1 00:00:00,460 --> 00:00:03,640 Well, good afternoon and welcome to the colloquium today. 2 00:00:03,970 --> 00:00:07,180 It's a great pleasure to welcome Professor Nicholas Bolton here. 3 00:00:07,540 --> 00:00:13,570 He's going to be giving a colloquium. Nicolette is her first degree in the University of Cambridge. 4 00:00:14,260 --> 00:00:17,860 After that, she moved to do her Ph.D. in Berkeley. 5 00:00:18,190 --> 00:00:23,950 And after that, some periods in Yale and then the University of California, Santa Barbara. 6 00:00:24,190 --> 00:00:28,780 She moved in 2010 to her current position as professor in the DCH. 7 00:00:28,780 --> 00:00:32,920 And Sir Nick has won a large number of prizes. 8 00:00:32,950 --> 00:00:41,169 She's a fellow of the American Physical Society. She has won the Cooper Prize, the James McCarthy Prize at the American Physical Society. 9 00:00:41,170 --> 00:00:47,139 And this year she has been awarded a L'Oreal Mexico women in science laureates in Europe, 10 00:00:47,140 --> 00:00:55,000 which is which is another one of these that's been on this lecture is probably best known for her work in multiple works. 11 00:00:55,600 --> 00:00:59,620 She writes a very beautiful paper explaining why there are so few for electrics. 12 00:00:59,860 --> 00:01:03,040 So she's made enormous contributions to the various condensed matter. 13 00:01:03,040 --> 00:01:10,680 But as you will discover this this afternoon, her interest is not only in condensed matter, but I'm looking at some of the applications more deeply. 14 00:01:10,690 --> 00:01:15,160 You can see from her title today, studying the universe under a microscope, 15 00:01:15,610 --> 00:01:19,470 that there are some applications in cosmology from the work that she's been doing. 16 00:01:19,720 --> 00:01:20,910 Thank you very much. Physics. 17 00:01:23,080 --> 00:01:35,650 So this picture shows a piece of force microscopy image of a furrow electric domain structure of a popular multi heroic material yttrium manganese. 18 00:01:35,950 --> 00:01:43,780 And the black and white regions are opposite orientations of the ferroelectric polarisation measured using piezo force microscopy, 19 00:01:44,110 --> 00:01:51,110 and it's embedded in what you may be recognised as a picture from the Hubble Telescope of the cosmic microwave background. 20 00:01:51,130 --> 00:01:59,140 So my goal for the next 45 minutes or so is to explain to you the connection between these two two properties. 21 00:01:59,830 --> 00:02:05,049 I have to make it. I should make a disclaimer before I start, which is that I'm a condensed matter physicist. 22 00:02:05,050 --> 00:02:11,740 So everything I say about cosmology, I learned from my cosmology friends in the last two or three years. 23 00:02:11,740 --> 00:02:15,910 And so I'm just reporting what, what, how I understood what what they told me. 24 00:02:15,910 --> 00:02:20,649 Are there any cosmologists or astrophysicists in the audience? Okay, so please shut up. 25 00:02:20,650 --> 00:02:25,390 If I say anything that's really flagrant is all or too much of an oversimplification. 26 00:02:26,380 --> 00:02:35,980 So let me start then with how to, as a material scientist, my early universe history to a material scientist. 27 00:02:36,400 --> 00:02:41,230 So we start with the Big Bang, which happened about 14 billion years ago. 28 00:02:41,590 --> 00:02:43,540 And after the Big Bang, 29 00:02:44,020 --> 00:02:52,570 it's believed that there was basically there was nothing in the universe that the universe was a vacuum and that it was a homogeneous vacuum. 30 00:02:53,470 --> 00:03:03,040 And we it's believed that the universe was was expanding very rapidly or to a condensed matter person. 31 00:03:03,710 --> 00:03:06,280 This is equivalent to cooling, 32 00:03:07,240 --> 00:03:16,630 but it remained this homogeneous vacuum that was expanding for quite some time until after about ten to the -30 7 seconds. 33 00:03:16,870 --> 00:03:25,270 The first real event in early universe history after the Big Bang happened and after ten to the -30 7 seconds, 34 00:03:25,840 --> 00:03:32,950 what's proposed is that there was a spontaneous symmetry lowering phase transition called the grand unification transition, 35 00:03:33,310 --> 00:03:37,030 in which the vacuum, which was still a vacuum, lowered its symmetry. 36 00:03:37,030 --> 00:03:46,300 So there was a vacuum to vacuum phase transition from high symmetry, homogeneous background to a lower symmetry vacuum. 37 00:03:47,020 --> 00:03:51,009 And again, this is this is a this is a proposal. 38 00:03:51,010 --> 00:04:00,520 Of course, nobody was around at the time. And this is proposed to be described by a free energy that has a mexican hat type form for the potential. 39 00:04:01,150 --> 00:04:10,809 So that's my understanding of kind of early universe history for the first subtract fraction, tiny fraction of a of a second Z. 40 00:04:10,810 --> 00:04:14,950 Okay. From the cosmology people and you think too glaringly wrong. 41 00:04:14,950 --> 00:04:23,649 Okay, good. So let me for the sake of the condensed matter, people describe kind of the equivalent scenario that we're, I think, 42 00:04:23,650 --> 00:04:30,610 all much more familiar with, which is a spontaneous symmetry lowering phase transition in a ferromagnetic material. 43 00:04:30,610 --> 00:04:36,729 I want to emphasise two aspects of spontaneous symmetry lowering phase transitions that I think is so familiar 44 00:04:36,730 --> 00:04:42,190 to us that we that we kind of we forget about what we didn't have to think about what this term means. 45 00:04:42,190 --> 00:04:45,590 Spontaneous symmetry during phase transition. So here's the, 46 00:04:45,610 --> 00:04:53,980 the scenario that from a condensed matter side we're all very familiar with and we'll come back and look at how this applies in the early universe. 47 00:04:54,610 --> 00:04:59,740 So in a format that at low temperature, these little arrows are supposed to. 48 00:04:59,910 --> 00:05:03,180 Represent magnetic moments on electrons at low temperature. 49 00:05:03,180 --> 00:05:10,710 If the exchange interaction between the the electrons or the atoms is is ferromagnetic, then they all line up. 50 00:05:11,100 --> 00:05:16,739 And this is a low symmetry state because if I sit on this electron and look to the right or the left, 51 00:05:16,740 --> 00:05:20,580 I see something different than if I look too up, up or down. 52 00:05:21,150 --> 00:05:27,150 And then as I heat up, eventually there's enough thermal energy that the spins get disordered. 53 00:05:27,390 --> 00:05:31,980 And this is a high symmetry state because wherever I look around this electron, I see the same. 54 00:05:31,980 --> 00:05:37,889 I see a disordered, disordered spin. Or if I come from the other direction, I start in the high symmetry state. 55 00:05:37,890 --> 00:05:42,360 I cool through some critical temperature and I lower the symmetry. 56 00:05:43,590 --> 00:05:50,579 And if my thorough magnet is uni axial, then there are two equivalent low symmetry states, 57 00:05:50,580 --> 00:05:55,020 one where the magnetic moments are pointing up and one where the magnetic moments are pointing down. 58 00:05:55,350 --> 00:06:04,020 And so if I plot the energy as a function of some order parameter, which in this case is how much these magnetic moments, these spins are lined up, 59 00:06:04,320 --> 00:06:10,799 then I have this characteristic double well potential spins pointing up on this side and spins pointing down on the side. 60 00:06:10,800 --> 00:06:17,040 So I have a potential, potential energy surface describing my symmetry lowering phase transition. 61 00:06:18,090 --> 00:06:23,819 So this is the first aspect of spontaneous symmetry breaking. I want to emphasise one, it happens spontaneously, 62 00:06:23,820 --> 00:06:31,080 so it lowers the energy to to become the lowest symmetry state and there are multiple equivalent grounds to get states. 63 00:06:31,080 --> 00:06:37,500 In this example, there are only two that the system can choose when it goes through this symmetry, low and phase transition. 64 00:06:39,470 --> 00:06:47,450 There's a second aspect of symmetry lowering phase transitions, which is not something that's something historically I ever thought about as much, 65 00:06:47,750 --> 00:06:54,200 which is that there's often defect formation associated with the formation of the low symmetry state. 66 00:06:54,440 --> 00:06:57,379 And so here's the example again of the furrow magnet. 67 00:06:57,380 --> 00:07:04,130 And I'm cooling my paramagnetic disordered material and starting to approach the phase transition. 68 00:07:04,460 --> 00:07:11,450 And one region might adopt the up spin state and another region might spontaneously adopt the down spin state. 69 00:07:11,450 --> 00:07:17,299 And then these two regions will launch large as I approach the phase transition until at the critical temperature, 70 00:07:17,300 --> 00:07:21,410 I transform to all the low symmetry state. 71 00:07:21,710 --> 00:07:30,560 But because of the initial choice of the different regions of the two available ground states, I have a defect where where they meet. 72 00:07:30,560 --> 00:07:37,490 So my spot, my low symmetry state is not perfect here an up spin electron with would like an up spin never has a downstream 73 00:07:37,490 --> 00:07:43,340 neighbour and I have a defect and of course we familiar with this defect as a as a ferromagnetic domain wall. 74 00:07:45,140 --> 00:07:48,500 Okay. So here's the roughly how many students are in the audience section. 75 00:07:50,080 --> 00:07:53,380 Okay. My student my review for the students is for you guys especially. 76 00:07:53,830 --> 00:08:01,570 So this is my review for the students of one of the key factors that we need to remember for spontaneous symmetry lowering phase transitions. 77 00:08:01,900 --> 00:08:03,760 They lower the symmetry. That's kind of obvious. 78 00:08:04,060 --> 00:08:11,440 What the spontaneous refers to is that they lower the energy and that there's a choice of multiple equivalent low symmetry states to in this case. 79 00:08:12,100 --> 00:08:16,930 And then the last point, which is going to become really important in the discussion of early universe behaviour, 80 00:08:17,320 --> 00:08:21,730 is that defects form at the intersections between the equivalent low symmetry states. 81 00:08:23,970 --> 00:08:27,000 Okay. So back to the early universe. Any questions on the. 82 00:08:31,080 --> 00:08:33,659 Okay. So remember off ten to the -30 7 seconds, 83 00:08:33,660 --> 00:08:39,780 we had our symmetry lowering phase transition in the early universe from the homogeneous vacuum to the vacuum of lower symmetry. 84 00:08:40,080 --> 00:08:51,209 And this is analogous then to our paramagnetic magnetic system lowering at symmetry to a fairer magnet in the universe. 85 00:08:51,210 --> 00:09:00,030 The expansion was the was the variable that caused this transition in the in of course, in the paramagnetic it's usually temperature. 86 00:09:00,840 --> 00:09:05,819 And remember we said that the rather than the double well potential we looked at for the case of the 87 00:09:05,820 --> 00:09:13,080 ferromagnetic potential describing this phase transition as this Mexican hat Mexican hat shape potential. 88 00:09:16,030 --> 00:09:23,500 And so as I approach the famous transition from the high symmetry, from the homogeneous vacuum to the lower cemetery vacuum, 89 00:09:24,010 --> 00:09:30,070 then just as in the foreign magnet, different regions of the material could adopt different orientations of the low cemetery state. 90 00:09:30,340 --> 00:09:36,579 Different regions of space can choose low cemetery vacuum with different choice of angle. 91 00:09:36,580 --> 00:09:39,970 So perhaps this region over here will adopt this angle here. 92 00:09:41,890 --> 00:09:49,810 Another region will adopt another angle and so on. And initially, these regions are small, as I as I'm approaching the phase transition. 93 00:09:50,110 --> 00:09:57,790 But as I start to cross the phase transition, these fluctuations of low symmetry vacuum out of the high symmetry vacuum start to grow. 94 00:09:58,180 --> 00:10:02,900 And eventually they meet. And where they meet. Is a defect. 95 00:10:03,770 --> 00:10:10,220 And this is one of the proposals of how mass could evolve from the vacuum in the early universe. 96 00:10:10,790 --> 00:10:15,200 The symmetry lowering phase transition to the lowest symmetry state. 97 00:10:15,410 --> 00:10:18,500 There are defects which of course have higher energy than the surrounding region. 98 00:10:19,040 --> 00:10:22,850 It's not so obvious to see on this picture of plus, this defect looks like a point, 99 00:10:23,180 --> 00:10:27,919 but actually it's a line defect which is set by the symmetry of the of the potential. 100 00:10:27,920 --> 00:10:36,260 So Mexican hat type potential, when one lowers the symmetry with such a potential, one ends up with with line defects in the low symmetry phase. 101 00:10:36,500 --> 00:10:40,580 And this defect is, is what's known as a cosmic string. 102 00:10:41,510 --> 00:10:45,890 So cosmic strings, I should emphasise, are completely different from string theory strings. 103 00:10:46,130 --> 00:10:54,830 These are proposed defects in the, in the structure of the universe that emerged from this symmetry lowering such as symmetry, 104 00:10:54,830 --> 00:11:00,190 law and phase transition in the early universe behaviour. Okay. 105 00:11:01,860 --> 00:11:06,060 So let me tell you a couple of details. 106 00:11:06,180 --> 00:11:10,860 So the next couple of starts are a little bit detailed about the physics of these these cosmic strings, 107 00:11:11,070 --> 00:11:16,590 because there were distinct predictions made about cosmic string formation, which would like to be able to test. 108 00:11:17,280 --> 00:11:21,990 So the first prediction is what determines the distance between the cosmic strings? 109 00:11:22,000 --> 00:11:25,620 How many cosmic strings should there be in the universe? 110 00:11:26,940 --> 00:11:30,239 And so the size of the domains that form which separate the, 111 00:11:30,240 --> 00:11:37,590 the the defects is a competition between the speed at which information propagates through the system. 112 00:11:37,590 --> 00:11:45,120 And this is believed to be set by the speed of light. So it determines whether if one region of the universe has has lowered its symmetry. 113 00:11:45,330 --> 00:11:52,170 How much time does it or how long does it take to tell its neighbours to adopt the same choice of face off the same angle? 114 00:11:52,380 --> 00:11:56,160 So the speed of information propagation, if my information propagation is very fast, 115 00:11:56,430 --> 00:12:01,410 then I would expect to get large domains with the same of the same the same phase angle. 116 00:12:01,980 --> 00:12:05,670 It's also dependent, of course, by how much time you spend at the transmission. 117 00:12:05,940 --> 00:12:10,680 How long do you have to for your your kind of freedoms to grow? 118 00:12:11,070 --> 00:12:16,650 And so if my transition happens more slowly again, my domains become quickly become larger. 119 00:12:16,830 --> 00:12:20,819 So if I expand slowly, then different regions can communicate their choice of phase. 120 00:12:20,820 --> 00:12:24,690 So I get large regions of the same choice and the low density of defects. 121 00:12:25,710 --> 00:12:32,610 Not so many cosmic strings. If I expand quickly, then there's not much time to communicate the choice of phase. 122 00:12:32,850 --> 00:12:36,690 I have many smaller regions with different choices of phase and a high density of defects. 123 00:12:37,050 --> 00:12:40,650 So this is kind of the physics of of such a phase transition. 124 00:12:41,040 --> 00:12:44,820 Sorry. One thing I realise I forgot to mention is that this cosmic string, 125 00:12:45,750 --> 00:12:52,739 because of the nature of the symmetry of this phase transition, is what's called topologically protected. 126 00:12:52,740 --> 00:12:55,560 It's a one dimensional and it's also topologically protected. 127 00:12:55,920 --> 00:13:03,690 And what this means is that the cosmic string can't go away unless it gets pushed out of the outside edges of the system, 128 00:13:03,930 --> 00:13:09,750 or unless two cosmic strings with opposite parity meet each other and annihilate. 129 00:13:09,780 --> 00:13:12,900 So this. This is a consequence of the symmetry. 130 00:13:13,840 --> 00:13:17,799 So there are two factors proposed for cosmic string formation. 131 00:13:17,800 --> 00:13:24,430 One is the type of logical protection, and one is this that the size of the domain separating them. 132 00:13:24,700 --> 00:13:31,510 And the first piece of physics was developed by by Tom Kebble and the second by Voytek Zurek. 133 00:13:32,450 --> 00:13:37,989 So when one combines these two properties together, one can write down a scaling law, 134 00:13:37,990 --> 00:13:41,380 which is called Kibble Direct Scaling for Cosmic String Formation, 135 00:13:42,640 --> 00:13:46,959 which basically just takes the physics that just described the competition between the speed 136 00:13:46,960 --> 00:13:51,760 of information propagation and how much time you have to grow domains and quantifies it. 137 00:13:51,760 --> 00:13:57,010 So I'm not going to derive this. It's not so it's it's rather straightforward to derive this expression here is if you 138 00:13:57,010 --> 00:14:02,380 assume that you're expanding linearly or you're crossing the phase transition linearly. 139 00:14:03,730 --> 00:14:09,610 And so it tells you that the size of the domains, the distance between the topologically protected defects, 140 00:14:09,610 --> 00:14:14,170 the distance between the cosmic strings is given by the correlation length. 141 00:14:15,950 --> 00:14:21,829 It's given by a factor tor q which is the volume at the critical point divided 142 00:14:21,830 --> 00:14:27,020 by the rate of expansion through the transition divided by the relaxation time, 143 00:14:27,320 --> 00:14:30,590 which is just the correlation length, divided by the speed of information transfer. 144 00:14:31,130 --> 00:14:40,280 And it's, it's a scaling law and it's the scaling is determined by some critical exponents which might be fluctuation dominated or, 145 00:14:40,550 --> 00:14:45,110 or might be mean field or could be somewhere in between. 146 00:14:45,980 --> 00:14:47,990 So this is the prediction. 147 00:14:48,830 --> 00:14:57,200 This is the quantifiable prediction for the kind of physics I've just described to you that tells me really for for a particular expansion rate, 148 00:14:57,200 --> 00:15:04,279 for the grand unification transition and a particular speed of information transfer, how many cosmic strings I should have them. 149 00:15:04,280 --> 00:15:07,940 So this is what we would like to be able to like to be able to test. 150 00:15:09,690 --> 00:15:13,420 Okay. Questions? Objections. 151 00:15:14,790 --> 00:15:18,109 Well. Okay. 152 00:15:18,110 --> 00:15:29,600 So so this is all very nice, I think. I think it's extremely creative, extremely conceptual, creative and very pleasant theory. 153 00:15:29,810 --> 00:15:33,170 But of course, one would like to know is, is it true to cosmic strings exist? 154 00:15:34,280 --> 00:15:39,050 And if so, how can how can we measure them? How can we detect them and how can we study them? 155 00:15:41,670 --> 00:15:48,780 And to to study anything in physics directly, then we need to have a probe which has a similar energy scale. 156 00:15:49,020 --> 00:15:58,379 So the thing that we'd like to study, of course, and the energy scale for Cosmic Strings is of the order of ten to the 15 giga electron volts. 157 00:15:58,380 --> 00:16:05,680 So if one had the number that I was told us, if one had a11 kilometre long cosmic strings, we'd have about the mass of the earth. 158 00:16:05,700 --> 00:16:11,819 So if one just kind of wandered in, we wouldn't have much opportunity to detect it before we were obliterated. 159 00:16:11,820 --> 00:16:15,990 I guess ten to the 15 giga electron volts is very energetic. 160 00:16:16,260 --> 00:16:21,149 The highest energy probes we have available at the moment, the largest Hadron Collider. 161 00:16:21,150 --> 00:16:24,990 There are about ten to the ten of the four giga electron volts. 162 00:16:24,990 --> 00:16:29,880 So we're really very far from any direct study of of cosmic string formation. 163 00:16:31,660 --> 00:16:40,300 So what one can do, rather, is observe to look for signatures of of cosmic strings in astronomical data. 164 00:16:40,660 --> 00:16:48,100 And in particular, there are well-defined predictions of signatures that should occur in the cosmic microwave background, 165 00:16:49,000 --> 00:16:55,420 which to date have not been seen. So there is an upper bound on the number of cosmic strings that can occur in the universe. 166 00:16:55,420 --> 00:16:58,600 But there's not based on observations of the cosmic string in. 167 00:16:59,760 --> 00:17:08,700 One can, of course, also do computer simulations. And this picture here is from my colleague Martin Quince at the University of Geneva, 168 00:17:09,030 --> 00:17:15,120 who simulated a symmetry lowering phase transition through that Mexican hat potential that we looked at earlier. 169 00:17:15,420 --> 00:17:23,430 And what he found was the formation of domains and domain intersections, which really form is one dimensional, one dimensional strength. 170 00:17:23,730 --> 00:17:30,750 So these are the two, I'd say, primary roots to studying cosmic string formation in the early universe. 171 00:17:31,530 --> 00:17:41,429 What we would like to do instead is to study the and equivalent to the grand unification transition in our laboratory. 172 00:17:41,430 --> 00:17:45,239 And this started as the Ph.D. thesis of Janet Griffin, 173 00:17:45,240 --> 00:17:50,220 who was a graduate student in my group and who's now a postdoc at the Molecular Foundry in Berkeley. 174 00:17:51,660 --> 00:17:57,810 And so our plan then is first to identify a material, a real condensed matter, 175 00:17:58,500 --> 00:18:08,250 solid with a symmetry lowering phase transition that's described by the same mathematics as that proposed for the grand unification transition. 176 00:18:08,670 --> 00:18:13,920 So what we want is a spontaneous symmetry breaking. That's described by a mexican hat potential. 177 00:18:14,940 --> 00:18:22,919 And then we can do or we will do all the experiments on our material that we would like to do on the early universe, 178 00:18:22,920 --> 00:18:31,020 which we can't do because we can't keep replaying the big bang. So we will look at the cosmic strings exist when we run through this transition. 179 00:18:31,020 --> 00:18:35,930 Do we find line defects in our system? Did they form as we think? 180 00:18:36,000 --> 00:18:41,100 In particular, do they follow this direct type scaling that I introduced to you earlier? 181 00:18:42,180 --> 00:18:45,360 How do they evolve when we wait and watch them? Do they recombine that? 182 00:18:45,360 --> 00:18:51,019 They move around. And what are their properties? Okay. 183 00:18:51,020 --> 00:18:54,080 So this is where I'm headed. Then for the second half of the talk, 184 00:18:54,800 --> 00:18:59,120 I'll show you a material that has a symmetry lowering phase transition that meets these 185 00:18:59,330 --> 00:19:03,410 chemical requirements for the formation of topologically protected one dimensional defects, 186 00:19:04,100 --> 00:19:09,259 and then will use electronic structure calculations to calculate all the parameters in 187 00:19:09,260 --> 00:19:14,900 that cables in the right formula and to predict if cables or a physics is being followed. 188 00:19:15,200 --> 00:19:19,520 How many defects, how many or what the domain size should be and how many domain intersections 189 00:19:19,850 --> 00:19:24,649 should form as a function of of how quickly we move through the transition. 190 00:19:24,650 --> 00:19:26,030 In our case, it's by cooling. 191 00:19:27,370 --> 00:19:33,910 Then we'll go to the lab and we'll measure how many topologically protected defects form as a as a function of cooling rate. 192 00:19:34,300 --> 00:19:36,490 And so we'll be able to answer the question. 193 00:19:36,490 --> 00:19:44,140 Does a system that's described by the same physics and symmetry as the grand unification transition exhibit the predicted Zurek behaviour. 194 00:19:47,280 --> 00:19:50,079 Okay. So any suggestions? 195 00:19:50,080 --> 00:19:56,799 If I'm looking for material that I want to have a spontaneous symmetry lowering phase transition described by a mexican hat type potential? 196 00:19:56,800 --> 00:20:01,760 Where might I look? Anything with a TV or anything with a 2D order parameter? 197 00:20:01,830 --> 00:20:06,260 Yeah. Any suggestions from the students? 198 00:20:07,340 --> 00:20:12,890 Stephen gave you a clue when he started it up. He said that I worked a lot on multiple heroic materials, 199 00:20:14,270 --> 00:20:21,980 so we started looking and videos of the multi multi for rock and the multi heroic material is a material that has multiple Farrokh orders. 200 00:20:22,310 --> 00:20:28,010 And the reason we chose multiple heroic materials is because each of these Farrokh orders can have a has a spontaneous 201 00:20:28,010 --> 00:20:34,309 symmetry lowering phase transition associated with it that has defects associated with that phase transition. 202 00:20:34,310 --> 00:20:37,250 And so they're all candidates for, for such behaviour. So. 203 00:20:37,450 --> 00:20:44,509 So I guess we were not particularly smart, we just thought if we had three times as many possible possibilities in a single material, 204 00:20:44,510 --> 00:20:47,810 we had more chance of finding a suitable order parameter. 205 00:20:48,140 --> 00:20:58,459 So multiple heroic then as a material that combines for electricity and or for magnetism and also elasticity in the same phase. 206 00:20:58,460 --> 00:21:03,500 And so it has a it can have a spontaneous magnetisation that's switchable by a magnetic field, 207 00:21:03,500 --> 00:21:09,920 like the three magnets we looked at earlier, a spontaneous electric polarisation that's switchable by an applied electric field. 208 00:21:09,920 --> 00:21:15,890 It's a for electric or a spontaneous defamation that's switchable by an applied stress that's a foreign elastic. 209 00:21:16,970 --> 00:21:25,520 And multiple rocks are actually not so uncommon or some types of multiple rocks are not a rather common. 210 00:21:25,760 --> 00:21:26,419 So, for example, 211 00:21:26,420 --> 00:21:36,170 thermoelectric electric elastics are very common when one has a structural phase transition that results in an electric dipole moment, 212 00:21:36,590 --> 00:21:39,620 usually associated with this, there's an elastic defamation. 213 00:21:39,890 --> 00:21:47,360 And what this leads to is a cross coupling between the stress and the polarisation of the electric field and the internal strain. 214 00:21:47,690 --> 00:21:56,600 And this gives you electric behaviour. So this is for example, how sonar converts a signal, 215 00:21:57,980 --> 00:22:05,660 a sound wave into an electrical signal through the of electric behaviour and likewise associated with a magnetic phase. 216 00:22:05,660 --> 00:22:11,870 Transition is often an elastic defamation and so thorough magnetic flow elastics are also rather common. 217 00:22:11,870 --> 00:22:15,380 And these are used, for example, for magneto, mechanical actuation. 218 00:22:16,820 --> 00:22:18,860 But many of us have been interested for, 219 00:22:18,860 --> 00:22:25,309 for some years in this side of the triangle materials that are for magnetic and for electric, which are rather uncommon. 220 00:22:25,310 --> 00:22:27,050 That's not what I'm going to focus on today. 221 00:22:27,290 --> 00:22:32,389 But they have the interesting behaviour that with them with an electric field, one can modify the magnetism. 222 00:22:32,390 --> 00:22:38,180 So one has the the potential for electric field control of magnetic phenomena, vice versa. 223 00:22:38,180 --> 00:22:41,360 With a magnetic field one can modify the electric polarisation. 224 00:22:42,650 --> 00:22:49,880 So this is all kept us busy trying to make materials that are for electric and for magnetic and to exploit their properties for many years. 225 00:22:50,330 --> 00:22:58,459 Today, what I want to focus on, rather, is that the defects that are that form from spontaneous, 226 00:22:58,460 --> 00:23:03,620 from spontaneous symmetry, lowering phase transitions in these various types of heroic order. 227 00:23:04,490 --> 00:23:10,970 So we mentioned already the thorium at the domain walls in ferromagnetic between opposite orientations of the magnetisation. 228 00:23:11,420 --> 00:23:21,770 There are similar domain walls in for electric materials between opposite orientations of the electric polarisation and in for elastics the 229 00:23:22,040 --> 00:23:29,570 mechanical twin boundaries one can also think of as a as a domain wall or is spontaneous a defect formed by the spontaneous symmetry line. 230 00:23:30,830 --> 00:23:34,940 So this was our motivation for looking in multiple rubrics for this behaviour. 231 00:23:36,370 --> 00:23:49,149 So the material that we we chose is it is a multi farai material called yttrium manganese yttrium manganese O3 which has a rather unusual structure. 232 00:23:49,150 --> 00:23:55,210 And this was the, the material I showed you showed you right on the first slide I showed you the is a force microscopy image of this material. 233 00:23:55,750 --> 00:24:05,350 So it has a crystal structure which consists of layers of manganese oh five triggered all by pyramids. 234 00:24:05,620 --> 00:24:12,909 So if I look from the top, I have a manganese atom in the middle of a triangle of oxygens which are corner shared and above. 235 00:24:12,910 --> 00:24:17,890 The manganese is an oxygen and also below the manganese. So that's an oxygen on top and an oxygen. 236 00:24:18,160 --> 00:24:24,550 So these are triggered by permits because they have a beautiful triangular lattice of the manganese ions. 237 00:24:25,790 --> 00:24:31,219 And these planes of manganese of five treadmill by pyramids are separated by planes 238 00:24:31,220 --> 00:24:36,830 of yttrium ions and at high temperature the structure has a centre of inversion, 239 00:24:36,830 --> 00:24:41,480 its power electric and there's no electric polarisation. 240 00:24:44,940 --> 00:24:50,700 This is how it looks like I had to show you this this picture, because I'm trained as an electronic structure theorist. 241 00:24:50,700 --> 00:24:55,170 And when I moved to the 8880 build, built an oxide single crystal growth lab. 242 00:24:55,440 --> 00:25:00,569 And so I'm very excited to show you the sample of it through manganese at three because it was actually grown in our laboratory. 243 00:25:00,570 --> 00:25:05,430 This is a beautiful cyber style furnace by Frank Lichtenberg as a member of my group. 244 00:25:05,700 --> 00:25:09,000 So you can see it's this is an insulator it's a through electric so rather good 245 00:25:09,150 --> 00:25:14,190 insulator it's kind of a dirty black colour because the bandgap is rather small. 246 00:25:14,190 --> 00:25:20,880 The bandgap is less than electron volt because of the, the, the electron states that are close to the Fermi energy. 247 00:25:22,810 --> 00:25:32,400 So this is all material. What's important for us is that it undergoes a symmetry lowering phase transition at around 1000 248 00:25:32,400 --> 00:25:39,450 Kelvin and at the cemetery lowering phase transition to two things happened to the structure. 249 00:25:39,990 --> 00:25:46,229 One is that there is a tilting of the trigger by pyramids in threes. 250 00:25:46,230 --> 00:25:49,920 So this one moves in, this one moves forward, and this one moves, moves to the left. 251 00:25:50,340 --> 00:25:57,209 So a traumatisation tilting. So on the view from the top, I've put arrows on the top oxygens to show the way that they tell. 252 00:25:57,210 --> 00:26:02,970 So there's a three foot three fold folding over or tilting of the pyramids. 253 00:26:04,620 --> 00:26:11,709 And at the same time or accompanying that there was a shift of the yttrium ions and there's the, 254 00:26:11,710 --> 00:26:20,100 the net shift of the it reminds us all in one direction. And because the it reminds a positive and the manganese of five layer is overall negative, 255 00:26:20,400 --> 00:26:24,020 this gives a net polarisation and so the low temperature state is far away. 256 00:26:26,750 --> 00:26:32,350 Questions on the crystal structure. Okay. 257 00:26:34,400 --> 00:26:38,270 Let's look a little bit in more detail at these structural distortions, 258 00:26:39,350 --> 00:26:44,150 and then I'll kind of crystallographic you, then I'll show you mathematically how they look at. 259 00:26:45,810 --> 00:26:53,910 So what point about this tilting, this trimer ization is let's say I decide to try MRI's about this point, which I called Alpha. 260 00:26:54,270 --> 00:26:58,800 So I tilt this oxygen outwards and this oxygen outwards in this option outwards around alpha. 261 00:26:59,460 --> 00:27:03,120 If I choose Alpha as my origin for the tilting in the crystal structure, 262 00:27:03,540 --> 00:27:09,360 then you can see straightforwardly that I can choose the Saturn beta as my origin. 263 00:27:09,390 --> 00:27:14,040 Because if I don't, you might tell me my origin. This oxygen would have to tilt up and left. 264 00:27:14,040 --> 00:27:21,390 And I've already, if you like, used it up, tilting up and right. And likewise, I can't choose Gamma as my origin if I've already chosen Alpha. 265 00:27:21,660 --> 00:27:27,239 So I have three possible origins which I can choose for this, this tilting. 266 00:27:27,240 --> 00:27:34,830 So this already gives me three three domains, three symmetry equivalent options for the for the low symmetry state. 267 00:27:37,440 --> 00:27:41,310 You might be thinking, well, I don't have to tilt out. What's your right? I could also tilt inwards. 268 00:27:41,670 --> 00:27:47,460 And so that gives me now six equivalent tilt things like a tilt in or I could tilt out at any of three origins. 269 00:27:48,060 --> 00:27:53,340 And this is rather convenient because if I tilt out then the yttrium iron that 270 00:27:53,340 --> 00:27:58,049 was sitting on top of this hole drops down to fill the space that I've made, 271 00:27:58,050 --> 00:28:02,220 and that will give me one orientation of my ferroelectric polarisation. 272 00:28:03,060 --> 00:28:09,850 Whereas if I tilt inwards, the yttrium iron that was sitting here in the power electric structure has to shuffle up to get out of the way. 273 00:28:09,870 --> 00:28:13,680 So this gives me the opposite origin of my ferroelectric polarisation. 274 00:28:14,010 --> 00:28:17,850 So I have six possible minima in my symmetry load state. 275 00:28:19,170 --> 00:28:24,300 And these are, if you like, a coupled to two opposite polarisations. 276 00:28:24,630 --> 00:28:28,230 And if one looks in detail at the symmetry, one finds that. 277 00:28:30,350 --> 00:28:32,300 Always this will this will always alternate. 278 00:28:32,540 --> 00:28:38,630 So immediately, I can understand this domain structure, this ferroelectric domain structure that I showed you right at the start. 279 00:28:38,660 --> 00:28:44,180 So again, this is the piece of force microscopy image of of yttrium magnet and the black and 280 00:28:44,180 --> 00:28:49,370 white regions correspond to opposite orientations of the for electric polarisation. 281 00:28:50,150 --> 00:28:53,830 What you can't see as a force microscopy is the origin of the tilting. 282 00:28:53,840 --> 00:28:57,380 This is not a parameter that shows up when you measure only the polarisation. 283 00:28:57,680 --> 00:29:04,190 But what you see is that there are always six domains of alternating polarisation that are meeting at a point. 284 00:29:09,130 --> 00:29:14,620 I should emphasise, I should point out also this of course is a two dimensional slice through the through the structure, it's the surface. 285 00:29:14,920 --> 00:29:21,549 And so the fact that these are meeting at a at a point, if one were to look in three dimensions, these are actually line defects. 286 00:29:21,550 --> 00:29:27,010 So these are going to be my strings. I'll come back to that in a second. Okay. 287 00:29:27,010 --> 00:29:31,540 So that's very hand-waving and qualitative, if you like, looking at atoms and crystal structures. 288 00:29:31,870 --> 00:29:42,909 One can also, of course, really make a symmetry analysis and write down the land of free energy as a function of the amplitude, 289 00:29:42,910 --> 00:29:45,910 of the tilting and the angle of the tilting. 290 00:29:46,120 --> 00:29:50,199 So here's my order parameter, which is a combination of the amplitude and the angle of the tilting, 291 00:29:50,200 --> 00:29:57,820 which is how pointed out is a two dimensional order parameter, which allows me then to have the Mexican hat type type potential. 292 00:29:58,960 --> 00:30:01,060 Okay. So this is this is this is what it looks like. 293 00:30:01,270 --> 00:30:07,149 And let me not go through the through the the details of the mathematics, but show you how it looks. 294 00:30:07,150 --> 00:30:13,660 If I actually plot this with these parameters all determined from electronic structure calculations. 295 00:30:14,500 --> 00:30:20,950 And so this is the plot of my energy is a function of as I come out from the middle. 296 00:30:22,410 --> 00:30:29,160 Q So the amplitude of the tilting as I come out from the middle. And as I go around the hat, the angle of the tilting. 297 00:30:30,030 --> 00:30:36,270 And what you can see is that my phase transition is described by a potential which I'd say is rather Mexican hat. 298 00:30:36,280 --> 00:30:43,110 Like it's not a perfect Mexican hat because it's a structural phase transition in a system that has six fold symmetry. 299 00:30:43,180 --> 00:30:48,930 And if the crystal structure has six fold symmetry, then that has to show up in the potential. 300 00:30:49,170 --> 00:30:57,170 And it does show up in the fact that there are six minima. So when I get to to the to the ground state, my potential has six minima. 301 00:30:57,390 --> 00:31:08,070 And so there's, there's a gradual crossover from the Z six symmetry of the ground state to an almost you one like symmetry at higher temperature. 302 00:31:08,070 --> 00:31:13,559 And you can see if you look in the in the expression that the fi dependence is coming it 303 00:31:13,560 --> 00:31:21,900 only at the angle dependence comes in only very high powers of of the tilting amplitude. 304 00:31:23,270 --> 00:31:26,690 So one might think, well, really what we wanted was a mexican hat potential. 305 00:31:26,690 --> 00:31:28,160 So this is really not perfect. 306 00:31:28,460 --> 00:31:35,930 But actually the fact that this is not a perfect Mexican hat is very convenient for us because it allows us to actually be able to rather, 307 00:31:35,930 --> 00:31:41,090 simply, rather trivially measure the defects when they form. 308 00:31:42,430 --> 00:31:53,680 So remember my six minimum I my six ground states have alternating orientations of the four electric polarisation and so. 309 00:31:55,210 --> 00:32:00,610 If I paint my alternating orientations black and white, corresponding to up and down polarisation, 310 00:32:02,590 --> 00:32:09,549 I can image the formation of the domain intersections, the formation of the defects using force microscopy. 311 00:32:09,550 --> 00:32:16,160 So this picture was taken by Martin Lilian Blum, who's a Ph.D. student in the and the group of of Manfred Physics. 312 00:32:16,930 --> 00:32:25,750 We have some related materials that have much closer that have basically a perfect Mexican hat type potential for a similar phase transition. 313 00:32:26,110 --> 00:32:31,989 And they're, of course, aesthetically, it's rather pleasing because it's really a an equivalent to the great unification transition, 314 00:32:31,990 --> 00:32:35,950 but then we can't measure the domain. And so this is this is rather helpful. 315 00:32:39,590 --> 00:32:47,300 So the meeting points to these ferroelectric domains, which look like points on this on this intersection are, in fact, one dimensional strings. 316 00:32:47,570 --> 00:32:53,890 This is a 3D simulation just of the of the potential energy I just just showed you. 317 00:32:53,900 --> 00:32:59,180 And you see that the the straight the the domain intersections are marked in red. 318 00:32:59,480 --> 00:33:05,090 And you can see a remarkable resemblance to the simulation of the early universe that I showed you right at the start, 319 00:33:05,090 --> 00:33:10,010 because essentially it's simulating the same potential with smaller small changes at low energy. 320 00:33:10,940 --> 00:33:16,370 We try very hard to image these strings in the in the real, real material. 321 00:33:16,370 --> 00:33:21,799 We have samples that we if anybody has an idea for how to do this directly, experimentally, we have many samples. 322 00:33:21,800 --> 00:33:30,680 We'll be very happy to send you. If you would like to like to try, it'd be really fun, I think, just to see them really experimentally in real life. 323 00:33:35,810 --> 00:33:42,110 Okay. So hopefully I can convince you then that the structural phase transition in multiple 324 00:33:42,110 --> 00:33:46,189 rocketry of mechanised provides us with an analogue to the grand unification transition. 325 00:33:46,190 --> 00:33:53,839 So in the early universe, the transition from the high symmetry vacuum to the low symmetry vacuum described by a mexican 326 00:33:53,840 --> 00:34:00,319 had potential forming cosmic strings and yttrium manganese at the transition between the High 327 00:34:00,320 --> 00:34:05,960 Symmetry Space Group to the low symmetry space group described by a mexican hat like potential 328 00:34:06,200 --> 00:34:12,620 with these six minima in the ground state that allow us to image our cosmic string analogues. 329 00:34:12,620 --> 00:34:22,880 So we have our we have our our material, our little cosmic string formation simulator, which we now go to the laboratory and to do measurements on. 330 00:34:24,980 --> 00:34:27,690 So what experiment would we like to do on the early universe? 331 00:34:27,710 --> 00:34:36,470 Then we'd like to expand it at different rates and cross the grand unification transition and see how many cosmic streams form in each case. 332 00:34:36,500 --> 00:34:41,000 So this would be it would allow us to test the so-called triple direct scaling. 333 00:34:41,480 --> 00:34:46,730 And since we can't do that, but we now have our our little cosmic stream formation simulator. 334 00:34:47,180 --> 00:34:56,510 Instead, we cool it. We're Mennonite a different race through the structural phase transition and we count how many domain intersections form. 335 00:34:57,020 --> 00:35:01,549 So here are two pictures of cooling yttrium manganese through the structural 336 00:35:01,550 --> 00:35:05,720 phase transition and the subsequent at different rates and the subsequent. 337 00:35:07,860 --> 00:35:13,799 PSA force microscopy images. And I want to emphasise that the scale bar is four microns. 338 00:35:13,800 --> 00:35:16,260 In each case. I didn't just take one of them and blow them up, 339 00:35:16,680 --> 00:35:22,140 although if I had he would not be able to tell the difference because they're they're they're self, self similar. 340 00:35:22,710 --> 00:35:30,150 And we got extremely lucky with yttrium manganese because these three images correspond to. 341 00:35:31,840 --> 00:35:36,610 Cooling through the transition by just switching off the furnace and leaving the sample in there, 342 00:35:37,120 --> 00:35:42,819 cooling through the transition by taking the sample out of the furnace and leaving it on the lab bench and cooling 343 00:35:42,820 --> 00:35:46,780 through the transition by taking the sample out of the furnace and putting it putting it in liquid nitrogen. 344 00:35:46,790 --> 00:35:51,610 So these are, if you like, the three most experimentally accessible cooling rates. 345 00:35:51,940 --> 00:36:00,880 And you can see that they give really distinctly different domain sizes and distinctly different concentrations of cosmic stream analogues. 346 00:36:01,210 --> 00:36:03,610 We were, of course, not the first people to have tried this. 347 00:36:03,610 --> 00:36:09,700 It's a very intriguing game to play, to try to use condensed matter systems to to replicate them, 348 00:36:11,440 --> 00:36:19,240 to replicate behaviours in other kinds of physics, but to get all of the factors to come together, to get the right kind of physics of your, 349 00:36:20,350 --> 00:36:23,170 have your transition, to get the right potential describing your transition, 350 00:36:23,530 --> 00:36:29,110 and then to get all the parameters right so you could actually access cooling rights that give you that gives you different results. 351 00:36:29,350 --> 00:36:33,759 One has to be extraordinarily lucky for those things to come together, I think. Okay. 352 00:36:33,760 --> 00:36:34,720 So then we have a, of course, 353 00:36:35,380 --> 00:36:42,330 a first year undergraduate research student sit and count how many germane intersections one gets in each different coding. 354 00:36:42,340 --> 00:36:49,120 Right. And we can then really go test this predicted Zurich scaling off of the defect information. 355 00:36:50,980 --> 00:36:53,980 Okay. So remember the domain size, the properties that it depends on. 356 00:36:53,980 --> 00:37:00,070 It depends on the zero temperature correlation length, which in a thorough electric is usually equated with this domain wall width. 357 00:37:01,380 --> 00:37:06,630 And this is something which at the time we we calculated my postdoc at the time, Joachim, 358 00:37:06,630 --> 00:37:13,740 a guy who's now a assistant professor in Kyoto University, made a big box of victory. 359 00:37:13,740 --> 00:37:23,160 A man tonight in the computer made to do domains and let the structure relax and measured how wide the intersection between the domains was. 360 00:37:23,610 --> 00:37:27,540 And this is very interesting. The domain, Woolworths was basically vanishing. 361 00:37:27,540 --> 00:37:31,799 It was a very abrupt transition from one ferroelectric domain to the next. 362 00:37:31,800 --> 00:37:36,000 This has since been confirmed with high resolution transmission, electron microscopy. 363 00:37:37,480 --> 00:37:44,100 The zero temperature relaxation time. This is, I'd say, rather obvious what one should use for this. 364 00:37:44,100 --> 00:37:50,700 We we took our zero temperature correlation length and divided by the speed of sound, 365 00:37:50,700 --> 00:38:00,330 which we also calculated from density functional theory we can discuss later whether that's the best measure of the relaxation time, 366 00:38:01,530 --> 00:38:02,850 the critical exponents. 367 00:38:04,430 --> 00:38:13,220 We used in that data I'm going to show you we we we use a ratio of 0.58 which which one sees from Monte Carlo simulations for 3D X Y model. 368 00:38:13,580 --> 00:38:19,549 And this is the number which one obtains for a fluctuation dominated transition. 369 00:38:19,550 --> 00:38:23,510 And again, I'll come back to that to discuss whether that's valid later. 370 00:38:23,510 --> 00:38:27,530 If one uses point five, that would describe a mean field type transition. 371 00:38:28,420 --> 00:38:33,280 And then the last parameter here t c the critical temperature divided by the cooling. 372 00:38:33,490 --> 00:38:36,610 The critical temperature we know from experimentally. And the cooling. Right. 373 00:38:36,610 --> 00:38:41,589 This is a thing we vary. So what we're what we want to calculate is d is a function of of cooling. 374 00:38:41,590 --> 00:38:45,950 Right. Okay. 375 00:38:46,700 --> 00:38:50,120 So then we can do that. We can calculate the vortex density as a function of, of cooling. 376 00:38:50,120 --> 00:39:02,630 Right. And this is what we find. So the red line is our calculations with a, a zero temperature correlation length of 0.06 angstroms. 377 00:39:02,930 --> 00:39:08,089 So this, if you like, was a fit. I told you that our domain wall, which was basically very close to zero. 378 00:39:08,090 --> 00:39:15,200 And so we just basically adjusted this line and that 0.06, it fits rather well with the data, which is the red point. 379 00:39:15,200 --> 00:39:22,099 So these are measured by two different groups by my colleague Mensa thebig and the group of Sang Chong in in Raqqa. 380 00:39:22,100 --> 00:39:26,479 So you can see that there's really a remarkable agreement. So we were very happy for a while. 381 00:39:26,480 --> 00:39:32,809 We thought we were we're still very happy, I guess, but we were even more happy for a while because we really thought we have the 382 00:39:32,810 --> 00:39:41,060 first solid state verification of cables are scaling in a in a real material. 383 00:39:42,340 --> 00:39:45,729 Which is really remarkable if you think about all the junk that exists in a real 384 00:39:45,730 --> 00:39:50,130 material to actually get some real fundamental physics scaling physics out as is, 385 00:39:50,140 --> 00:39:58,100 I think, really, really surprising. Oh, she made me point out here that if we taken a critical exponent of point five rather than .58, 386 00:39:58,400 --> 00:40:01,730 I would say that it gives it more or less equally good fit on the scale. 387 00:40:01,740 --> 00:40:05,780 It's not so clear that that this has to be fluctuation dominated. 388 00:40:07,100 --> 00:40:14,780 Okay. So we were extremely happy for a while and then we got intrigued that things were not as straightforward as we thought. 389 00:40:15,320 --> 00:40:22,940 So when my colleague Manfred Seaburg went and took more data at lower cooling rates and at higher cooling rates, 390 00:40:23,210 --> 00:40:26,900 we found some deviations from the expected people's direct scaling behaviour. 391 00:40:27,140 --> 00:40:30,380 And again, maybe this we should think this makes us more happy because we still have something to do. 392 00:40:30,710 --> 00:40:38,360 So these are very, very slow, slow cooling rates is a 100th of a kelvin per minute. 393 00:40:38,360 --> 00:40:46,790 This is extremely slow. And what Martin, the student of Manfred, has been studying is that we think when one calls this slowly, 394 00:40:47,030 --> 00:40:51,679 that one actually has annihilation of the domain walls, 395 00:40:51,680 --> 00:40:56,390 that we actually have a drop off from Kepler's direct behaviour because the domains are growing, 396 00:40:57,080 --> 00:41:01,880 because the, the, the strings are starting to meet and annihilate each other. 397 00:41:02,180 --> 00:41:05,749 And the reason that we think we have a difference between these two data sets is because these 398 00:41:05,750 --> 00:41:11,360 samples have grown under different conditions in which they have more real physical defects. 399 00:41:11,360 --> 00:41:13,819 And this gives the domain walls much higher mobility. 400 00:41:13,820 --> 00:41:22,100 So, Martin, in so many tests in this region and so we think we very much understand this behaviour and this deviation from people's direct behaviour. 401 00:41:23,690 --> 00:41:30,920 The deviation and fast cooling is much more. Its explanation is proving much more elusive, shall I say? 402 00:41:31,490 --> 00:41:36,649 And I say we still don't know for sure whether this is something intrinsic physics, 403 00:41:36,650 --> 00:41:42,800 whether we've really discovered some antique people Zurich or beyond people's behaviour or it's something just with the. 404 00:41:44,780 --> 00:41:55,940 At these very fast cooling rates we can't expect. We can't expect really to be able to to to study any intrinsic physics at all. 405 00:41:56,810 --> 00:42:01,490 We also find an extremely unexpected dependence on the chemistry. 406 00:42:01,730 --> 00:42:06,290 So the initial data I showed you were for urban manganese, then the initial data set. 407 00:42:06,290 --> 00:42:11,390 These all have exactly the same crystal structure, exactly the same type of phase transition, very similar. 408 00:42:11,570 --> 00:42:14,600 They should have very similar correlation then similar speeds of sound, 409 00:42:14,900 --> 00:42:20,450 nothing that would expect us to have attended the full difference in vortex density for the same cooling rate. 410 00:42:20,720 --> 00:42:27,530 So this is something that's definitely not captured by standard people's direct theory and we really don't understand at all. 411 00:42:28,040 --> 00:42:31,720 So I guess this young this is what we should be happy about because it keeps us busy. 412 00:42:31,730 --> 00:42:35,630 This is not the Ph.D. student of the of the next student to work on this project. 413 00:42:36,020 --> 00:42:40,159 Quintin Meyer So we try to understand what causes this chemistry dependence. 414 00:42:40,160 --> 00:42:44,450 Is it something fundamental or is it just something in the processing of the different materials? 415 00:42:45,470 --> 00:42:52,700 What's the origin of the turn around? Is there really some physics in this beyond people Zurich regime? 416 00:42:52,910 --> 00:42:56,460 And I'd say the answer to that is that we don't know. 417 00:42:56,480 --> 00:43:00,350 We certainly don't know whether it's relevant for early universe behaviour. 418 00:43:00,560 --> 00:43:10,459 But in the last couple of minutes let me just show you our current favourite idea for why this turnover might be happening. 419 00:43:10,460 --> 00:43:17,930 And I think that we have many other ideas, but none of them do we have really any any reason to believe is is correct. 420 00:43:18,890 --> 00:43:26,260 So what I think would be rather charming is if one had a crossover from fluctuation dominated cable, 421 00:43:26,330 --> 00:43:31,309 Zurich, which has an exponent of 0.58 to mean field dominated Zurich. 422 00:43:31,310 --> 00:43:37,459 So this would be scale regions with different slopes. And one could convince oneself that perhaps as the cooling rate gets faster, 423 00:43:37,460 --> 00:43:42,670 one would move from a fluctuation dominated regime to a mean field dominated regime and so on. 424 00:43:42,680 --> 00:43:46,920 And then to get between these two slopes, one would have to drop down in between. 425 00:43:47,270 --> 00:43:54,980 And this might explain our turnover. So now we try to cool it really very fast rates to see if we see a turn around again, which would verify this. 426 00:43:55,430 --> 00:43:59,540 This I wouldn't even call a model. It's a kind of idea. 427 00:44:01,420 --> 00:44:05,440 But I have yet no basis for thinking this is particularly correct. 428 00:44:07,780 --> 00:44:18,620 Good. So then let me summarise. We think that yttrium manganese, it seems to provide the first example of zurek scaling in a condensed matter system. 429 00:44:18,620 --> 00:44:23,390 And that cosmologist got it right. Cosmic strings, if they exist at all form the way they think. 430 00:44:24,350 --> 00:44:30,350 Hopefully I've persuaded you that the use of real materials to explore questions in cosmology is really a lot of fun. 431 00:44:31,070 --> 00:44:38,570 I like this article in The Economist now is a few years ago there was a quote from Cliff Burgess, who's a theoretician at the Perimeter Institute. 432 00:44:39,380 --> 00:44:45,590 He has his doubts that we do anything useful, but he thinks the experiments are worth pursuing, like tap dancing snakes. 433 00:44:45,590 --> 00:44:48,920 He says. The point is not that they do it well, but that they do it at all. 434 00:44:49,820 --> 00:44:53,480 So thanks a lot for listening and I'll be happy to take any questions or comments you have.