for the students and postdocs in the audience.
The building block for a complex oxide of the form ABO3 is an octahedron with the A atom (a transition metal) at the center and oxygen atoms at the six vertices of the octahedron. This is also the basic perovskite structure, Ramesh noted. It is possible to manipulate—or “play with”—this structure in various ways, he said, and ultimately what is going on is that one is working with the electronic structures of the constituent atoms in the material and how they interact with one another. Oxides present a broad spectrum of crystal structures and physical phenomena and are a very heavily studied class of materials, he said, showing the Hamiltonian equation that describes the various interactions, and “one can start to play games with this, both with the spin–orbit coupling and, of course, the charge–charge interaction between the electrons, leading to some very exotic phases.”
In these systems, he continued, there is very strong coupling among the lattice, charge, orbital, and spin degrees of freedom. A good example is lanthanum manganese oxide. The manganese is in the +3 oxidation state, so it has 4d electrons, and so one would expect it to be a good metal. But it is not—it is a Mott insulator with a band gap of about 2 eV—because of the so-called Coulombic repulsion effects. Similarly spin–orbit coupling can lead to some very exotic phases, which is of great current interest in topological insulators.
“But the fun thing about oxides,” Ramesh said, “is the very large, diverse set of crystal structures you have.” Those crystal structures include the perovskite structure, pyrochlores, layered structures, spinels, and rock salts. The bismuth superconductors are a good example of a complex oxide with a layered structure, where there is strong bonding within the planes and very weak bonding between the planes, making it possible to cleave the materials in a way similar to how mica cleaves. “So you can have materials that look almost like graphene,” he said.
The complex oxides also have a huge diversity of physical properties. Some of the better known perovskites are high-temperature superconductors, such as YBa2Cu3O7–x, which was intensely studied beginning in the late 1980s. Other complex oxides are ferroelectrics (BaTiO3), ferromagnets (SrRuO3), topological insulators (Y2Ir2O7), multiferroics (BiFeO3), photovoltaics, and P-type and N-type semiconductors.
But can these complex oxides be fabricated as two-dimensional materials in the same way that graphene and TMDs can be? That is the key question, Ramesh said. Typically one produces these two-dimensional materials with exfoliation—cleaving single two-dimensional layers from a three-dimensional slab—or through self-limiting growth through chemical vapor deposition (CVD) or atomic layer deposition (ALD), but the bonding in these systems is quite different from the bonding in perovskites, he noted. Typically perovskite oxides have a three-dimensional crystalline network, and the crystalline chemistry of the oxides is typically less covalent than that of the TMDs. This makes the oxides less amenable to the exfoliation or CVD/ALD approaches.
One solution, he said, would be to use a bottom-up method with atomically precise layer-by-layer growth in which a two-dimensional layer is laid down and the substrate is then removed. And that, he said, would be the focus of the remainder of his talk—putting down ultra-thin layers of complex oxides on a substrate, removing them from the substrate to create freestanding monolayers, and then working with these monolayers, including the creation of moiré-type structures.
USING EPITAXY TO CREATE COMPLEX OXIDE SUPERLATTICES
In the next segment of his talk, then, Ramesh spoke about the use of epitaxy to create thin layers of complex oxides. To learn useful techniques, the complex oxide community turned to the semiconductor community, which has been using epitaxy techniques, such as molecular beam epitaxy (MBE) to create thin layers of semiconductors such as gallium arsenide for decades. And over the past 10-plus years, he said, the complex oxide community has made “fantastic progress” in learning to creating thin films of complex oxides.
In particular, he said, working with the complex oxide superlattices—that is, materials consisting of periodic alternating thin layers of two or more complex
oxides—has led to the discovery of a large number of unexpected behaviors in the materials, and Ramesh described a number of interesting behaviors in atomically perfect oxide superlattices in this portion of his talk. Referring back to his comment that complex oxides have a strong coupling among the lattice, charge, orbital, and spin degrees of freedom, he said, “You can bring all of them together.”
The key to the resulting interesting behaviors, he said, can be found at the boundaries between layers of different oxide materials in a superlattice. For example, he showed an image of a material made with alternating thin layers of lead titanate (PbTiO3) and strontium titanate (SrTiO3), where each layer was 12 unit cells across. “You can actually count the number of unit cells based on the atoms,” he said, since the lead and strontium atoms each appeared as bright dots in the image. By choosing the two (or more) materials used as layers in the superlattice so that there are interesting mismatches between them in different properties, one can create superlattices with a wide variety of properties, including some quite surprising one.
For example, Ramesh said, in the superlattice material he would be focusing on, while the crystalline structures of the two materials in the superlattice are very similar—matching to within 1 percent lattice mismatch—there is a large polarization gradient across the interfaces. Other possible gradients one could work with across the interfaces of a superlattice include an elastic gradient, a dielectric gradient, and a gradient in the Landau potential. “But the key is all of this is atomically precise synthesis,” he said, and this can be achieved in various ways—MBE, laser MBE, ALD (which uses chemical processes instead of physical processes to lay down the layers but still allows precise control of the layering), and others.
To illustrate what is possible with this approach, Ramesh then described some examples of complex oxide superlattices that have been studied to date. His first example dealt with creating polar textures using the epitaxy approach.
The work began more than a decade ago, with the goal of creating phonon localization. The idea was that by creating artificial superlattices, for certain periodicities of the phonon, you would get a crossover from incoherent particle-like behavior to wave-like behavior. However, when they created a superlattice with lead titanate and strontium titanate, they found so many other types of interesting physical phenomena that “we still haven’t done any phonon measurements!”
Showing a STEM image of one of these materials done with atomic-scale resolution (see Figure 5-2), Ramesh pointed to the “polar textures” that could be observed in the lead titanate layers. The small arrows (vectors) superimposed on the image show the relevant displacement of the titanium ion with respect to the lead ion in each unit cell, he explained. What this means is that the dipoles in the system—which are the core of the material’s ferroelectricity—are not up/down or left/right, which is what one would normally expect, but instead are rotating. These
vortices alternate rotating left and rotating right in domains which are about as wide as the lead titanate layer is thick (Das et al. 2019; Yadav et al. 2016).
Looking into the physics of what is happening in terms of the Hamiltonian for the system, Ramesh said that of the Hamiltonian’s four terms, two are most important—the elastic energy coming from the lattice and the electrostatic energy which is coming from the fact that at the interface between the lead titanate and the strontium titanate, there is a polar discontinuity. There is a huge polarization of 80μC/cm2 (microcoulombs per centimeter squared)—approximately one electron per unit cell—in the lead titanate, but that goes to 0 in the strontium titanate, right across the interface. To accommodate that, the system puts the polarization in-plane, but that causes the lattice to distort by 4–5 percent in-plane, which is resisted by the elastic energy in the layer. The system compromises to accommodate both energies, which leads to the curling polarization. This has huge consequences, which he would describe a bit later.
Before that, though, he showed an image of a three-layer system of strontium titanate/lead titanate/strontium titanate with what he referred to as “membrane structures.” A vortex lattice forms in the material with is very clear in the image, with various interesting details—domain walls and defects, among others. In particular, he pointed to dislocations that could be seen forming in the material and said that he believes these are progenitors of a phase transition. And pointing to a domain boundary, he said, “we believe now that these are chiral domain boundaries, that these are regions of different chirality.”
Coming back to the vortices, Ramesh spoke about the energy landscape inside a vortex and the possibility of negative permittivity in a vortex. He described an experiment in which an electron beam was sent through the material and the angular momentum of the beam measured at different points. What happens, he said, is that the vortices apply a torque to the electron beam, they transfer angular momentum to the electrons in the beam, and the direction of that angular momentum depends on the rotation of the vortex (see Figure 5-2f). Combining the measurement of the torque at different places in a vortex with the local potential distribution, Ramesh’s team was able to calculate the potential energy at points within the vortex. What they found was that there were points in the vortex region where the potential energy had large maxima. That implies, he said, that there are places within the vortex where the curvature is negative. Numerical simulations run on the vortices reproduce the observed values of the polarization and the electric field quite well, and they also indicate regions of local negative permittivity right at the center of the vortex where the polarization goes to zero.
Switching gears, Ramesh then described another interesting thing that happens in these materials, this one in the optical domain. Chirality, or handedness, appears in such polar vortices although the individual materials themselves are not chiral. It describes the direction of the spiral on a screw, for instance; vari-
SOURCE: Ramamoorthy Ramesh, University of California, Berkeley, presentation to the workshop, May 19, 2021; reprinted by permission from Springer Nature: A.K. Yadav, C.T. Nelson, S.L. Hsu, Z. Hong, J.D. Clarkson, C.M. Schlepütz, A.R. Damodaran, et al., 2016, “Observation of Polar Vortices in Oxide Superlattices,” Nature 530:198–201, https://doi.org/10.1038/nature16463, © 2016.
ous organic molecules, such as glucose, have chirality, being either left-handed or right-handed. Magnetic skyrmions—an example more familiar to the audience of the workshop—also have chirality. To probe the existence of chirality in the vortex structures, Ramesh said, one can use resonant soft X-ray diffraction–based techniques or other optical measurements.
It turns out, he said, that when one probes the vortices in a superlattice—which are not just on the surface but also extend into the body of the material—the vortices not only have a rotational component going clockwise or counterclockwise, but they also have an axial component pointing into or out of the material. Because of that, the vortices can be either left-handed or right-handed. (The mnemonic for right-handed chirality is to use the right hand with the thumb pointing out and the four fingers curled around, like a loosely held hitchhiker’s symbol; the thumb points along the axis, while the fingers indicate the rotation in right-handed chirality.)
Ramesh then describes several tools that can be used to probe the chirality in these materials. For example, resonant soft X-ray diffraction can be used with circularly polarized light to prove the existence of circular dichroism in these
materials. There are only a few ways to get such circular dichroism, and one likely explanation is that the material is indeed chiral. A second tool was confocal optical microscopy, which was used to image the material with left and right circularly polarized light. By mapping the dichroism between the left-handed and right-handed images, one discovers a collection of different regions on a scale of around 500 nm where the regions have either positive or negative dichroism. “This is the true mapping of the change in handedness,” he said. Yet another experiment involved applying in-plane electric fields to the layered material and switching the chirality back and forth.
To study the nature of the boundaries between the regions with positive and negative dichroism, Ramesh described yet another tool, 4-dimensional STEM (4D-STEM). This is a powerful tool for characterizing materials he said, and it collects two-dimensional information at each point along the two-dimensional surface of a sample, which is why it is called four-dimensional STEM. The tool can collect various sorts of information at each point on the surface, but the option that Ramesh described was observing both the lateral component of the polarization (lateral to the vortices) and the axial component of the polarization. Using 4D-STEM it is possible to show that the boundaries between the regions of differing dichroism are those places in the material where there is a change in chirality essentially at the atomic scale. This is a conclusion that couldn’t be made with other types of STEM, he said.
In work done in collaboration with researchers at Argonne National Laboratory, Ramesh and the others used ultrafast light to manipulate the vortices, making them “coherently jiggle around.” They are coherent modes of the vortices, he said, with the entire vortex going up and down. This collective motion of the vortex has been named the “vortexon.”
In a different direction, theoretical calculations have indicated that by varying the substrate on which the lead titanate is deposited, one varies the strain between the two layers, which in turn varies the sorts of behaviors one observes. In particular, Ramesh said, using substrates with the right substrate lattice constant—including the strontium titanate—one can produce polar skyrmions. Visualizations of the skyrmions show dipoles coming out of the surface and creating a flower-like object, but they also also have a Bloch-type component that circles around on the surface and defines a handedness. This type of skyrmion, he said, is formally called the “hopfion.”
Switching back to the topic of negative permittivity in these superlattices, Ramesh said that the layered materials have a much higher permittivity than either lead titanate or strontium titanate on their own. The reason, he said, is that the surfaces of the skyrmions are regions of negative permittivity. When an electric field is applied, the skyrmions start to disappear, and there is a topological phase transition from the skyrmions to a uniform polarization, so the permittivity decreases.
As he was finishing up, Ramesh spoke very briefly about the role of mechanics in free-standing multi-ferroics and giant flexoelectricity in freestanding BiFeO3.
As a conclusion, Ramesh looked to the future. It should be very interesting, he said, to layer TMDs on multiferroic oxides, such as BiFeO3. Calculations indicate that with such a material it should be possible to tune the structure, polarization, and electric and magnetic properties with an applied electric field. However, he said, it has proved much more different to build such structures in the lab than in simulations. “Interfaces are very important,” he said. “We still need to learn how to make this interfaces, but this is indeed a huge opportunity.”
DISCUSSION
After Ramesh’s presentation there was a short question-and-answer period moderated by Aharon Kapitulnik. One question concerned the possibility of growing oxides between layered two-dimensional materials. Ramesh answered that the non-oxidic, two-dimensional materials will not tolerate the amount of oxygen involved in laying down complex oxides. “This is a good challenge,” he said. “This is not a trivial question. There is much to be done there, but we need to be watchful of chemistry.” One possible approach is to create a “heterogeneous sandwich” consisting of a few monolayers of a tungsten diselenide or any of the TMDs, then put five to seven layers of bismuth ferrite, and then more layers of tungsten diselenide. “I think that’s doable,” he said.
Kapitulnik followed up on that by asking if Ramesh had thought about using some of the same techniques applied to create moiré patterns, such as putting a twist between different layers. Ramesh replied that he had thought about it but not tried to execute that because his group has not yet managed to achieve interfaces that are good enough to have real communication between the TMD and the oxide. In particular, in the case of good interfaces there will be significant valley splitting, but so far his group has not seen any measurable valley splitting. “Once we see that,” he said, “I think we can start to do the full twisting operation to get the various moiré structures.”
The next question concerned the FCGT material: Given that the scanning transmission electron microscope images seemed to show that symmetry was breaking locally, why were there skyrmions everywhere? Ramesh answered that in the AA' phase with 50 percent cobalt there is a long-range ordered twisted structure, so the symmetry is long-range. Also, for the AA' phase there are only six layers of iron/cobalt atoms, so even within one layer it breaks inversion symmetry because there are different layers on either side of the germanium. “If you’re exactly at the AA' phase, which means long range it is the same, then it is breaking inversion symmetry macroscopically, which is why you see the skyrmions everywhere.”
Kapitulnik then asked his own question, beginning with the observation that speakers during the workshop’s first day had talked about the possibility of three-dimensional moiré patterns in some of the TMD materials. Given that Ramesh had said that people are only in the very beginning of obtaining moiré patterns in the growth direction of thin films, wouldn’t it be easier now to create moiré patterns in the third dimension, that is, at the interface of domain walls? Ramesh answered that this was a great observation and that he agreed with Kapitulnik. Kapitulnik then followed up by asking if there have been any simulations in this direction? Ramesh answered that the length scales are such that only phase field calculations will work; ab initio calculations cannot get to these kinds of length scales. Some researchers are trying to use phase field calculations to examine, for example, chiral domain boundaries. Because phase-field calculations are macroscopic and miss some details, his group is looking to combine phase field and ab initio calculations to get both the length scales and the details.
REFERENCES
Das, S., Y.L. Tang, Z. Hong, M.A.P. Gonçalves, M.R. McCarter, C. Klewe, K.X. Nguyen, et al. 2019. “Observation of Room-Temperature Polar Skyrmions.” Nature 568:368–372.
Li, Q., V.A. Stoica, M. Paściak, Y. Zhu, Y. Yuan, T. Yang, M.R. McCarter, et al. 2021. “Subterahertz Collective Dynamics of Polar Vortices.” Nature 592:376–380.
Yadav, A.K., C.T. Nelson, S.L. Hsu, Z. Hong, J.D. Clarkson, C.M. Schlepütz, A.R. Damodaran, et al. 2016. “Observation of Polar Vortices in Oxide Superlattices.” Nature 530:198–201.
