WEBVTT There's a noise. Thank you, Sank. Uh, and thanks to everyone for, uh, coming in. Okay, I'll try… I'll try to keep it going on that. Maybe I won't be quiet for too long, and I might stop again, but… 00:00:00.000 --> 00:00:04.000 Anyway, yeah, I'm going to talk a little bit, some different stories. 00:00:04.000 --> 00:00:06.000 about perovskites. 00:00:06.000 --> 00:00:09.000 And in the… in the first part of the talk, 00:00:09.000 --> 00:00:11.000 I'll be talking about… 00:00:11.000 --> 00:00:18.000 grass guides that are nominally cubic, you'll see maybe some distortions a little bit away from cubic, but mostly cubic, and 00:00:18.000 --> 00:00:23.000 And the focus there is going to be, uh, looking at the magnetism when we have heavy 00:00:23.000 --> 00:00:27.000 Uh, transition metals, particularly osmium and rhenium, 00:00:27.000 --> 00:00:33.000 And then, uh, and then the rest of the talk, I'll be talking about these hexagonal perovskites, and I'll… I'll introduce those. 00:00:33.000 --> 00:00:37.000 As we go. Okay, so… 00:00:37.000 --> 00:00:42.000 Just to kind of maybe set the stage for the first part of the talk, when we're thinking about, um, 00:00:42.000 --> 00:00:45.000 these double perovskites, so we've got 00:00:45.000 --> 00:00:51.000 this structure, which you could think of this as, uh, basically the sodium chloride structure with different 00:00:51.000 --> 00:00:59.000 types of octahedra. And you can make, of course, well, there's probably thousands of double peroxides now, but today, what I'm going to talk about 00:00:59.000 --> 00:01:02.000 is where one of the octahedric… 00:01:02.000 --> 00:01:08.000 Um, a third row transition metal ion, and, you know, we'll be… mostly, I'll be talking about 00:01:08.000 --> 00:01:19.000 compounds where there's one electron in the 5D orbitals, but I'll… I'll start by giving you a little bit of a summary of some things we've done with 2 and 3 electrons. One of the things when you have 00:01:19.000 --> 00:01:27.000 Um, these third-row transition metal ions is these EG orbitals are so sufficiently antibonding that you… 00:01:27.000 --> 00:01:32.000 You practically will never see a case where you have any population of those orbitals. 00:01:32.000 --> 00:01:37.000 And so, once you have these kind of configurations, you're going to, first of all, we have 00:01:37.000 --> 00:01:45.000 pretty high oxidation states here, plus 5, plus 6, plus 7, so you'll have a lot of covalency with oxygen, which is important. 00:01:45.000 --> 00:01:48.000 And then, um, for the, um… 00:01:48.000 --> 00:01:56.000 Do you D1 and D2 cases? Of course, we can't have distortions that might be, uh, Jan Teller-like distortions, and we'll also 00:01:56.000 --> 00:02:01.000 for sure have strong spin-orbit coupling. 00:02:01.000 --> 00:02:05.000 Okay, so it's going to be about magnetism, and these are… 00:02:05.000 --> 00:02:16.000 Uh, I can show you if you want to see it, I don't have any in the talk, but they're all basically localized electron systems there. None of them are metallic, they're… they're insulators to varying degrees. 00:02:16.000 --> 00:02:23.000 And so, when we think about this double perovskite structure, which is basically magnetic ions on an FCC lattice, 00:02:23.000 --> 00:02:28.000 Then we have two different… potentially two different super exchange pathways. 00:02:28.000 --> 00:02:33.000 you have this 90-degree nearest neighbor pathway, which would be 00:02:33.000 --> 00:02:41.000 could be direct overlap of the d orbitals, or more likely, maybe some, uh, through the oxygen p-pi orbitals. 00:02:41.000 --> 00:02:48.000 And then we could have this kind of sigma pathway that's through, um, the intervening diamagnetic cations. 00:02:48.000 --> 00:02:53.000 So, with the… with these 5D systems, actually, this pathway is going to be 00:02:53.000 --> 00:02:58.000 very, very weak, and I mean, mostly dominated by this pathway. 00:02:58.000 --> 00:03:13.000 If you were to look, uh, if you were to do, um, let's say a relatively straightforward theory, well, not by my standards, but by this department, uh, let's say you were going to do a Heisenberg theory of 00:03:13.000 --> 00:03:17.000 Magnetic ions on an FCC lattice, people have long ago worked out 00:03:17.000 --> 00:03:26.000 what kinds of magnetic structures you ought to get, depending on the sign and the strength of these two exchange coupling mechanisms. So, first of all, 00:03:26.000 --> 00:03:34.000 of course, SET Lattice is a frustrated lattice. We can't have all of the stamped anti-parallel to their nearest neighbors. 00:03:34.000 --> 00:03:45.000 And so, if you have, let's say, the dominant spin would be the nearest neighbor interaction, antiferromagnetic, normally you get this, what's called a Type 1 structure. 00:03:45.000 --> 00:03:47.000 So the Type 1 structure has 00:03:47.000 --> 00:03:49.000 Ferromagnetic layers. 00:03:49.000 --> 00:03:58.000 And then the neighboring layers are ferromagnetic in the opposite way, right? And so if you have this, what you would… if I look at one ion, and its 12 neighbors, 00:03:58.000 --> 00:04:03.000 You see 8 of them in the layers above and below are going to be antiferromagnetic. 00:04:03.000 --> 00:04:05.000 And a board would be ferromagnet. 00:04:05.000 --> 00:04:08.000 But, if you have strong 00:04:08.000 --> 00:04:13.000 Super exchange coupling through the diamagnetic cation along the sigma bond pathway. 00:04:13.000 --> 00:04:23.000 And this is what you invariably get when you have first-row transition metal ions that are not LDG orbitals, like nickel, cobalt, manganese, iron. 00:04:23.000 --> 00:04:26.000 then you tend to get what's called a Type II structure, 00:04:26.000 --> 00:04:32.000 Where you have there… where this pathway being anti-ferromagnetic is gone. 00:04:32.000 --> 00:04:40.000 Um, and in principle, of course, you could have ferromagnetism, but in, you know, to my knowledge, there aren't any… 00:04:40.000 --> 00:04:47.000 Uh, so it's a simple double perovskites, where you get a ferromagnetic structure, although what we're going to see today is something that looks 00:04:47.000 --> 00:04:53.000 a little bit like, uh, the intersection of these two things. 00:04:53.000 --> 00:04:59.000 Okay, so, yeah, I wanted to talk mostly about the D1 case, but let me just, uh… 00:04:59.000 --> 00:05:05.000 give you, uh, one slide each, a little recap of what we've learned about when you have other electron cans. 00:05:05.000 --> 00:05:09.000 So, if you have a D3 ion, 00:05:09.000 --> 00:05:11.000 Like Osmium 5+. 00:05:11.000 --> 00:05:16.000 Um, what you see here, here's a couple of compounds where that happens. 00:05:16.000 --> 00:05:20.000 And the main takeaway is that you're going to get 00:05:20.000 --> 00:05:22.000 Anti-paramagnetic ordering. 00:05:22.000 --> 00:05:26.000 Uh, temperature here, we have 90 Kelvin. 00:05:26.000 --> 00:05:28.000 Here, it's about 70 Kelvin. 00:05:28.000 --> 00:05:34.000 Uh, the difference between these two is this one, because of the tolerance factor reasons, is cubic. 00:05:34.000 --> 00:05:41.000 Whereas this one, we have octahedral rotations, this kind of octedral tilting, which lowers the symmetry to… 00:05:41.000 --> 00:05:43.000 on a clinic, but… 00:05:43.000 --> 00:05:49.000 Uh, and of course, that changes the frustration a little bit. So this one has less frustration than that one, but I think… 00:05:49.000 --> 00:05:55.000 One of the things… a couple of things just to keep in mind as we talk about these compounds. 00:05:55.000 --> 00:06:03.000 One of the things that surprised me a lot is if you think about it, there is no… there is no… if this is, uh, let's say this is osmium, 00:06:03.000 --> 00:06:08.000 There's no oxygen connection to another osmium, right? So, one might think, 00:06:08.000 --> 00:06:10.000 that the super exchange is going to be 00:06:10.000 --> 00:06:18.000 maybe not so strong. But in fact, when we look at the device temperature, we see that the super exchange is incredibly strong. 00:06:18.000 --> 00:06:23.000 You know, it's almost… it's of the order of minus 700 Kelvin, right? So this is like… 00:06:23.000 --> 00:06:28.000 Uh, lanthanum iron O3-type strength of super-exchange coupling. 00:06:28.000 --> 00:06:34.000 The magnetic ordering is at lower temperatures because there's a lot of frustration here due to the FCC lattice. 00:06:34.000 --> 00:06:38.000 Then we have frustration factors that are, let's say, 7 to 10. 00:06:38.000 --> 00:06:42.000 Another thing to keep in mind is that we are going to have… 00:06:42.000 --> 00:06:49.000 We have 3 unpaired electrons, and so if we look at the ordered moment, what we would see from neutron diffraction 00:06:49.000 --> 00:06:58.000 If you had something like a Chromium 3 plus ion, like lanthanum chromium O3, we would get a neutron moment of about 2.5. 00:06:58.000 --> 00:07:02.000 And so here we see that the neutron moment is… 00:07:02.000 --> 00:07:10.000 markedly lower, and the reason for that is because there's really a lot of covalency with the oxygen. 00:07:10.000 --> 00:07:17.000 How do you extract new effective? Is that from, uh… That's from… well, to the… That's the Curibites fit here, yeah, yeah. 00:07:17.000 --> 00:07:19.000 Now, of course, you might say, 00:07:19.000 --> 00:07:27.000 How are we high enough above it? But, I mean, this is the Curie Weiss bit we're getting here. And so we're seeing, actually, a little bit of spin-orbit coupling. 00:07:27.000 --> 00:07:30.000 This moment, the spin-only moment, actually, is very close to this. 00:07:30.000 --> 00:07:34.000 I will say that, uh, actually, on this compound, we did, uh, 00:07:34.000 --> 00:07:42.000 Rick's resident inelastic X-ray scattering, and we found, um, that definitely there is some mixing of the higher order excited states 00:07:42.000 --> 00:07:56.000 That gives you a little bit of spin orbit coupling here, even though that electron configuration is D3. Yeah, same. So, field cooling is going up there. Yeah. That means there is probably a spin. There's a spin canting. How is your spin? 00:07:56.000 --> 00:08:04.000 It's… well, if you look… if you look at the neutron, you… it's… you can't measure it. You can't… it's too small to measure. 00:08:04.000 --> 00:08:10.000 It's very small, I think. Yeah. 00:08:10.000 --> 00:08:12.000 Maybe I… 00:08:12.000 --> 00:08:25.000 I want to say a .01, .02 muB. I think… but I can't… I don't remember for sure. It's pretty small. So it just re-pushes this, so it looks like the blue is osmium, right? Yeah. It is tilted. 00:08:25.000 --> 00:08:29.000 Yes. So, compared with the TT angle. 00:08:29.000 --> 00:08:48.000 How does in that moment do you have? That's kind of my… Ah, yeah, yeah, yeah, yeah. So, since it's an ID system, you know, recovery may be huge, so that there may be very luzzy, kind of a spin, can't think… Sure. Just because… just because of the tilting, you get the… I mean, of course, once you have the tilting, of course, you'll get a Kalasinski, well… 00:08:48.000 --> 00:08:53.000 No, you wouldn't. That would be an irregular perasket, right? 00:08:53.000 --> 00:08:58.000 So, that's the kind of question. So, even though teaching is the same direction, 00:08:58.000 --> 00:09:05.000 User DM interaction, use your TTO has alternate. Right. But this is a one-tick thing. 00:09:05.000 --> 00:09:10.000 somehow giving… saying, how are you going to have a DM 00:09:10.000 --> 00:09:19.000 Because inversion symmetry is present in both of these structures. Right, but one direction, one kind of… But I think… okay. 00:09:19.000 --> 00:09:22.000 Yes. Well, okay, I think, though, that… 00:09:22.000 --> 00:09:39.000 when you think about the DM, you're thinking about the symmetry actually at the ligand, right? And of course, normally when you have tilting, you break the inversion symmetry. But it's a little different here, because remember, this is a non-magnetic object. 00:09:39.000 --> 00:09:43.000 I haven't… I haven't thought about that. The magnetic structure break the symmetry? 00:09:43.000 --> 00:09:46.000 Yeah. Uh, the magnet? 00:09:46.000 --> 00:09:55.000 Let's see, the magnetic structure is the type 1 structure here. I'm trying to think of the magnetic pointer. 00:09:55.000 --> 00:10:13.000 Probably not. Probably not. I don't think it will. Well then, overall, you should not have net, uh… I see. Yeah. Also, um, is there only one Osmium per cell, or…? In the crystallographic, yeah, in the crystallographic unit itself, for sure. So it sits on its own inversion center, so this should… That's right, that's right, that's, yeah, yeah, that's right. 00:10:13.000 --> 00:10:21.000 So, okay, I mean, so I guess I hadn't thought in great detail about this camping, but, um… It can be exchanged properly. All screens are kind of… 00:10:21.000 --> 00:10:27.000 Just because of it, because there's an easy access within the OctaHetron? I… 00:10:27.000 --> 00:10:29.000 They all do, yeah. 00:10:29.000 --> 00:10:37.000 I will say, that goes away when you have the cubic structure, right? This is not a cancel structure. So it is probably… 00:10:37.000 --> 00:10:42.000 related in some way, that I haven't thought deeply about to the tilting. Yes? 00:10:42.000 --> 00:10:44.000 Um, could you tell us a little bit about… 00:10:44.000 --> 00:10:49.000 the field versus zero field cooling of your compound on the left. 00:10:49.000 --> 00:10:52.000 Do you… do you think of it as urgent? 00:10:52.000 --> 00:10:58.000 Well, um… Oh, is that the same question? Yeah, I mean… 00:10:58.000 --> 00:11:04.000 I didn't understand your question, sorry. Well, I think, yeah, the reason why we have a divergence at the nail temperature here 00:11:04.000 --> 00:11:12.000 is because I believe because there's a canning. That would, I think, be the explanation for that. 00:11:12.000 --> 00:11:18.000 Okay. You're saying there's more canting on the left than on… Well, I think there's no canting. There's no canting here. 00:11:18.000 --> 00:11:23.000 Because there's no divergence between the two. Yeah. There's some kind of… 00:11:23.000 --> 00:11:32.000 I don't know, maybe some… impurity, probably, that gives that a little turn up at lowest temperature. 00:11:32.000 --> 00:11:39.000 Um, okay, oh, what I was going to say next, though, is, uh, has to do with… two things that are interrelated. First of all, 00:11:39.000 --> 00:11:43.000 How is it that the exchange coupling is so strong? 00:11:43.000 --> 00:11:47.000 And secondly, why is that the moment so much smaller than you would think it would be? 00:11:47.000 --> 00:11:55.000 And so, I mean, I think the answer to both questions has to do with very high covalency with the oxygens that surround 00:11:55.000 --> 00:12:06.000 the osmium here. This is formerly Osmium 7+, but of course, it's not anywhere close to 7+, it just means that there's a great covalency with the oxygen. 00:12:06.000 --> 00:12:16.000 So these are calculations that David Singh did of this structure, and in the DFT calculations, he's getting the moment on Osream to be 00:12:16.000 --> 00:12:23.000 1.8 mu v per osmium, which is not that far from what we're seeing in the neutron moment at 1.6. 00:12:23.000 --> 00:12:28.000 There's a little bit of orbital contribution here, but it's pretty small. 00:12:28.000 --> 00:12:36.000 So, I was going to ask about that. So, in orbit, it's not playing much of a role, it sounds like. You haven't mentioned it. It's more just the fact that 5Gs are big. 00:12:36.000 --> 00:12:40.000 Yes, I think… I think for the D3 case, that's correct. 00:12:40.000 --> 00:12:48.000 The main thing is the spatial extent of the d orbitals, and then the high oxidation state, which gives a lot of covalency with the oxygen. 00:12:48.000 --> 00:12:54.000 We'll see in a minute when we go to D2 and D1, then spin orbit coupling starts to become important. 00:12:54.000 --> 00:12:56.000 And maybe also keep in mind that the… 00:12:56.000 --> 00:13:01.000 We also have experimental measures of this, but the T2GEG crystal field… 00:13:01.000 --> 00:13:05.000 Splitting is a… is almost 5 electron volts here. 00:13:05.000 --> 00:13:16.000 So, um, which is probably… depending on what first row of transition metal you pick, maybe, you know, double what you would see for a 3D transition metal line. 00:13:16.000 --> 00:13:19.000 Okay, let's do one, one, one… 00:13:19.000 --> 00:13:23.000 kind of review of what happens when we're now going to go to two electrons. 00:13:23.000 --> 00:13:28.000 transition metal, per osmium again here, and so this is… 00:13:28.000 --> 00:13:31.000 Um, strontium to magnesium osmiomostics. 00:13:31.000 --> 00:13:34.000 And this one, um, has… 00:13:34.000 --> 00:13:40.000 we have 6 plus, which is 5D2, and with this particular combination of diamagnetic ions, 00:13:40.000 --> 00:13:45.000 You get a tetragonal structure at room temperature. It's I4 over M. 00:13:45.000 --> 00:13:50.000 And this comes about, well, two things happen here. First of all, we have rotations. 00:13:50.000 --> 00:13:53.000 of the octahedra, about the C-axis, so… 00:13:53.000 --> 00:13:57.000 this anti-phase tilting about the C-axis. 00:13:57.000 --> 00:14:02.000 But that also breaks the symmetry in a way that allows the octahedron to distort. 00:14:02.000 --> 00:14:07.000 And if you go down to… this is the bond distances from the 10 Kelvin structure. 00:14:07.000 --> 00:14:12.000 And what we see is that the axial bonds in the Z direction are 00:14:12.000 --> 00:14:15.000 are elongated with respect to the equatorial bonds. 00:14:15.000 --> 00:14:20.000 So this is gonna break the degeneracy of the T2G orbitals, 00:14:20.000 --> 00:14:23.000 And it does it in such a way that we would expect 00:14:23.000 --> 00:14:29.000 the YZ and the XZ, too, that would be lower in energy, and the XY to be higher in energy. 00:14:29.000 --> 00:14:31.000 So this is the distortion you would expect. 00:14:31.000 --> 00:14:36.000 let's say from a kind of Jan Teller-type considerations. 00:14:36.000 --> 00:14:42.000 But it also is going to be the distortion that's going to maximize your spin-orbit coupling. And in this case, 00:14:42.000 --> 00:14:46.000 I would say that they work together. 00:14:46.000 --> 00:14:49.000 What that does is it means that if we have… 00:14:49.000 --> 00:14:53.000 The XZ and the YZ orbitals both have occupied, 00:14:53.000 --> 00:14:55.000 And then that we should get… 00:14:55.000 --> 00:15:03.000 quite strong anti-ferromagnetic exchange coupling between this osmium and the osmium in the layer above. 00:15:03.000 --> 00:15:09.000 But by emptying out the DXY orbitals, it means the coupling in this plane now is pretty weak. 00:15:09.000 --> 00:15:12.000 And if you think about the frustration here, 00:15:12.000 --> 00:15:17.000 This is the… if it all wants to be anti-ferromagnetic, I mean, this is… this is… 00:15:17.000 --> 00:15:25.000 a fantastic… there's… you've basically eliminated the frustration, because now it's very weak in this plane where you have the ferromagnetic neighbors. 00:15:25.000 --> 00:15:30.000 And, um, much stronger in the direction where you have the antiferromagnetic element. 00:15:30.000 --> 00:15:34.000 And so the nail temperature is 108 Kelvin here, which… 00:15:34.000 --> 00:15:41.000 As far as I know, for a double perovskite, this is maybe the highest that's known. 00:15:41.000 --> 00:15:43.000 The neutron moment now… 00:15:43.000 --> 00:15:49.000 We have two electrons per osmium, but in neutron diffraction, we see a moment of only about 0.6 muB per… 00:15:49.000 --> 00:15:52.000 Um, for Osmium. 00:15:52.000 --> 00:16:04.000 And notice that the device temperature is not 7, minus 700 anymore, it's still pretty strong, but we've reduced the frustration quite a lot in this compound. 00:16:04.000 --> 00:16:07.000 Okay. 00:16:07.000 --> 00:16:14.000 So now, let's turn… let's take one more electron out, alright, so by manipulating the dimagnetic cations… 00:16:14.000 --> 00:16:16.000 Now we're going to put, um… 00:16:16.000 --> 00:16:21.000 We're going to look at one… these two have, uh, rhenium 6+, 00:16:21.000 --> 00:16:25.000 which has 1D electron, and this is osmium 7+. 00:16:25.000 --> 00:16:27.000 And I might… at the beginning, I want to acknowledge 00:16:27.000 --> 00:16:35.000 a little bit that other people have also worked on these compounds, and so this was really the first compound that people got interested in, and that work. 00:16:35.000 --> 00:16:38.000 was initially kicked off by Ian Fisher, 00:16:38.000 --> 00:16:40.000 Um, and… 00:16:40.000 --> 00:16:48.000 You know, also, uh, the Canadians at McMaster, John Green and Bruce Gallin have studied these things, as have, um… 00:16:48.000 --> 00:16:51.000 Zinji Hiroi and… 00:16:51.000 --> 00:17:02.000 Gago Karai in Japan. So, mostly I'll show wherever I can, I'll show artwork, but in some places I'll also show the work from the literature, and basically, it's all more or less in agreement with each other. 00:17:02.000 --> 00:17:11.000 But the question becomes, alright, so you've got these compounds, or you could say they're doppelgangers of each other, they're isoelectronic, isostructural. 00:17:11.000 --> 00:17:14.000 They're all cubic at room temperature. 00:17:14.000 --> 00:17:19.000 If we look at the magnetism, now when we get down to low temperature, below 00:17:19.000 --> 00:17:22.000 let's say, 18 to 7 Kelvin, 00:17:22.000 --> 00:17:27.000 If you get a state that looks… basically looks like it becomes ferromagnetic, right? We're seeing 00:17:27.000 --> 00:17:30.000 Hysteresis here, um… 00:17:30.000 --> 00:17:39.000 relatively soft magnetism. The saturation magnetization, pretty small, right? If you have one unpaired electron per formula unit, and we're getting… 00:17:39.000 --> 00:17:44.000 about, uh, saturation magnetization of about one quarter of that. 00:17:44.000 --> 00:17:49.000 And, um, so, you know, this is different groups at different times. 00:17:49.000 --> 00:17:53.000 measuring these samples. So what is this magnetic state? 00:17:53.000 --> 00:17:57.000 I mean, initially, it was just called the ferromagnetic state, but really… 00:17:57.000 --> 00:18:03.000 The right way to look at it is probably something like this. I mean, I have to say that 00:18:03.000 --> 00:18:09.000 There still are no neutron diffraction measurements of this magnetic structure. 00:18:09.000 --> 00:18:12.000 I'll come back to that at the end here. 00:18:12.000 --> 00:18:14.000 But based on… 00:18:14.000 --> 00:18:23.000 sodium NMR measurements, that Desmond Petrovich that Brown did, magnetometry on single crystals, resonant X-ray diffraction, people think 00:18:23.000 --> 00:18:25.000 that the magnetic structure looks like this. 00:18:25.000 --> 00:18:28.000 Ferromagnetic layers, okay? 00:18:28.000 --> 00:18:33.000 tanted with respect to each other by about 90 degrees. So it's almost halfway. 00:18:33.000 --> 00:18:40.000 In between the Type 1 structure and the Type and the collinear Ferramay. 00:18:40.000 --> 00:18:43.000 Are you averse to calling it an ultra-magnet? 00:18:43.000 --> 00:18:56.000 Uh, well, I mean, we published this work before… well, I mean, we started working on this before I knew about ultramagnets. I don't know… I'm not averse to that. Would you say that this is an ultra-magnet? 00:18:56.000 --> 00:18:59.000 Uh, well, we don't know, because we… 00:18:59.000 --> 00:19:08.000 There's no, uh, you can't… I'll come back to, in the end, you can't get any new… we can't see any magnetic diffraction. And part of the reason 00:19:08.000 --> 00:19:13.000 is maybe because they might not be dipolar magnetism's possible. So there's that moment. 00:19:13.000 --> 00:19:17.000 There is in that moment you can measure in magnetization. 00:19:17.000 --> 00:19:21.000 The sodium NMR is consistent with there being a net moment. 00:19:21.000 --> 00:19:25.000 Um, and also there… the Japanese have done some… 00:19:25.000 --> 00:19:28.000 Resonant x-ray scattering that shows that there's a moment. 00:19:28.000 --> 00:19:33.000 So this is zero field structure. This is the zero field structure. Yes. 00:19:33.000 --> 00:19:43.000 You're doing this now, why this train decant thing happens? Yeah, yeah, I'm gonna come to that, yeah, yeah, yeah. 00:19:43.000 --> 00:19:49.000 So, first of all, what we wanted to understand, okay, is there… 00:19:49.000 --> 00:19:55.000 any, you know, is there any signature of a structural phase transition that happens when you enter into the magnetic state? 00:19:55.000 --> 00:20:01.000 And, you know, for whatever reason, that was never really studied on the sodium osmate. 00:20:01.000 --> 00:20:06.000 But, um, and I think the problem is because it's pretty subtle, but here we have… 00:20:06.000 --> 00:20:10.000 a sample. This is, um, barium zinc renate. 00:20:10.000 --> 00:20:13.000 And these, uh, synchrotron powder diffraction data. 00:20:13.000 --> 00:20:18.000 Collected Oregon, and you can see that when you get down to low temperature, 00:20:18.000 --> 00:20:23.000 Yeah, you start to see this peak splitting, which is characteristic of a tetraagonal distortion. 00:20:23.000 --> 00:20:27.000 And here's the C over A ratio, and so you can see that start set. 00:20:27.000 --> 00:20:30.000 somewhere in the vicinity of 25K. 00:20:30.000 --> 00:20:33.000 Here's our specific heat data. 00:20:33.000 --> 00:20:45.000 And you might not be very, very convinced that there's a feature here, although the Japanese data on single-crystal samples actually is a little bit more pronounced. So we have two features in the specific heat. And what's happening 00:20:45.000 --> 00:20:48.000 is the higher temperature feature. 00:20:48.000 --> 00:20:59.000 is associated with a tetragonal structure, and what that tetragonal structure is, it's not a rotation of the octahedron. The octahedron do not tilt or rotate, but instead what happens is, let's call this the X direction, 00:20:59.000 --> 00:21:03.000 And this is the Y direction. So in the X direction, we have 00:21:03.000 --> 00:21:09.000 Two oxygens moving in, and in the Y direction, the, uh, the oxygens move away. 00:21:09.000 --> 00:21:12.000 Okay? And if we were to go to the next layer… 00:21:12.000 --> 00:21:18.000 up or down, we would see basically the opposite distortion. There, the X… 00:21:18.000 --> 00:21:24.000 Ligands… the ligands in the X direction move away, and the ligands in the Y direction move in. 00:21:24.000 --> 00:21:27.000 And then it's only at this lower temperature 00:21:27.000 --> 00:21:30.000 Um, here we think, um, 16 Kelvin. 00:21:30.000 --> 00:21:35.000 that we see magnetic order. So we have a structural phase transition that happens first, 00:21:35.000 --> 00:21:39.000 Followed by a magnetic phase transition. So Cassie connects your ultimate phase. 00:21:39.000 --> 00:21:46.000 And then, like, spin direction is also 90 degrees, so… Yeah, yeah, yeah. 00:21:46.000 --> 00:21:54.000 Uh, so, well, I'm… yeah, I mean, I'm happy to hear that that resonates with people. But I thought you said it was a fair amount. 00:21:54.000 --> 00:22:01.000 Well, okay. Well, okay, I mean, the magnetic strip… okay, we'll come… we'll come back to that in a minute. I mean, it's not… 00:22:01.000 --> 00:22:06.000 But the magnetic structure at zero field is thought to be, um… 00:22:06.000 --> 00:22:10.000 I had it here, this thing, right? Yeah, that's a ferromagnet. 00:22:10.000 --> 00:22:15.000 Well, unless it… unless it alternates from layer to layer. 00:22:15.000 --> 00:22:17.000 I mean, this layer is pointing… 00:22:17.000 --> 00:22:21.000 Addison that layers in the board, and this layer is that. I mean, have us. 00:22:21.000 --> 00:22:29.000 I mean, I call this a canted paramagnet, and some people object to that terminology, but yeah. 00:22:29.000 --> 00:22:32.000 Well, it has… yes, it does. Let's do it in Ultimate. 00:22:32.000 --> 00:22:45.000 It's… yeah, you're right, it's not… it's not an… it's not, like, we're not being anywhere close to a simple anti-theroin, that is correct, that is correct. 00:22:45.000 --> 00:22:48.000 Um… 00:22:48.000 --> 00:22:55.000 Okay, so the question is, why do we get this structure? That was your question, Sen. Why do we have this canting? 00:22:55.000 --> 00:22:57.000 Which hasn't been seen before. 00:22:57.000 --> 00:23:04.000 And… and what… and what stabilizes this structure, right? I mean, this isn't… this structure wasn't known in any of the… 00:23:04.000 --> 00:23:08.000 double perovskites with ruthenium, or any of the 4D ions. 00:23:08.000 --> 00:23:11.000 So this is… this is theory done by my colleagues. 00:23:11.000 --> 00:23:15.000 Mohit Randiria and Nandini Trivedi and their students. 00:23:15.000 --> 00:23:21.000 So the idea is, think about that structure of distortion. What you're basically doing is in 00:23:21.000 --> 00:23:27.000 Uh, this layer, you have, uh, the atoms that are in the X direction move in. 00:23:27.000 --> 00:23:34.000 the oxygens, and the oxygens in the y-direction move away. And so you would preferentially populate 00:23:34.000 --> 00:23:39.000 this one electron goes into the DYZ orbital, mostly. 00:23:39.000 --> 00:23:46.000 And in the layer above, you have the opposite. Now you're preferentially populating the XC orbit. 00:23:46.000 --> 00:23:49.000 And so, when you think about the super exchange between the layers, 00:23:49.000 --> 00:23:52.000 It's this half-built, empty kind of super exchange 00:23:52.000 --> 00:23:55.000 which wants to give you a ferromagnet. 00:23:55.000 --> 00:24:01.000 So you have these kinds of interactions, which become now basically ferromagnetic super exchange. 00:24:01.000 --> 00:24:11.000 The reason what my colleagues tell me about the canting, though, is that comes from the strong spin order coupling. The strong spin orbit coupling 00:24:11.000 --> 00:24:14.000 Here you can see the L and the S. 00:24:14.000 --> 00:24:20.000 plays a role in why you get a canted structure, rather than a collinear ferromagnet. 00:24:20.000 --> 00:24:25.000 So that's… that's the basic idea of it. 00:24:25.000 --> 00:24:30.000 90 degree rotation? 00:24:30.000 --> 00:24:33.000 Well, it, uh… 00:24:33.000 --> 00:24:43.000 Would they… I mean, they're getting rid of your… They're getting something like this. I mean, it depends a little bit on what you put in for your parameters. What is the hopping parameter? What is the J? 00:24:43.000 --> 00:24:48.000 What are… okay, one of the things I didn't say, but is important, 00:24:48.000 --> 00:24:51.000 Why do we get this unusual kind of orbital ordering? 00:24:51.000 --> 00:24:54.000 Where we have… 00:24:54.000 --> 00:25:03.000 what the theory would say is that the orbital ordering is driven by the Coulombic repulsion between electrons in these 5D orbitals. And because the 5D orbitals 00:25:03.000 --> 00:25:11.000 have such a large spatial extent, they can feel each other, much more so than they could be if they were, you know, your small 3D orbits. 00:25:11.000 --> 00:25:16.000 And also, the theory and the experiment both say orbital ordering happens first. 00:25:16.000 --> 00:25:21.000 You do not get the magnetic ordering until you get the orbital ordering, and it happens at a lower temperature. 00:25:21.000 --> 00:25:24.000 And I think the orbital ordering would explain 00:25:24.000 --> 00:25:39.000 roughly why you have this 90-degree rotation, because basically the one orbital ordering is in the X direction, is related to the next one in the next layer that's in the Y direction, so the anisotropy tends to get rotated and become the anisotropy tensor. 00:25:39.000 --> 00:25:45.000 Yeah, that makes sense, that makes sense. And then next red layer, 00:25:45.000 --> 00:25:55.000 Okay, so many decisions. Well, these are parallel to each other. Yeah, yeah, yeah. That's right. The, um… I mean, the magnetic unit cell is only this big. 00:25:55.000 --> 00:26:08.000 So these are magnetically different, but the red ones are the same. They're related by translation symmetry. 00:26:08.000 --> 00:26:15.000 Okay, so then the last thing I want to say is, well, how, um, robust is this 00:26:15.000 --> 00:26:19.000 kind of state, and what happens if we were to… here we're just changing 00:26:19.000 --> 00:26:23.000 the diamagnetic cation. So let's take the barium out and put in a serum tune. 00:26:23.000 --> 00:26:30.000 And here, we're going to change barium and sodium for serontium and lithium. And this will reduce the tolerance factor. 00:26:30.000 --> 00:26:35.000 And then we're going to get, in both cases, these two compounds would get these rotations 00:26:35.000 --> 00:26:38.000 of the Octiva about the C-axis. 00:26:38.000 --> 00:26:41.000 As shown here. So we get this kind of A minus… 00:26:41.000 --> 00:26:48.000 may not, may not see mine as tilting, but the more important thing, probably, is now we get a distortion of the octahedron, 00:26:48.000 --> 00:26:53.000 Where the bonds in the Z direction are a little bit longer. It's not that much. 00:26:53.000 --> 00:26:56.000 0.03, .02 angstroms. 00:26:56.000 --> 00:26:59.000 longer than the bonds in the XY plane. 00:26:59.000 --> 00:27:05.000 But this happens, uh, this distortion happens above room temperature. 00:27:05.000 --> 00:27:08.000 But it changes magnetism totally. 00:27:08.000 --> 00:27:12.000 So, for the strontium lithium osmate, we see 00:27:12.000 --> 00:27:15.000 This kind of behavior we see at… 00:27:15.000 --> 00:27:20.000 a freezing temperature, we see a divergence between the field-cooled and the zero field-cooled. 00:27:20.000 --> 00:27:25.000 And we don't see anything in the specific heat, so we're assigning this some kind of 00:27:25.000 --> 00:27:32.000 glassy-like state. And this, uh, this compound, which this is work done in Japan, I want to point out, 00:27:32.000 --> 00:27:40.000 they see, um, they do see something in the specific heat, and so there's… they think that this is an anti-therromagnetic transition. 00:27:40.000 --> 00:27:47.000 Also, this happens at temperatures that are considerably higher. This is 55K and this is 30K. 00:27:47.000 --> 00:27:52.000 Sorry, in DC, also signatures of this orbital ordering in specific heat in the Stratwork? 00:27:52.000 --> 00:27:59.000 So, okay, I mean, yeah, let me go to the orbital, or I'll talk about that on the next slide. 00:27:59.000 --> 00:28:01.000 What I think… 00:28:01.000 --> 00:28:05.000 My explanation for what's happening here is because you've… 00:28:05.000 --> 00:28:17.000 Basically, you've reduced the tolerance factor, you've given the octahedron a little bit more room to distort, you might think. At any level, you have change to the symmetry so that these orbitals are no longer 00:28:17.000 --> 00:28:22.000 fully degenerate. And here, you could think about two kinds of distortions. We could… 00:28:22.000 --> 00:28:25.000 compress along the z-axis, 00:28:25.000 --> 00:28:27.000 Alright, that would give us this one… 00:28:27.000 --> 00:28:34.000 one down, two up distortion. This would be if Jan Teller considerations alone would predict this. 00:28:34.000 --> 00:28:40.000 Or, and this is what happens, we could elongate along the z-axis, which would give us this kind of filling. 00:28:40.000 --> 00:28:46.000 And now, you might say, why does this happen? But I think this happens because now we're retaining 00:28:46.000 --> 00:28:54.000 We don't totally quench the skin-orbit coupling. So the spin-orbit coupling itself favors this distortion over the other one. 00:28:54.000 --> 00:28:57.000 Any evidence was a lithium disorder? 00:28:57.000 --> 00:29:01.000 Uh, lithium disorder, you mean with opium? 00:29:01.000 --> 00:29:05.000 Yeah. We don't see all vacancies, or whatever. 00:29:05.000 --> 00:29:20.000 Yeah, it's good. Is it the best… is it the best trick? Well, it's a… it would be a heavy, expensive way to make a battery compound, I guess. No, no, but it's also spin glass, right? Oh, yeah, yeah, yeah, yeah, well… 00:29:20.000 --> 00:29:24.000 Yeah, I mean, okay, I mean, you know, when you're doing x-ray diffraction, 00:29:24.000 --> 00:29:28.000 Also, a neutron diffraction. Lithium's very light. I mean, that would… 00:29:28.000 --> 00:29:36.000 That would make Osmium plus 8, which it can reach, but that's a very high oxidation state. So, the answer is… 00:29:36.000 --> 00:29:42.000 I don't… I don't know for sure, but I don't see anything that would… I don't have any evidence for that. 00:29:42.000 --> 00:29:46.000 But if you do have this pattern, then, of orbital ordering, 00:29:46.000 --> 00:29:48.000 And, um… 00:29:48.000 --> 00:29:55.000 Mohit and Nandini, uh, and their student Wen Juan, did the theory about what happens if you distort the octahedron, 00:29:55.000 --> 00:29:58.000 If you elongate the octahedron, so now… 00:29:58.000 --> 00:30:01.000 The only orbitals of interest are the YZ and the XZ. 00:30:01.000 --> 00:30:07.000 Then you can turn on some spin orbit coupling, which splits them into 3 halves and one half, 00:30:07.000 --> 00:30:12.000 But you basically… the bottom line is that you have these half-filled 00:30:12.000 --> 00:30:14.000 Y, Z, and XZ orbitals, and that… 00:30:14.000 --> 00:30:19.000 then tends to give you anti-ferromagnetic super-exchange, and so you get 00:30:19.000 --> 00:30:26.000 basically the Type 1 structure, with ferromagnetic layers coupled to antiferromagnetically to each other. That's what the theory would say. 00:30:26.000 --> 00:30:32.000 This is presumably what the barium, or the strontium-magnesium-henium is doing. 00:30:32.000 --> 00:30:35.000 Why the lithium compound forms a spin glass, 00:30:35.000 --> 00:30:41.000 Well, I mean, it probably does come down to some kind of disorder that we're not detecting, I suppose, but we don't know that. 00:30:41.000 --> 00:30:45.000 That's speculation on my part. 00:30:45.000 --> 00:30:47.000 So, I think, you know, 00:30:47.000 --> 00:30:54.000 Ah, this is the final thing. So the question is, of course, we don't know anything about the magnetic structure because 00:30:54.000 --> 00:30:57.000 Basically, none… nobody has ever seen 00:30:57.000 --> 00:31:05.000 any magnetic scattering in neutron diffraction. And so, this was actually data that was collected by 00:31:05.000 --> 00:31:10.000 John Green and Bruce Galen, and I got to talking to them, and we kind of worked together, but 00:31:10.000 --> 00:31:12.000 This is, uh… 00:31:12.000 --> 00:31:14.000 this compound, and… 00:31:14.000 --> 00:31:24.000 It's going to be at… this is at D20 at ILL, so it's a kind of rather large sample, I think, and this is a very high-intensity beamline. And here are some places… 00:31:24.000 --> 00:31:27.000 Where there ought to be 00:31:27.000 --> 00:31:29.000 magnetic brag scattering. 00:31:29.000 --> 00:31:33.000 If it was the magnetic structure that we think. And so, 00:31:33.000 --> 00:31:35.000 If you subtract 30… 00:31:35.000 --> 00:31:40.000 the 1.5K data from the 30K data, or vice versa, I guess. 00:31:40.000 --> 00:31:48.000 Um, here's where the magnetic reflections ought to be. This is how strong they ought to be if the moment was 0.4 mu v, which is, um… 00:31:48.000 --> 00:31:53.000 what it works out. Probably would be less than that. It probably would be something like 0.2 Nuv. 00:31:53.000 --> 00:31:59.000 There's absolutely no magnetic scattering there that we can see. The question is, 00:31:59.000 --> 00:32:05.000 Is that just because the moment is so small, we can't see it? But another possible explanation is that… 00:32:05.000 --> 00:32:12.000 If it were… um, and this is what both John and Bruce think it is, if it were a magnetic octopole, 00:32:12.000 --> 00:32:18.000 then the form factor is very different than a magnetic dipole, and then it would be even much harder to see, and you wouldn't expect 00:32:18.000 --> 00:32:26.000 To see these things. So I think it's really kind of still an open question.romagnetic octopus? 00:32:26.000 --> 00:32:30.000 You can… okay, so I think you can have ferro octopolar ordering. 00:32:30.000 --> 00:32:37.000 Um, if I'm not… but rather magnet. Yeah, because you really do. 00:32:37.000 --> 00:32:40.000 Oh, you don't. 00:32:40.000 --> 00:32:44.000 That's it. 00:32:44.000 --> 00:32:46.000 Yes, this is the magnesium compound. I mean… 00:32:46.000 --> 00:32:51.000 This is somewhat speculative, and I… I mean, a simpler explanation is just that 00:32:51.000 --> 00:32:56.000 Because of the strong covalency and the small moment in the spin-orbit coupling, it's just really hard to see, but… 00:32:56.000 --> 00:33:00.000 This is probably… I don't know, if you can't see it here, it can be… 00:33:00.000 --> 00:33:04.000 Pretty hard to see, uh, anywhere. 00:33:04.000 --> 00:33:07.000 At that barrel moment. 00:33:07.000 --> 00:33:10.000 shows ferro component? 00:33:10.000 --> 00:33:14.000 No, in the neutrons, you can't see anything from them. There's no difference. I mean, this would be… 00:33:14.000 --> 00:33:19.000 Well, whether… oh, even if you… okay, if you looked at the nuclear peaks… 00:33:19.000 --> 00:33:25.000 You don't really… I mean, if you refine it with a pharaoh or with no magnetism at all, it's basically the same. 00:33:25.000 --> 00:33:29.000 So you don't… it's not big enough to pick up. 00:33:29.000 --> 00:33:34.000 Why did they not suggest magnetic quadrupole? 00:33:34.000 --> 00:33:39.000 It jumped to Octopold? Yeah, uh… 00:33:39.000 --> 00:33:44.000 I think that's inconsistent with… 00:33:44.000 --> 00:33:49.000 symmetry is the fact that there's cubic symmetry, I think. Is inversion symmetric? 00:33:49.000 --> 00:33:54.000 I mean, the space group here is still, uh… 00:33:54.000 --> 00:34:03.000 Well, we don't know. I mean, the nuclear structure is, yeah, it's FM3 barM. It's got inversion symmetry. We don't know the magnetic structure, so I don't… I can't comment on what… 00:34:03.000 --> 00:34:06.000 If the magnetism would change the symmetry, yeah. 00:34:06.000 --> 00:34:12.000 If it retains inversion symmetry, then it can be heroic quadruples. 00:34:12.000 --> 00:34:18.000 That was the reason why we didn't do quadrupulse, because we're assuming that the symmetry is still too big, yeah. Okay, yeah. 00:34:18.000 --> 00:34:25.000 So, to just show tight where I am… It's, uh, yeah, I did, uh… 00:34:25.000 --> 00:34:37.000 It's basically looks ferromagnetic like the others. Could I just ask… Yeah, yeah, yeah, let me, uh… 00:34:37.000 --> 00:34:43.000 So, if you applied pressure, if you applied… 00:34:43.000 --> 00:34:48.000 uniaxial pressure, then it should… if it is optical, then it should go quadrupole. 00:34:48.000 --> 00:34:59.000 And then you should see a nonlinear system. Yes. I mean, if it is Dr. Paul, then applying pressure would bring it down to the pool. 00:34:59.000 --> 00:35:05.000 We've reduced it to wonderful. Yeah, nonlinear susceptibility. Yeah, yeah, it's been done on hard nodes, exactly the way… 00:35:05.000 --> 00:35:10.000 I mean, that's a good suggestion. It's a very hard experiment to do. 00:35:10.000 --> 00:35:14.000 Osmium is pretty volatile, so single crystal growth is… 00:35:14.000 --> 00:35:28.000 is a non-trivial kind of exercise. Also, it's highly toxic, which is another thing that makes people, uh, not so crazy about growing single crystals out of it. But, I mean, that's a… that is a good suggestion. 00:35:28.000 --> 00:35:33.000 Okay, well, I mean, I think this… the summary, then, on this, uh… 00:35:33.000 --> 00:35:38.000 First bit of the talk is… sorry, right here… is just… 00:35:38.000 --> 00:35:48.000 what we're seeing in the 5D1 system, I would say, boils down to the following points, that you have Coulomb repulsions between these electrons in the 5D orbitals that drives 00:35:48.000 --> 00:35:50.000 an orbital order. 00:35:50.000 --> 00:35:53.000 Actually, in the literature, it's generally called 00:35:53.000 --> 00:35:55.000 uh, they call it a quadrupolder. 00:35:55.000 --> 00:36:00.000 electric quadrupolar ordering, but I would just call it an orbital ordering. 00:36:00.000 --> 00:36:04.000 And then once that happens, at some temperature not too far below that, maybe… 00:36:04.000 --> 00:36:07.000 It's about 10 degrees below that, then you see… 00:36:07.000 --> 00:36:10.000 Uh, this magnetic order. 00:36:10.000 --> 00:36:14.000 Which, um, is largely probably thought to be these 00:36:14.000 --> 00:36:17.000 ferromagnetic layers canted with respect to one another. 00:36:17.000 --> 00:36:22.000 And, you know, basically this super exchange interactions 00:36:22.000 --> 00:36:35.000 The strong spin orb coupling the anisotropy, or basically the explanation for that structure, but it's pretty fragile, because if I even put a little tilt in there, and I change the orbital order in a way that took that totally 00:36:35.000 --> 00:36:39.000 This never happens. Then we just go into something that would be 00:36:39.000 --> 00:36:45.000 I'd say a more conventional anti-ferromagnet. 00:36:45.000 --> 00:36:52.000 Okay, well, let's see… we'll see how far we get. But now I want to shift gears a little bit, and I want to talk about… 00:36:52.000 --> 00:36:57.000 hexagonal curve, right? And this is largely the work of two of my graduate students, 00:36:57.000 --> 00:37:00.000 David and Sierra. 00:37:00.000 --> 00:37:07.000 So, just… some people will know this already, but just to remind you, what do I mean when I say hexagonal perovskite? If we think about… 00:37:07.000 --> 00:37:13.000 cubic perovskites, you know, you can think about the cubic perovskite as a close packing, 00:37:13.000 --> 00:37:16.000 of AX3… 00:37:16.000 --> 00:37:20.000 AO3 layers, and then you put the, um… 00:37:20.000 --> 00:37:22.000 a small cation, like your titanium, 00:37:22.000 --> 00:37:26.000 in the octahedral holes that don't have 00:37:26.000 --> 00:37:29.000 a cation nearby. 00:37:29.000 --> 00:37:36.000 And if you were to think about the stacking of these AO3 layers, it would be ABC, ABC, ABC, ABC. So it's a cubic close time. 00:37:36.000 --> 00:37:39.000 But, you could… 00:37:39.000 --> 00:37:41.000 Instead, do… 00:37:41.000 --> 00:37:44.000 A B, A, B, A, B packing. 00:37:44.000 --> 00:37:47.000 you know, hexagonal closed packing of these layers. 00:37:47.000 --> 00:37:51.000 And then, the octetro holes that are available 00:37:51.000 --> 00:37:54.000 give you a different topology where you have infinite 00:37:54.000 --> 00:37:59.000 one-dimensional columns of face-sharing octahedra. 00:37:59.000 --> 00:38:02.000 Then, you have, uh… 00:38:02.000 --> 00:38:06.000 Just like you get if you look at metals, if you look at the lanthanide metals, 00:38:06.000 --> 00:38:14.000 You know, you get mixed hexagonal cubic packing, and that happens here in the hexagonal perovskites. 00:38:14.000 --> 00:38:25.000 Where you can get, for example, if you have A, B, AC repeating packing, then you get this structure called the 4-H structure, because there's four layers, and the symmetry's hexagonal. 00:38:25.000 --> 00:38:29.000 or six layers, or 9 layers, or 12 layers. You can get up… there's a whole… 00:38:29.000 --> 00:38:32.000 family of these compounds. 00:38:32.000 --> 00:38:37.000 And largely, what stabilizes these compounds is the fact that you're 00:38:37.000 --> 00:38:43.000 group cation here is too big, so to the tolerance factor is bigger than 1, and to give it a little bit more room, 00:38:43.000 --> 00:38:46.000 you end up getting this, um, face sharing. 00:38:46.000 --> 00:38:55.000 So, but for us, or for me anyway, what was interesting here is to think about, okay, if we put these metals in close proximity with one another, 00:38:55.000 --> 00:38:59.000 Can we get, let's say, are we going to get bonds between the meds? 00:38:59.000 --> 00:39:04.000 I have what's going to be the nature of the magnetic interaction through these shared faces. 00:39:04.000 --> 00:39:08.000 Can we, um, maybe think of this whole thing like, uh, 00:39:08.000 --> 00:39:21.000 like a cluster. So David Pomsky used to refer to these compounds as molecules and solids, right? Can we make something where we have this molecular-like cluster, but that is arranged with the kind of symmetry 00:39:21.000 --> 00:39:24.000 of, uh… of a crystal. 00:39:24.000 --> 00:39:30.000 And of course, the symmetry that you get is kind of interesting in the sense that whether you talk about these layers, 00:39:30.000 --> 00:39:32.000 or whether you're talking about these clusters, 00:39:32.000 --> 00:39:34.000 They're both on, uh… 00:39:34.000 --> 00:39:40.000 A crystallographer wouldn't call them a triangular lattice, but a physicist probably would. So, I mean, where every, every… 00:39:40.000 --> 00:39:48.000 cluster has, you know, 6 clusters near it, and so this is going to be another frustrated topology, right? 00:39:48.000 --> 00:39:51.000 Okay, so we want to understand 00:39:51.000 --> 00:39:57.000 this, and when we have structures like this, we have an additional tuning knob, in that we can 00:39:57.000 --> 00:40:01.000 If we put dynamic cations here, 00:40:01.000 --> 00:40:06.000 You can magnetically try to isolate the clusters, and therefore accentuate 00:40:06.000 --> 00:40:10.000 them as molecules, and also accentuate the 2D 00:40:10.000 --> 00:40:12.000 Uh, triangular lats. 00:40:12.000 --> 00:40:20.000 Whereas if we put magnetic ions here, then we can have actually strong coupling between the layers. And I'll show you examples of both. 00:40:20.000 --> 00:40:27.000 So, before we go too far down the road, and here I'm gonna… for a little bit, we're gonna talk about chlorides rather than oxides. 00:40:27.000 --> 00:40:32.000 I want to just talk about two compounds from the literature that are 00:40:32.000 --> 00:40:36.000 Vacancy ordered 6H bioska, so that… 00:40:36.000 --> 00:40:41.000 That ion that was… that octahedron that was just sharing corners is gone here because we've left this vacant. 00:40:41.000 --> 00:40:43.000 So here we have two… 00:40:43.000 --> 00:40:48.000 Chromium 3 plus ions, or these are iron, iron 3 plus, and here's 2. 00:40:48.000 --> 00:40:51.000 Chromium 3 plus ions, and then… 00:40:51.000 --> 00:40:53.000 you know, we might think about 00:40:53.000 --> 00:40:59.000 If we look at the structure, the first question as a chemist I might ask is, what is the nature of the interaction between the metals? 00:40:59.000 --> 00:41:03.000 But here, because Chromium is pretty large, 00:41:03.000 --> 00:41:07.000 The distance, the chromium-chromium, or iron-iron distance, is 00:41:07.000 --> 00:41:09.000 well over 3 angstroms, whereas in 00:41:09.000 --> 00:41:13.000 Iron metal or chromium metal, it's about 2.5 angstroms, so… 00:41:13.000 --> 00:41:15.000 I think there's gonna be… 00:41:15.000 --> 00:41:17.000 Not nearly enough. 00:41:17.000 --> 00:41:21.000 orbital overlap to form something like a bond here. 00:41:21.000 --> 00:41:25.000 But, that doesn't mean that the magnetic coupling between the two 00:41:25.000 --> 00:41:27.000 might be, um… 00:41:27.000 --> 00:41:31.000 No, it could… it is still significant, I would say. 00:41:31.000 --> 00:41:35.000 And then the interesting thing when you look at these two compounds, when you look at their magnetism, 00:41:35.000 --> 00:41:37.000 is that they're very different. 00:41:37.000 --> 00:41:41.000 So the chromium compound, you have a magnetism that 00:41:41.000 --> 00:41:47.000 Uh, and when you get to low temperature, it basically plummets towards diamagnetism, and this is… 00:41:47.000 --> 00:41:57.000 Back to B, because you're forming a spin dimer. So you're getting, within that cluster, the spins are strongly coupled to anti-ferromagnetic to each other, and that makes the cluster basically 00:41:57.000 --> 00:41:59.000 Uh, diamagnetic, or at least… 00:41:59.000 --> 00:42:04.000 strongly anti-ferromagnetic. Do you see a large C versus AB on isotropy, so… 00:42:04.000 --> 00:42:07.000 So this measurement, for example, where's the field? 00:42:07.000 --> 00:42:10.000 Yeah, I mean, they don't magnetically order, uh… 00:42:10.000 --> 00:42:14.000 But this is the stability visit. Yeah, that's… 00:42:14.000 --> 00:42:19.000 Yeah, uh… I don't know the answer to that. This is… 00:42:19.000 --> 00:42:23.000 Yeah, that's a good point. I don't know the answer yet, it's short. 00:42:23.000 --> 00:42:26.000 Um, whereas if we look at the iron compound, 00:42:26.000 --> 00:42:30.000 What we see is, you know, that looks like pretty conventional 00:42:30.000 --> 00:42:33.000 to revise kind of magnetism, um, 00:42:33.000 --> 00:42:38.000 And then this one actually magnetically orders at 5.5 Kelvin. 00:42:38.000 --> 00:42:42.000 And, um, actually has a very interesting 00:42:42.000 --> 00:42:50.000 magnetic phase diagram as a function of temperature and field. This is from this, uh, relatively recent paper from Japan. 00:42:50.000 --> 00:42:57.000 And so here, it's known both from analysis of the susceptibility of single crystals, 00:42:57.000 --> 00:43:04.000 As well as, um, looking at the magnetic structure that the irons within the dimer are coupling ferromagnetically to each other. 00:43:04.000 --> 00:43:11.000 Okay, so here we have ferromagnetic coupling within the dimer, and here we have anti-therromagnetic coupling. 00:43:11.000 --> 00:43:14.000 And, you know, the reason for that 00:43:14.000 --> 00:43:21.000 is because we have two competing kinds of exchange interactions going on here. 00:43:21.000 --> 00:43:29.000 Um, you renormalize the d orbitals in this symmetry, and you end up getting something like the DZ squared orbitals point in this way, and so you can absolutely get 00:43:29.000 --> 00:43:36.000 direct exchange, and for both D3, D3, and D5, D5, that's going to be anti-theromagnetic. 00:43:36.000 --> 00:43:43.000 You also have this bond angle is about 80 degrees, so we're going to use 90 degrees super exchange rules here. 00:43:43.000 --> 00:43:49.000 And the 90 degree super exchange, whether it's V3, V3, or D5, V5, is ferromagnetic. 00:43:49.000 --> 00:43:55.000 But apparently, what's important is the super exchange is a lot stronger for D5 than it is for D3, 00:43:55.000 --> 00:44:00.000 And so this wins out in the iron case, and this wins out 00:44:00.000 --> 00:44:04.000 in the chromosome case. 00:44:04.000 --> 00:44:07.000 So, I don't know. 00:44:07.000 --> 00:44:09.000 My student David was working on 00:44:09.000 --> 00:44:13.000 he was working on halides, and we kind of got into this area. 00:44:13.000 --> 00:44:16.000 And, you know, he first made this compound. 00:44:16.000 --> 00:44:19.000 So, this compound, it's kind of related to this one. 00:44:19.000 --> 00:44:26.000 But what we have here is we've… he's put a manganese 2 plus and an iron 3 plus in here, so the charge is only 5. 00:44:26.000 --> 00:44:31.000 And then that's charge compensated because we have sodium going into this later. 00:44:31.000 --> 00:44:34.000 And after he did that, I said, well… 00:44:34.000 --> 00:44:37.000 It would be interesting if this could be iron 2 and Iron 3. 00:44:37.000 --> 00:44:44.000 Because then we would have a mixed valency. And so then, with a little bit of effort, he was able to 00:44:44.000 --> 00:44:46.000 grow crystals, uh, where we had that. 00:44:46.000 --> 00:44:50.000 So here we have iron 2.5. 00:44:50.000 --> 00:44:54.000 And in these compounds, you know, 00:44:54.000 --> 00:44:59.000 I feel the metals are pretty far apart, although I will say this… this… 00:44:59.000 --> 00:45:05.000 term right here is that if the metal stayed right in the center of its octahedron, this would be 1. 00:45:05.000 --> 00:45:12.000 And so as it gets bigger than 1, it tells you that the metal is shifting away from the shared face, and if it gets less than one, shifting toward the shared face. 00:45:12.000 --> 00:45:22.000 So the one thing I can say is they're all shipping away, but not quite so far in this compound as the other two. 00:45:22.000 --> 00:45:28.000 So, what about the magnetism? Well, I mean, at one level, you might say the magnetism isn't that interesting, because 00:45:28.000 --> 00:45:30.000 There, um… 00:45:30.000 --> 00:45:36.000 At least down to pretty low temperatures, there's not, uh… well, this one orders at 5 Kelvin. 00:45:36.000 --> 00:45:39.000 This one, we don't think… 00:45:39.000 --> 00:45:43.000 It's hard to say what's happening. I don't really understand what's happening here, but maybe… 00:45:43.000 --> 00:45:47.000 Maybe there's some impurity giving a curry tail here, and there's some other… 00:45:47.000 --> 00:45:49.000 something else happening here. 00:45:49.000 --> 00:45:52.000 Um, this one probably does… 00:45:52.000 --> 00:45:56.000 You'd think it maybe orders at between 2 and 3 Kelvin, but we only measure down. 00:45:56.000 --> 00:46:02.000 to Kelvin. But what's interesting to me is if we extract the… 00:46:02.000 --> 00:46:05.000 device temperature out, what we see is that 00:46:05.000 --> 00:46:10.000 This one here, which has the mixed valent iron, it has positive 00:46:10.000 --> 00:46:13.000 Base temperature. So it's telling us that. 00:46:13.000 --> 00:46:17.000 of all the interactions in this, this one is the only one where we have 00:46:17.000 --> 00:46:25.000 net ferromagnetic interactions, and the other two are anti-ferromagnetic. And in fact, in this family, this is the only one I know of that has 00:46:25.000 --> 00:46:27.000 this positive ice temperature. 00:46:27.000 --> 00:46:29.000 Why is a good question? Yes, yes, of course. 00:46:29.000 --> 00:46:38.000 On the compound on the very left, where you have TN is less than 2K, if you looked at fuel-cooled versus zero-fuel-cooled? 00:46:38.000 --> 00:46:47.000 Uh, yes, yes, yes, that's… oh, it's there. Okay, I didn't… Yeah, they're… I think they're just basically right on top of each other. Oh, they're on top of each other? Oh, no! 00:46:47.000 --> 00:46:51.000 Oh, wait a minute. This… my student did this plot, let's see. 00:46:51.000 --> 00:46:56.000 Uh, yeah, and I guess they're both… no, this is not labeled right, I don't think, because… 00:46:56.000 --> 00:47:11.000 Unless it… if it is that right on top of each other. Well, I was thinking of the one all the way to the left, with TN less than… This one here? Oh, all the way. Yeah, yeah, okay, this one, yes. And so I was wondering if you've looked at two cool verses 00:47:11.000 --> 00:47:24.000 I'm pretty sure, I'm pretty sure we don't… we don't see any, we don't see any divergence between the field-cooled and the zero field cooled, if I remember correctly. I mean, I think they're… I think they're both plotted here. 00:47:24.000 --> 00:47:41.000 But, well, but these symbols don't look right, because one of them… They do, they do. He's in the back. I guess it's just right on top. I think they're right on top of each other. Well, I can't see it even from here, so no need to apologize. Okay, so they're actually on top of each other. I wasn't sure. 00:47:41.000 --> 00:47:46.000 Yeah, yes, yes. 00:47:46.000 --> 00:47:53.000 So, I mean, the question is what's happening in this mixed valent iron compound, but because it's iron, we can do a Musbauer spectroscopy. 00:47:53.000 --> 00:47:57.000 And that's pretty interesting. So… 00:47:57.000 --> 00:47:59.000 Depending on what you see, let's start at low temperature. 00:47:59.000 --> 00:48:02.000 So if we look at 4 Kelvin… 00:48:02.000 --> 00:48:13.000 First of all, we see the MOS power lines here still… we don't see a sextet, but there's quite a bit of broadening compared to 50 Kelvin, so we think that we are getting pretty close to the magnetic order in temperature. 00:48:13.000 --> 00:48:16.000 But if you look at the cyan and the green lines, 00:48:16.000 --> 00:48:18.000 What we see is, basically, 00:48:18.000 --> 00:48:21.000 Um, you can fit it… this is 50 Kelvin. 00:48:21.000 --> 00:48:25.000 Okay, we can fit it to a 1 to 1 ratio of iron to 00:48:25.000 --> 00:48:31.000 and iron-3. But as we warm up, by the time we get to 100 Kelvin, 00:48:31.000 --> 00:48:38.000 See, here's your Iron 2, and here's your Iron 3. Those have become only, um, let's see, what are we estimating? 00:48:38.000 --> 00:48:40.000 About 17% of the signal 00:48:40.000 --> 00:48:43.000 But most of the signal now is this 00:48:43.000 --> 00:48:48.000 Intermediate spin, uh, or not spin, but oxidation state, which 00:48:48.000 --> 00:48:53.000 all of its characteristics are characteristic of iron 2.5. 00:48:53.000 --> 00:48:55.000 So the picture is that 00:48:55.000 --> 00:48:58.000 As you want… yeah, at low temperatures, you have 00:48:58.000 --> 00:49:00.000 Iron 2, and Iron 3. 00:49:00.000 --> 00:49:08.000 But as you warm up, on the MOSF hour timescale, actually, these two, there's an electron that's going back and forth between them, 00:49:08.000 --> 00:49:13.000 fast enough on the miles per hour timescale that they look like the same kind of iron. 00:49:13.000 --> 00:49:16.000 Okay, and so… so then… 00:49:16.000 --> 00:49:19.000 What would that be that's happening? 00:49:19.000 --> 00:49:22.000 I mean, the idea is this, if you have… 00:49:22.000 --> 00:49:25.000 Iron 2, and iron 3… 00:49:25.000 --> 00:49:29.000 And this one electron, I mean, this one electron is basically 00:49:29.000 --> 00:49:33.000 Hopping back and forth between the two iron centers. 00:49:33.000 --> 00:49:36.000 Um, as this scintillating animation shows, 00:49:36.000 --> 00:49:41.000 And, um, and that's also why they're ferromagnetically coupled, because the only way it can hop. 00:49:41.000 --> 00:49:45.000 between the two is if they have ferromagnetic alignment. So… 00:49:45.000 --> 00:49:48.000 you know, I would call this, um, basically, 00:49:48.000 --> 00:49:56.000 like a zero-dimensional double exchange. So within the dimer, we have a double exchange hopping, even though the irons are, you know, they're over 3 angstroms apart. 00:49:56.000 --> 00:49:59.000 So, they might not be bonding, but there's rapid… 00:49:59.000 --> 00:50:08.000 Probably, you know, mixed valency going on between the irons here. 00:50:08.000 --> 00:50:15.000 Now, what happens if we were to go to oxides, um, and we're… once again, here, we still want to keep 00:50:15.000 --> 00:50:23.000 these things, uh, isolated from one another. So now what we're doing is we're putting now… this is chromium here, chromium-3. 00:50:23.000 --> 00:50:26.000 And then we're putting molybdenum 00:50:26.000 --> 00:50:28.000 molybdenum 6 into these… 00:50:28.000 --> 00:50:37.000 spots here. And so both with x-ray and neutron diffraction, we get occupancies which are basically no anti-asite disorder, but keep in mind, 00:50:37.000 --> 00:50:43.000 There are a few… the error bars are a few percent. So there could be a little bit of anti-site disorder, but we don't think… 00:50:43.000 --> 00:50:47.000 That is very significant. 00:50:47.000 --> 00:50:49.000 So what's the magnetism like now? 00:50:49.000 --> 00:50:59.000 Sorry, I interced between what Chromium and molybdenum? Chromium and molybdenum, yeah. I guess I should say a little bit what's… well, let me say a little bit about the structure before we move on. 00:50:59.000 --> 00:51:05.000 The main thing that you see is that when you go to an oxide, because oxygen's much smaller, and chloride, 00:51:05.000 --> 00:51:11.000 Now, our chromium-chromium distance is 2.45 angstroms, much, much shorter. 00:51:11.000 --> 00:51:17.000 of course, it's shorter, I don't know if this is a good point of comparison, but shorter than it is in chromium metal itself. 00:51:17.000 --> 00:51:19.000 And that's, let's say, unlike… 00:51:19.000 --> 00:51:21.000 Chromium-203, 00:51:21.000 --> 00:51:25.000 Where, um, I mean… 00:51:25.000 --> 00:51:31.000 you… when you put… when the two octahedra share a common face, then the metals are going to be close to each other. There's just no way around it. 00:51:31.000 --> 00:51:37.000 But you can see here that the chromiums are trying to get as far apart from each other as they have. 00:51:37.000 --> 00:51:42.000 This parameter is up to 1.4, this is significantly elongated, so… 00:51:42.000 --> 00:51:44.000 You know, I'm not saying that we're getting 00:51:44.000 --> 00:51:47.000 short enough to say there's a bond here, but certainly… 00:51:47.000 --> 00:51:56.000 they're… they're pretty close… close enough to interact in a way that would be more significant than in the halides. 00:51:56.000 --> 00:52:05.000 And then you have this picture, which has been known for a long time, about if we take the T2G orbitals and renormalize things, we can have a sigma bond, 00:52:05.000 --> 00:52:08.000 Looks like this, we can have a sigma antibond that looks like that. 00:52:08.000 --> 00:52:11.000 We can have two things that look like a pie. 00:52:11.000 --> 00:52:18.000 And a anti-bonding orbitals from these other linear combinations of the DA work. 00:52:18.000 --> 00:52:22.000 So, if you're in this picture, you know, 00:52:22.000 --> 00:52:27.000 And you put in, let's say, you know, the electrons, you might get a very different kind of magnetism than if you're in 00:52:27.000 --> 00:52:32.000 just thinking about 2 chromium 3 plus signs. 00:52:32.000 --> 00:52:34.000 The magnetism here… 00:52:34.000 --> 00:52:36.000 looks like… 00:52:36.000 --> 00:52:40.000 I mean, when you first look at it, you're like, okay, that looks… 00:52:40.000 --> 00:52:43.000 That looks normal, but in fact, when you plot the 1 over 00:52:43.000 --> 00:52:46.000 Kai, it doesn't look normal at all, right? I mean, this is, uh… 00:52:46.000 --> 00:52:49.000 This is not Curie Weiss-like. 00:52:49.000 --> 00:52:54.000 paramagnetism, if you plot chi-T, right, which would be just a straight line, 00:52:54.000 --> 00:52:57.000 for a perfect curate, uh… 00:52:57.000 --> 00:53:02.000 pure behavior, but instead it's going to zero. So we're definitely getting this kind of 00:53:02.000 --> 00:53:07.000 temperature-dependent effective moment, which is indicative of forming a kind of a spin dimer. 00:53:07.000 --> 00:53:12.000 And you can model that with, um, something called the Heisenberg-Dirac-N-Blecht 00:53:12.000 --> 00:53:19.000 a behavior, and so that's… that's what we're doing here. We collect a susceptibility out to 700 elkins. 00:53:19.000 --> 00:53:22.000 I still think maybe… maybe we could… 00:53:22.000 --> 00:53:26.000 This modeling is a little bit tricky, but what we're getting out of this is, uh… 00:53:26.000 --> 00:53:30.000 is a J value of 308 Kelvin anti-therromagnetic. 00:53:30.000 --> 00:53:35.000 Um, versus in this… in this case, it was 17. 00:53:35.000 --> 00:53:38.000 Is there anything happening in specific heat? 00:53:38.000 --> 00:53:41.000 Simultaneously. We haven't… we haven't measured that yet. 00:53:41.000 --> 00:53:50.000 That's a good… I don't… yeah, we haven't measured… we have not measured, although I don't see any sign abruptly of some kind of phase transition. 00:53:50.000 --> 00:53:56.000 We have measured variable temperature diffraction, and we don't see anything. 00:53:56.000 --> 00:54:02.000 Uh, this just shows… so, okay, so one of the things that may be a little bit confusing, if you really just had 00:54:02.000 --> 00:54:07.000 spin dimers, and you, you know, this is the kind of behavior you want to get from 00:54:07.000 --> 00:54:10.000 this, uh, this kind of a… 00:54:10.000 --> 00:54:13.000 splitting of energies. Um… 00:54:13.000 --> 00:54:15.000 We obviously have… 00:54:15.000 --> 00:54:20.000 curry tail at low temperature. We have a pretty big carried tail at low temperatures. 00:54:20.000 --> 00:54:25.000 And the question of where that comes from is, you know, I mean, it could just be anti-psych disorder, although 00:54:25.000 --> 00:54:30.000 In our neutron and X-ray diffraction, we don't see it, but, um… 00:54:30.000 --> 00:54:37.000 Yeah, well, we're still trying to understand this, but the bottom line is that you have kind of a spin dimer behavior here, and you have pretty strong coupling 00:54:37.000 --> 00:54:40.000 between the chromium atoms across that. 00:54:40.000 --> 00:54:42.000 face. So… 00:54:42.000 --> 00:54:46.000 how I'm given out time, probably not well. I mean, ah, it's about this group. 00:54:46.000 --> 00:54:51.000 Okay, I'm going to talk a little bit now about what we're going to do, though. I mean, ultimately… 00:54:51.000 --> 00:54:58.000 having something where the spins coupling goes diamagnetic at low temperature, it's only so interesting, right? So, not… 00:54:58.000 --> 00:55:00.000 Not that much use for it, but… 00:55:00.000 --> 00:55:04.000 Uh, you know, the thought would be, what happens if we… 00:55:04.000 --> 00:55:12.000 put in some magnetic ions in these sites, right? And so, in this part of the talk, I'm going to talk about 00:55:12.000 --> 00:55:18.000 basically hexagonal double perovski, and so we're going to have ordering of the octhedral cations, and 00:55:18.000 --> 00:55:23.000 When you do that, let me just say that sometimes you can have an ordering that's kind of 00:55:23.000 --> 00:55:25.000 natural or commensurate with 00:55:25.000 --> 00:55:30.000 The way that the octheedra are. So it doesn't change the symmetry. 00:55:30.000 --> 00:55:33.000 But then, I'll show you some other examples. Well, maybe one or two. 00:55:33.000 --> 00:55:36.000 Where we have a kind of symmetry 00:55:36.000 --> 00:55:41.000 The ordering actually changes the symmetry of the structure. And so, 00:55:41.000 --> 00:55:45.000 you know, that might be interesting if you're looking for 00:55:45.000 --> 00:55:49.000 Ultra Magnets, or you're looking for, uh, some kind of… 00:55:49.000 --> 00:55:54.000 Magnetoelectric coupling. Your 6H structure, is that a typical… 00:55:54.000 --> 00:56:02.000 Post for ultramagnetists. Is that right? It's like a G-Wave Ultramagnet. Okay, okay. 00:56:02.000 --> 00:56:14.000 made bespoke. All right, well, we hope you could… Yeah, okay, okay, that's good to know, because we definitely have, uh, definitely have some magnetic ordering in that structure, and that's, that's kind of where I'm going to go first. 00:56:14.000 --> 00:56:18.000 What we're going to do here, remember I talked about Chromium-2 molybdenum 1. 00:56:18.000 --> 00:56:23.000 Let's just change… replace the molybdenum with a rhenium-6. 00:56:23.000 --> 00:56:26.000 Okay, so Rhenium-6 is a D1. 00:56:26.000 --> 00:56:30.000 So we're trying to get the same structure, just with a magnetic ion here now. 00:56:30.000 --> 00:56:33.000 And in this case, we definitely do have 00:56:33.000 --> 00:56:37.000 some anti-psych disorder. So it's about 14% 00:56:37.000 --> 00:56:39.000 Uh… 00:56:39.000 --> 00:56:45.000 Chromium goes here, and that means that that amount of rhenium has to go here. 00:56:45.000 --> 00:56:49.000 But the symmetry is still P63 over NMC. 00:56:49.000 --> 00:57:01.000 And, uh, you know, the chromium… the distance is here, and the chromium-chromium distance actually doesn't change that much. It's a little different, but not that different. 00:57:01.000 --> 00:57:04.000 Oh, that's shown here. Anyway, bottom line is, it goes from… 00:57:04.000 --> 00:57:10.000 2.45 to 2.54, so it may be a little weaker. 00:57:10.000 --> 00:57:17.000 But it's still relatively close to each other. But the real question is, what's the magnetism look like? 00:57:17.000 --> 00:57:20.000 Okay, so now we get, um… 00:57:20.000 --> 00:57:25.000 We do get magnetism. Actually, the magnet… there are two magnetic transitions. 00:57:25.000 --> 00:57:32.000 It initially magnetically orders at 290 Kelvin. I don't have it here, but that assignment's based on 00:57:32.000 --> 00:57:34.000 Um, specific heat measurements. 00:57:34.000 --> 00:57:46.000 Um, and the magnetic structure, okay, so why are there two magnetic transitions? There's two magnetic transitions because at 290K, the ordering is such that the moments are pointing along C. 00:57:46.000 --> 00:57:49.000 And then a 230 Kelvin, 00:57:49.000 --> 00:57:52.000 we get a spin reorientation, 00:57:52.000 --> 00:58:02.000 Where the moment's now reorient in the AV plan. This is actually like, um, something called the Morin transition that happens in FE203. 00:58:02.000 --> 00:58:07.000 But the super… the exchange coupling we can understand pretty well, because in this… 00:58:07.000 --> 00:58:13.000 Dimer, now we have anti-therromagnetic coupling between chromiums. And so this is… 00:58:13.000 --> 00:58:16.000 Teutron diffraction magnetic structure, there's no doubt about this. 00:58:16.000 --> 00:58:22.000 And that means that the direct exchange is definitely stronger than the super exchange. 00:58:22.000 --> 00:58:26.000 And you are sure that there's no finite cube? 00:58:26.000 --> 00:58:32.000 You mean that it's commensurate with the line? I mean, we don't see anything that would make us think it's incommensurate, yeah. 00:58:32.000 --> 00:58:35.000 Um, and in fact, the Q vector here is 000. 00:58:35.000 --> 00:58:42.000 Um, so yeah, we don't see anything that would suggest otherwise. 00:58:42.000 --> 00:58:51.000 Yeah, so there's that. We got direct exchange leading to anti-ferromagnetic coupling here, and then you have, uh, along this 180 degree, 00:58:51.000 --> 00:58:55.000 interaction we also have anti-therromagnetic coupling. 00:58:55.000 --> 00:58:59.000 All of that leads to something that's basically an antiferromagnet. 00:58:59.000 --> 00:59:03.000 Although, if I don't have the field… there is… 00:59:03.000 --> 00:59:09.000 a little bit of a hysteresis loop, and I think that comes about because of the anti-site disorder gives you some uncompensated plumage. 00:59:09.000 --> 00:59:12.000 And the other important thing is the Chromium moment 00:59:12.000 --> 00:59:24.000 2.4 mu b is about… is about what it should be, right? And if we were having some kind of chromium-chromium bond, you wouldn't have 3 impaired electrons anymore, and you would not get that movement. 00:59:24.000 --> 00:59:30.000 Uh, you can make this compound also with varying ratios. You can make it chromium 00:59:30.000 --> 00:59:32.000 1.5 rhenium 1.5. 00:59:32.000 --> 00:59:35.000 And that, um, that one… 00:59:35.000 --> 00:59:40.000 only has moments along C, but basically looks, um, more or less the same. 00:59:40.000 --> 00:59:44.000 But this, uh, magnetic structure breaks the non-symorphic symmetry. 00:59:44.000 --> 00:59:50.000 Yeah, yeah, that group. It does. Yeah, then you only retain… have translation plus time reversal. 00:59:50.000 --> 00:59:56.000 So this will not be an ultra-magnet, it's just a doubly degenerate anti-ferromagnet. I see, okay. 00:59:56.000 --> 01:00:04.000 Not this. So, yeah, okay. I mean, then this one, I don't think it's written on here, but yeah, the magnetic space group is orthorhombic here. 01:00:04.000 --> 01:00:13.000 But, um, between 290 and 260, actually, you do have the same… it's along C, and therefore you don't… you don't break the 6th of 3 screw. 01:00:13.000 --> 01:00:15.000 And if you change acromion, 01:00:15.000 --> 01:00:19.000 uranium ratio, you can get that C-axis all the way down to low temperature. 01:00:19.000 --> 01:00:23.000 David. 01:00:23.000 --> 01:00:31.000 Here's another one that we did, which is kind of interesting. Here, we're mixing nickel and osmium. Nickel 2 plus osmium 6. 01:00:31.000 --> 01:00:35.000 And now we get also the 6H structure, but you can see that the ordering is different. 01:00:35.000 --> 01:00:38.000 Now we have Osmiums going… 01:00:38.000 --> 01:00:44.000 Well, both in this site and in this site, we have a 50-50 mixture of nickel and osmium. 01:00:44.000 --> 01:00:46.000 Um, and interestingly, 01:00:46.000 --> 01:00:49.000 Both the Osmium sublattice 01:00:49.000 --> 01:00:55.000 And the nickel sub-lattice are independently ferromagnetic. So the osmium would have one spin up, 01:00:55.000 --> 01:00:59.000 Two spin downs, and for the nickel, we have one spin up. 01:00:59.000 --> 01:01:06.000 are two spins up and one spin down. So, I mean, then that… the net effect is still a feron magnetism. 01:01:06.000 --> 01:01:08.000 That order's at about 100 and… 01:01:08.000 --> 01:01:11.000 108 Kelvin. 01:01:11.000 --> 01:01:20.000 And these are both just driven by super exchange, so there's no direct exchange here, because the osmium electron configuration, if you filled up the T2G orbitals now. 01:01:20.000 --> 01:01:22.000 And then this one is interesting. 01:01:22.000 --> 01:01:28.000 We tried to make, you know, we made the Rhinium analog, and we tried to make the osmium analog, and… 01:01:28.000 --> 01:01:35.000 you kept getting something that looked like a 6H phase, but wasn't, and turned out, then we figured out we were making a 4H phase, 01:01:35.000 --> 01:01:38.000 And we need a 1 to 1 ratio of chromium to osmium. So, 01:01:38.000 --> 01:01:44.000 This one… yeah, I think this is the first example of a cation-ordered 4H structure. 01:01:44.000 --> 01:01:47.000 Um, this one is actually, um… 01:01:47.000 --> 01:01:53.000 magnetic, up to almost 650 Kelvin, so very high temperature magnetism here. 01:01:53.000 --> 01:01:58.000 space group is polar, P63MC, at least that's the crystallographic space group. 01:01:58.000 --> 01:02:00.000 Um, and here you have… 01:02:00.000 --> 01:02:03.000 Yeah, super exchange. Well… 01:02:03.000 --> 01:02:10.000 This is very strong direct exchange here in the instances for exchange here. 01:02:10.000 --> 01:02:18.000 Okay, well, I've gone on for quite a while, so I'll just say at the end, just very quickly, 01:02:18.000 --> 01:02:20.000 We wanted to… 01:02:20.000 --> 01:02:31.000 do something where now we want to… we want to go to a trimer, we want to magnetically isolate these things, so we're going to put mixed valent ruthenium in here, we're going to put antimony 5 plus here. 01:02:31.000 --> 01:02:34.000 And, uh, 01:02:34.000 --> 01:02:37.000 Then what you do is then you, in principle, have this 01:02:37.000 --> 01:02:43.000 this kind of a molecular orbital picture. But the thing here is, because of the electron count, 01:02:43.000 --> 01:02:50.000 You know, it will… even if it won't go to a spin dimer, because you have an odd number of electrons here, so you end up going to something with half 01:02:50.000 --> 01:02:55.000 In principle, half of one unpaired electron per cluster. 01:02:55.000 --> 01:03:00.000 And what does the magnetism look like? Well… 01:03:00.000 --> 01:03:02.000 At high temperature, it has something that looks… 01:03:02.000 --> 01:03:05.000 Looks like the intermediate spin state. 01:03:05.000 --> 01:03:11.000 Where we have… spend 3 halves per cluster, but then as you go to low temperature, 01:03:11.000 --> 01:03:14.000 the effective moment definitely goes down. 01:03:14.000 --> 01:03:16.000 Maybe just spend one half. 01:03:16.000 --> 01:03:19.000 And then… so we thought, well, maybe this could be… 01:03:19.000 --> 01:03:21.000 Maybe a quantum spin liquid, so we… 01:03:21.000 --> 01:03:26.000 We reached out to Sarah Halfrer at Duke, and in her group, they measured 01:03:26.000 --> 01:03:31.000 magnetization and specific heat down to, um, 01:03:31.000 --> 01:03:35.000 60 millikelvin in one case, and then 300 millikelvin 01:03:35.000 --> 01:03:40.000 And so we don't see any magnetic ordering, and we do have a specific heat that's linear here. So… 01:03:40.000 --> 01:03:49.000 We think this could be kind of an interesting, you know, if those clusters were all spin-half, and they're on a triangular lattice, maybe… may be an interesting quantity. 01:03:49.000 --> 01:03:51.000 Okay. Well, I will… 01:03:51.000 --> 01:03:54.000 I will stop now. Thank you for your patience. 01:03:54.000 --> 01:03:56.000 Um, and uh… 01:03:56.000 --> 01:03:59.000 Maybe just also thank… thank my group. 01:03:59.000 --> 01:04:07.000 And lots of great collaborators. Thank you. 01:04:07.000 --> 01:04:11.000 Great question. One questions. 01:04:11.000 --> 01:04:13.000 Yes. Okay. 01:04:13.000 --> 01:04:16.000 Very interesting, Frederick, very good thought. 01:04:16.000 --> 01:04:21.000 The… I have two questions. One is very simple. 01:04:21.000 --> 01:04:27.000 I noticed that you've worked with Osmi and Ridium. Why Ridium is absent? 01:04:27.000 --> 01:04:34.000 Yeah, well, I think two reasons why we did… we haven't done much with Iridium. I mean, in part, 01:04:34.000 --> 01:04:50.000 Um, because a lot of other people had, uh, but… but the other thing is, um, also Iridium is a lot more difficult for neutrons, so if you want to do neutron diffraction, osmium and rhenium are quite friendly, and iridium has a pretty high absorption cross-section. 01:04:50.000 --> 01:04:54.000 Um, the other thing is… 01:04:54.000 --> 01:05:03.000 Some of the upper oxidation states, like plus 6 and plus 7, are more difficult to stabilize in the iridium cases than they are for osmium and uridium. But, I mean, I think… 01:05:03.000 --> 01:05:09.000 They're really analogs of this could, and some work has been done on those are also interesting. 01:05:09.000 --> 01:05:16.000 And my second question is, uh, maybe more to theorist than to you. So, I wonder… 01:05:16.000 --> 01:05:25.000 what stabilizes these molecules inside the solid? What particular part of the energy balance compared to the bulk? You know, why I would see the… 01:05:25.000 --> 01:05:27.000 But kind of one of those suit names. 01:05:27.000 --> 01:05:31.000 chemistry, so… Well… 01:05:31.000 --> 01:05:33.000 I mean, when… I guess when we say… 01:05:33.000 --> 01:05:38.000 I mean, this is the way I think about it anyway. If I think about it, the key has to be that 01:05:38.000 --> 01:05:41.000 that the D orbitals overlap to form 01:05:41.000 --> 01:05:44.000 molecular-type orbitals. 01:05:44.000 --> 01:05:51.000 rather than just, uh… so there's a… there's… the wave function, uh, goes across the whole cluster. 01:05:51.000 --> 01:05:55.000 for these D orbitals. And so, in that sense, that's 01:05:55.000 --> 01:05:57.000 That then would make it like a molecule to me. 01:05:57.000 --> 01:06:02.000 Um, I mean, it's really just the fact that you're… if that happens… 01:06:02.000 --> 01:06:14.000 Um, the reason what's driving that to happen is that you have brought the metals in close proximity to one another, so that they're… you would never get that through corner sharing, because then the d orbitals are not going to overlap. 01:06:14.000 --> 01:06:21.000 I don't know if that… I don't know if that's an answer you're looking for, but that's at least how I think about it. 01:06:21.000 --> 01:06:24.000 I mean, uh, it's an open question. 01:06:24.000 --> 01:06:28.000 We have some preliminary DFT calculations that, um… 01:06:28.000 --> 01:06:39.000 collaborator has done the look. It's kind of an… I think the answer is maybe it's a little bit in between just individual ions magnetically coupling to each other, and the full molecular orbital picture. 01:06:39.000 --> 01:06:41.000 So, for example, in that, uh… 01:06:41.000 --> 01:06:48.000 one that has three, the trimer, actually, it looks like the strongest coupling is between the outer rudeniums. 01:06:48.000 --> 01:06:53.000 antiferromagnetic to one another, and there's a frustration within the cluster. 01:06:53.000 --> 01:06:59.000 That is the lowest energy configuration. So, I think it's kind of interesting to think about, but… 01:06:59.000 --> 01:07:05.000 maybe not totally understood yet. 01:07:05.000 --> 01:07:08.000 The other questions? 01:07:08.000 --> 01:07:14.000 Okay, I have a number of questions. Let me just do. 01:07:14.000 --> 01:07:23.000 Uh, so this, uh, spin dimerization, especially in cium chromium pisses, cium chromium chromium piece, spin diamondation. 01:07:23.000 --> 01:07:29.000 Is there really phase transition, or when you fill out these kind of just the next station? 01:07:29.000 --> 01:07:35.000 Yeah, I don't think… I don't think there is any phase transition, so it's not like it, uh, is… goes… 01:07:35.000 --> 01:07:41.000 through some kind of… it's, uh, let me see, I had a picture… one way to think about it, probably, is this… 01:07:41.000 --> 01:07:46.000 So, this kind of way. So, you can just imagine that you have… 01:07:46.000 --> 01:07:53.000 you know, this is where all the spins are parallel, this is where they're all end up, and there's this thermal population of those levels, yeah. 01:07:53.000 --> 01:08:01.000 Okay, and then we'll go back to this, uh, zinc radio case. Can you find this data where you see tiny anomaly at orbital? 01:08:01.000 --> 01:08:04.000 Sure. Yeah, sure. 01:08:04.000 --> 01:08:10.000 So, you know, if there's an orbital order, or a Yanteller, and… 01:08:10.000 --> 01:08:13.000 for T2G, that's not something I'm, uh… 01:08:13.000 --> 01:08:17.000 So, capacity. 01:08:17.000 --> 01:08:22.000 So, if you capacity, and then let this parameter changes about… 01:08:22.000 --> 01:08:34.000 So, 14 caliber, 20 caliber. Well, here, that's probably the best thing to look at here is your C over A ratio, which you might say, shouldn't it go to 1, but I think, uh… 01:08:34.000 --> 01:08:50.000 We refined even a cubic phase as tetragonal. I think that's just an offset in the data, but it's probably around between 20 and 25 Kelvin that you start to see a tetragonal distortion. Right, I see. So, so you would… the one that you were discussing this orbitron order is, in some sense, kind of an anti-federal 01:08:50.000 --> 01:08:58.000 electric motor. Yes, I think that would be the right way to… that's… I think that would be the right way to describe it, yeah. 01:08:58.000 --> 01:09:05.000 Sure, I don't see much, but do you see… so at the menu transition, she overbra should not change too much. 01:09:05.000 --> 01:09:19.000 So I just wonder if there is some kind of coupling between how the coupling between magnetism and the orbital order is going to happen. So, for example, like, a second biggest restriction, or piezo medal… Got it. So, there is… 01:09:19.000 --> 01:09:27.000 Okay, so in single crystal diffraction studies done on the magnesium compound by, uh, 01:09:27.000 --> 01:09:33.000 Sinji, Hiroi, and Taigo Harai in Japan, they do see that the C over A ratio 01:09:33.000 --> 01:09:35.000 gets bigger, 01:09:35.000 --> 01:09:47.000 Once you get to the magnetic ordering. So it goes up, and then it goes up even steeper once it magnetically orders him back. We don't really see that in our data. Yeah. I mean, it would be right here, maybe there can… I don't know. 01:09:47.000 --> 01:09:56.000 Excellent. It's… so maybe, maybe. So, you know, since it's kind of a strange effect, kind of having 45 degree, and then, you know… 01:09:56.000 --> 01:10:02.000 I wonder, by the primary field, whether it could change or not. At least. 01:10:02.000 --> 01:10:08.000 Ah! Right, right, right, right, right. Uh… 01:10:08.000 --> 01:10:11.000 Yes, I mean, I think that's an interesting idea. 01:10:11.000 --> 01:10:16.000 I think just as grammar is crucial, we feel what the low temperature means. 01:10:16.000 --> 01:10:18.000 I mean, the moments… 01:10:18.000 --> 01:10:21.000 They accepted magnetic structure, the moments are in the AB plane. 01:10:21.000 --> 01:10:30.000 Right? And so, yeah. You might see something like that. 01:10:30.000 --> 01:10:38.000 Yeah, you'd need single… obviously a single Christmas. But they did grow very small single crystals. 01:10:38.000 --> 01:10:41.000 This is 300 or 400, uh, microns, yeah. Okay. 01:10:41.000 --> 01:10:44.000 Okay, okay? 01:10:44.000 --> 01:10:46.000 Okay, any more questions? 01:10:46.000 --> 01:10:54.000 Otherwise, unless thank you. That's very good. 01:10:54.000 --> 01:11:07.000 So, that you are the next, correct? I'm next. 01:11:07.000 --> 01:11:09.000 I have one other… yeah. 01:11:09.000 --> 01:11:23.000 You had a 10-degree window between… 01:11:23.000 --> 01:11:29.000 I'm wondering… No, but we'll see it later. 01:11:29.000 --> 01:11:38.000 Some kind of two-dimensional magnitude. 01:11:38.000 --> 01:11:43.000 Because the coupling for the second layer above, whether it's… 01:11:43.000 --> 01:11:45.000 pharaoh or anti-Pharaoh. Yeah. 01:11:45.000 --> 01:11:55.000 I would imagine is very… Were you asking? Sure, sure. That doesn't sound entirely. I just… I wonder, yeah. 01:11:55.000 --> 01:12:16.000 Although, but although the main, the main super exchange… It would just be a two-layer kind of thing, uh, I mean, basically… Yeah, I sort of still waiting for the approval from the ministry. 01:12:16.000 --> 01:12:26.000 Okay, okay. Anyway, thank you. Yeah, many years ago, right? You were still Arkansas then, I think. Yes, yes. Yeah, well, it's gonna end. 01:12:26.000 --> 01:12:46.000 But