 listed in this box. And I had a lot of pleasure to work with experimentalist within U of T as well as outside U of T. Summer works are not related to Gitae, but it was going through the summer places in Japan and thinking about spinovic coupling and how the correlations combined effect appears and that's about 10 years ago. So I listed some of those who were kind of motivate me to start thinking about this area. Natasha and I are writing us some review articles, hopefully we'll finish in a month. No push, but we will hopefully have some review article on this part as well. Okay, so let's begin something that we all very familiar with. I'll be talking about the spin model. I just want to remind you that the basically a magnetism is nothing but the quantum physics and the electron-electron interactions. And we'll be talking more in the honeycomb lattice. So we all know that you go through the hopping process and the exchange and that'll give us exchange interaction. We open folder J and we end up with Heisenberg interactions, which si is that si.sj. So those spin interactions, we open think about just the single orbital and no spinovic coupling and that's because they are dominant in the most material, but in certain situations that may not be the case. So you can see that it's actually SU2 and that's coming from the Hubbard interaction, which has very high symmetry and then we have single orbital and no spinovic coupling. When orbital angular momentum as well as spins are not conserved due to the spinovic coupling, of course we have this general form of the Hamiltonian which are now written in terms of three by three matrix and symmetry of the model will constrain the matrix element because the hopping is some of them are allowed by the symmetry of the lattice and that one is going to restrict which part of matrix element of finite and some as zero. Of course they are not sufficient to understand why one term is larger over the other. So we'll have to go through some microscopics to tell in under what condition we will have certain interaction become dominant over the others. So that's why we are working on this microscopic theory. Okay, so before I go into the microscopic theory of the Gitaev, I haven't even got into you my outline. In fact, these are all still on the introduction. I just want to remind you about the Heisenbaum model. If you open up the textbook, for example, you can in fact think about the spin half Heisenbaum model in terms of the bone singlet. So here you can see that IJ which define with a singlet and I use this bond with the blue, recovering the singlet and one can introduce the bond operator which I'll call the QIJ here and you write down the SI-SJ Heisenbaum interaction in terms of the half minus two of the SI.SJ and that will be on my bond operator here and one can show that if you operate the QIJ on an IJ bond here and that will generate some constant eigenvalues here with IJ. So that means it's an eigen operator for the bond singlet and if you have two bonds here, which is the JK with IJ and KL, in fact, that will switch the bond. So that's exactly this resonating between two so-called Ruhmer diagrams, Q2I acting on this two-bond product of the two-bond singlets will generate the other two bond singlets. So that's nice because one can work it out the ground state of this resonant balance model and if I have a full-size problem, one can show that in fact my ground state of this bond singlet is actually at the ground state of this Heisenbaum model. One can show that in fact that it's a well combination of the two possible singlets and therefore the local order parameter here is a zero. On the other hand, one do develop the anti-ferro correlations by looking at SI as two and then say Z correlator. One can show that this is exactly a minus one over six. Okay, so that's nice but one can also extend to the bigger size. You can work on the A side and so on and so forth and then extend to a bigger size this LVB with the different lengths of the Ruhmer diagrams start to show up and the probability of finding these longer ones in fact one can show it's smaller than the shorter ones and so on. One can cover entire lattice with the bond singlet. However, and the degeneracy of this type of the linear combination of bond singlet in fact grows to the two to the end. So it's a thermodynamic growth. So that's basically as you know well the field and this is a proposal of the LVB in the demands on higher than the one. So it's a two-dimensional LVB was based on this ideas but unfortunately if you have a skill artist in the thermodynamic limits in fact that this continuous symmetry breaking occurs and this is why we know that the magnetic ordering appears. In other words anti-ferromagnetic ordering it's a SIS. The expectation value will take this form of the sub lattice magnetic order. Okay, good. So since then just back to 1973 the quantum spin liquid again you know higher dimensions to the in particular has been a lot of interest and many of us has been working for finding both theoretically as well as experimentally and the real materials etc. So the idea or concept has developed drastically as well because it's not only a disorder state we have learned that in fact that there will have well actually we knew that there has been fractionalized extations but concept of long-ranging tanglement is rather new so kind of modern concept. Okay so as we discussed that the skill artist is in fact has anti-ferromagnetic order but because of that idea in the back and still alive is that you can use the geometric of frustration to avoid the magnetic ordering and that's why we study like a triangle lattice or gargoyle lattice or tetrahedrons and many of those frustrations avoiding the magnetic order set by the Heisenbaum order. Okay and those frosty magnets insulators they come with many shapes own characters and there are many of those researches are going on and hopefully that and I don't know if you have a I don't think we have one but you can probably hear from many others about this geometrically frustrated magnets. All right on new angle to the frustration you can think about is that instead of having because those geometric frustrations are based on the idea that the Heisenbaum interaction is the one interaction that we are dealing with. On the other hand one can also think about the frustration coming from a different type of the interactions rather than Heisenbaum. So in other words if you have the interaction which depends on the bond like here honeycomb lattice has X bond, Y bond and Z bond these are colored by the red, blue and green and if each of the bond has a different interactions and spins is doesn't know where to point and that will in fact generate the frustrations and this is another way to get a quantum spin like this and that's precisely the idea from the Gitaev. So Gitaev interaction is nothing but bond dependent ising interactions with the strengths of the K here S gamma gamma gamma depends on the bond so XYZ here Z is the Z Z and X is the X X and Y bond has the Y Y. All right and the graphical representation of Hamiltonian these are all from the Gitaev's original paper you can check it out with this original paper which is really a nice one of the beautiful paper that I would strongly recommend. So you can write down the spin here in terms of the two myaranis with the B gamma and C both are myaranis and of course once you write this in terms of spinning to the two myaranis the Hilbert space is enlarged and therefore one has to bring back to the physical Hilbert space which are written in terms of D here D is going to be a product of D myaranis the B X B Y B Z with a C myaranis and if you propose this condition to apply the state and back to its own state that's the bring back to the physical space so that's basically a gaze field that comes in and once you do that Hamiltonian can be written in terms of this C myaranis with the product of this U IJ and U IJ is a product of this B myaranis and one can show that the ground state which a product of U IJ going along this bond and open this up called the flux operator WP one can show that the ground state is having all WP being a one and once that become number become a constant here is this one become a constant we end up with a bico-radic Hamiltonian with a C that's C C there and therefore one can solve it exactly and that's what guitar did and the ground state is known to be a guitar spin liquid and emulsion particle becomes myaraniformium which is a C and then the bisone or called the WP here G2 quantum vortex here which will take either press one or minus one okay so far so good then smoking on experiment signature will be also from the guitar's original paper here is going to be the half integer quantized the thermal hole conductivities and that one he has shown that using the time reversal brocon symmetry here time reversal brocon symmetry Hamiltonian here which is HX, HY, HZ with sigma is basically as X, S, Y, S, Z I just want to point it out here because this one is not a German field but you are breaking them by putting time reversal breaking come here so that's one thing we'll come back okay good all right so now guitar material so so really good so the pure guitar interactions in fact is going to give us a guitar spin liquid but in real material again the problem is that we are not only having a guitar interaction but it will have other interactions so the way that I'm going to define the guitar material is that where the guitar interaction is the largest interaction in the full Hamiltonian okay so we say guitar material does not mean that we just have a guitar interaction it's just the largest interaction in the full Hamiltonian and it's not easy to satisfy the condition by the way so one thing we have to do is that the necessary requirement is not even sufficient because even we have all these conditions we may not end up with the guitar material the open happens to be second largest or third largest it is allowed by the symmetry so we know that it's present as long as you know the coupling is there it's there it's just that they are so small that we can simply ignore it and just work on the Heisenberg interaction so the necessary requirement or conditions first of course we need a honeycomb mult insulator with a strong electron-electron interaction and that reason the transition metal would be a good candidate and the bone dependent spin interaction requires a multi orbital because remember that the one has to change the angular momentum as well as spin through the spin of your coupling to generate to those such a bone dependent interaction and avoided Heisenberg interaction so that's the and honeycomb is bipartyl lattice therefore if you have a Heisenberg model it'll be just up down up down will end up with anti-baromagnet and so we do need the different types of interaction to generate the frustrations and end up with some long you know searching you know the spin liquid that we've been searching for quite a long time okay so the candidate material that was suggested in the very early days so was back in here in fact this is the iridate which stacked honeycomb iridate with offside and then a few days later it was alpha-routinium criteria that U of Toronto group has been first suggested and that would be a really a good candidate even better than the iridate due to the different stacking here it's a more two-dimensional but of course in real life all of candidate that we have suggest so far all have magnetic ordering at low temperature okay none of them is disordered disordered meaning not like due to the imperfection of the lattice it's just a real quantum disorder so the magnetic ordering at low temperature meaning that we have non-github interaction present in the material in real solid-state material so the question is that what's their walls that's the what I'm going to address so here's my outline so yeah please yeah yep uh no you yes so it's actually coming so when I'm coming talking so the question was that the whether the github interaction is largest in a full Hamiltonian does not does mean that the when you project into the spinning spin space or whatever the lowest state that I'm going to be interested in generate only the github interaction and then forget about the rest that's not the case so we will I will show you in fact that that's a part of half of my talks I'll show you how the how the microscopically github interactions are generated and when you do that the rest of them follows and we are not going to ignore them okay so this spin sector and yes yes so that's precisely my outline so there'll be a non-github interaction including the Heisenberg interactions and there are other interactions that are also present and the question is what they do do they generate the magnetic order they better to because in real material we do have magnetic order at low temperature right so it's coming so next is that that's precisely my question so I have a two I actually have a two question that I want to address and hopefully that I'll give at least a part of answers on this one question is that the so basically what are the role of non non-github interactions so where the non-github including Heisenberg and in this github materials despite the github is a largest and that's where the microscopic theory will be really helpful and then the second one that I want to address is okay you said a github is a material has a github interaction largest but there are other interactions there and often we have hard time to find it out their size and their size so we like I like to address this one here is that when you have a general spin not just the spin half like a spin one spin three half and so on how to estimate the github interaction based on the symmetry of the Hamiltonian so I'll get back to that and then I'll summarize okay so let's begin the first one a microscopic model role of the non-github interaction in this github materials where other interactions do exist okay open the non-github interactions lead to a magnetic order okay and so Heisenberg will be as I said this is a pipa tylaris it will give you a magnetic ordering so here's a one naive scenario where naturally appears will be that I have increased the non-github interaction so my x-axis is the increase of the non-github interaction and there are more and more than one kind okay but let's think about one kind and that will probably generate the magnetic order at some point here is the pure github model where I represent as ksl meaning github spin liquid will survive of the certain or certain size of non-github interaction but then it'll have magnetic order that's precisely what probably happens in actual systems but a finite temperature of course this github spin liquid it's a 2d with the g2 is not well defined in high finite temperatures so you will have some crossover to a some kind of maximally entangled state and then we'll have this magnetic order which will definitely survive there are some finite temperatures here and therefore we can see that even we have magnetic order if you are close by the github spin liquid a finite temperature will see the some kind of feature of the github physics because it has the largest interactions yes question rachel repeat what is known about the quantum phase transition between so here we go please repeat the question yeah so the question was that the what is known about the quantum phase transition between the github spin liquid and the magnetic order so here's my quantum phase transition t equal zero which is now this axis here and I put some parameter which is actual parameter that we can access in the lab which is basically a magnetic field so I applied the magnetic field I put a question mark so that's precisely that we are looking for and numerical calculation which unfortunately well actually I have some numerical calculations so that I will show you that this github spin liquid can be extended at a certain magnetic field that depends on the sign of the github interactions if you have ferro github interactions it is very very small magnetic field is actually detrimental like two percent of magnetic field in terms of github strength so you will kill the github spin liquid and then how that is extended under above this magnetic ordering is unknown yet okay and then it'll be linked to the current experiment of this famous domo hall so I'll bring back there again but yes that's the sum of questions that arise and this might also depends on not only the sign of github interaction but also depends on the direction of the magnetic field because recall that the what github's this interaction here you see that the why the form of the non-time reversal breaking symmetry time reversal symmetry breaking time has been added the way that hx, hy, hs this one here sx, sy, ss in the quantization axis that we are using it's going to be perpendicular to the honeycomb direction so that is the direction which is out of the honeycomb plane and that means that if you put a field within the plane this form is going to change and things is different so you're not going to open up the here what you're putting this time reversal symmetry breaking term one is going to get out the c-myaranus that I defined and then you'll get the so-called non-Avellian anions and that c-myaranus is the one that you know kept out meaning that you will have a propagating mode at the etch of this etch of this the honeycomb and that is responsible for this half quantized domo hall and why it's half because it's a half of the complex form of myaranus half so that's where that's coming from yep just to follow up on my question my question was what is known about the nature of the quality phase condition for example is it in the eisen universe out in class is there any element of deep and fine criticality taking place there is nothing known like your answer I suspect nothing is known yeah the answer is still looking for it yeah the question was that see what is the nature of the quantum phase transition known in this one here in other words is that the quantum criticality or is that some posse transition and so and it's not known it's numerically has a lot of studies but again that suffered from a finite size and so I wouldn't bet that going to either first or second at this stage so there's a strong question mark here and on the other hand I'm going to actually say even a little more radical here that not always this non-github interaction leads to the magnetic ordering it might have been that this depending on the what's the non-github interaction that I'm adding it it might have its own character so here's another proposal that I had stuck with the github spin liquid and my you know this non-github interaction is actually another spin liquid in that situation so putting in a finite temperature all of this is going to be all crossover from one to the other spin liquid it's a wild speculation at this point and then there will be as I said there are not one github interaction there are more than one so if I come up with another non-github interaction such as Heisenberg mode Heisenberg interactions I'll generate the magnetic order on some of this in that situation so if I'm in the magnetic order state and increase the temperature here at the low temperature we'll have magnetic order but at high temperature we might show some other spin liquid physics which may may not be the similar to the github spin liquid so that's the another one again T40 quantum phase transition here a very high field of course will have polarized state it's going to be all aligned direction of the field and that will be adiabatically connected to classical polarized state but in the low field there might be something interesting going on and that is again very unknown at this point and as I said if the github and non-github interaction well not if github interaction is on isotropic but non-github interaction can also be on isotropic in this situation this p0 phase diagram will strongly depend on the direction of the field that we are applying in the lab okay um okay so to understand what the type of the non-github interaction we have and there are rules I'm going to go through the little bit of the microscopic model for honeycomb multinsulator with a strong spinoid coupling all right so here is the wave function that I'm going to work on of course one can have different different situations but this is the most well known so I'm going to just review this part it's a bit of old now but j-fective half is the coming from spinoid coupling with with the octahedral environment so if you have an environment which are different then we'll have to start from a different crystal field so we begin with the d orbitals and putting in the cubic crystal we know that from a space group that it's a t2g e g splitted and if I have a d5 I'll fill up the five of electrons in this t2g and then putting on strong spinoid coupling this t2g will act like a effectively angular momentum minus one due to this crystal field and that bring this into the two sub sub end one will be j-fective half and the other will be j-fective three half because I have d5 I'll filling only fill up completely three half here and fill a half of end will be left and formulavel lives in this half of this j-fective half and that's a half bill j-fective half end this was studied actually motivated by the high tc because strontium 2 iridium o4 was the initial multilateral people study and this has an isostructure to the culprit and yeah yes this is from a jennifer evouie and he or she says what do you mean by non pitae ferro magnetic heisenberg or anti ferro it can be heisenberg it can be other bone dependent oh this one is online so I don't have to repeat I repeat the question from the from here yes yeah so when I say the non pitae actually it's widely defined anything different from pitae interaction is all non pitae and the reason I'm going through this is to show you what types of non pitae interaction comes in and which one is dominant we may end up with something very different from non pitae the heisenberg and that's I'm going to introduce the gamma interaction so that is something new okay and the gamma interaction is also frustrated and that's why my second scenario coming in I'm dealing with the one frustrated interaction pitae and another frustrated interaction which is called gamma and then we see what happens between the interplay between the two so it's I'm not defining ferro heisenberg or anti ferro I'm going to come up with something completely new to some of you okay yeah so here is the half field the effective happen as I said this was initially motivated by the high tissue and that's that's where I mean I'm from high tissue too that's why I started thinking about this problem back in like a quite a while ago anyway yeah so starting from here one when you're thinking about the microscopic the first thing we have to identify is a local the onsite my wave function or my my state that I'm dealing with so Z effective half pictorially is is the mixtures of the angular momentum and a spin due to the spin of the coupling you can see that it's mixed with the three equally mixed with the three t2g x y y z and x y x z and color is blue and red represents spin up and spin down and you can see that these arrows are moving around because of this imaginary I well I have to do it twice to the same I'm I'm I'm pointing the arrows in the in the zoom here and then pointing here so my two hands are moving around hopefully I do the good job here yeah so here is the eye here is representing that we have finite angular momentum it's moving in this case one arrow here so you can see that angular momentum one and the zero and that makes the Z effective half and the other half you can get it by time reversal operation so that'll be at the other half with the time reversal operation from up to the bottom okay and that's very important job because I'll show you why okay so that's my way function that I'm dealing with if I'm dealing with the for example spin one or different my way function is going to be different so starting from the local wave function in this case effective half with the mixtures so we'll be telling you the momentum and a spin then now we need to find out the exchange interaction so that exchange interaction for the Heisenberg was nothing but just put a u there and then move the you know electrons up back and forth and I'll generate Heisenberg but here I have multi orbitals I have a 3d2g so what we have to use is going to be this on-site ganamori interaction limited to the t2g if you extend it to the easy one has to worry about little other terms although they are slightly small but in any case we'll be limiting ourselves in the t2g and use this so-called ganamori havers interactions which contains the wounds coupling here and that's quite important and after that what we do is that okay we are going to work on the hoping parameter here just like Heisenberg model hoping from a two-site of hoping back and forth we'll do the hoping hoping from xc yz xy and there are form of hoping parameter here the reason that this is zero here in this one this is hoping between x y to xc or yz xy is 2d looking x y is like this one here it's in the plane while the xc yz are defined on this x yz is defined on the octahedra surrounded by this transition metal okay so this is xz for example and the other is yz here these two xc yz have this so-called t2 hoping here while the other one said zero because of the c2 symmetry going around this bond so that is going to be important as well okay then what you do is that the h effective you can get it from strong coupling expansions that's a well-known formula well-known techniques we basically do in our second order perturbation theory and then that's exactly what we project on the Z-pictive app there was a question that appeared all year so if you do that what happens okay so we are going to do the standard procedure including the t orbitals with a spin over coupling and then going back and forth between the two sides and then project on the z- effective half so that's the procedure all right so if you do the procedure even though it's a z- effective half it's better to think because whooping is made between the orbital so better to think about in terms of their ingredient which is the those orbitals so let's consider the second I'm going to consider only a one bond here which is the represented by red collar here and then moving around the electrons from one side of ruthenium for example to the other side ruthenium and then in the middle there's a p orbital so I'm going to go through this indirect hoping meaning I'm assuming that there's no direct hoping between the xc or xy xy here but it'll be an indirect through the p orbitals sitting in the middle which are probably oxygen or chlorine which are some halogens as well okay so and then we have to do the other bottom here so there'll be a 90 degree x bond sharing here and that's the process we are going to go through so if I expand it to mean that's the picture like this these are lg equal to a one y minus one orbital moving through the pz orbitals here and that is one of the whole thing that dominate all right so then this effective t naught here is going to be this p xc yz which I call t2 square divided by delta pd where delta pd will be atomic potential difference between p orbital and the d orbital that's how I have to pay to go between this two hoping process so if you do that then the hoping the other p orbitals it's called indirect exchange between this one or backwards so I'll have t naught and t naught twice or going through t pd pi security divided by delta pd here this one here and then we end up with some interactions but you see that because xy orbital in this case there's no hoping between them because p z here is a meter odd under the z and minus z so if you remember the wave function over wave function low the top is plus and bottom is minus so the hoping integral is going to be zero due to the meter symmetry between top and bottom of the funicum layers okay so now let's look at this one in here so if I hoping from the exit to the yz here through the pz orbitals though the change of the total angular momentum is going to be press minus two and that's because xz orbital look at this one here wave function of j effective half xz orbitals and we are not going to change the spin because you can change the spin by hoping that can force but orbital is not conserved so you can change the angular momentum so xz is falling into the j effective half and then with down here and then the other one falling into the j effective impact minus half so this hoping process is not going to conserve the angular momentum and therefore jz effective half is also not conserved press minus two by looking at this one can immediately tell that there is no Heisenberg interaction because Heisenberg interaction is too symmetric so I cannot I'm not allowing any Heisenberg interaction so that's why you can get rid of the Heisenberg interaction okay doesn't have to go through bottom and top and cancel it's just the projecting onto the j effective half you will get the zero Heisenberg interaction. Any questions you have from Ahmed Stela? What's the advantage of the Heisenberg model and the Heisenberg model? So that means so Github interaction is not going to give a magnetic order while the Heisenberg interaction will give a magnetic order so if you are interested in the magnetic order one can just study Heisenberg but I'm actually interested in the quantum spin like this so that's why we are interested in the Github interaction yeah and try to avoid the Heisenberg as much as possible and if you look at this process effective half with the p orbital mediated we're actually not going to get the any Heisenberg and by the symmetry so that's a strong statement unless you break the mirror jet symmetry or unless we introduce the direct hoping between the between the between the orbitals so this inter-orbital between this 1d model like x not the 1d orbital xzyz is going to generate only something else not the Heisenberg interaction and so the only way they can generate the pseudo spin interaction is going to go through the intermediate state because remember that the second order of activation we had to go something in the middle and that's something in the middle state is the higher state so we have to include a higher state in the Heisenberg model the higher state is the hobbit interaction so it's a doubly occupied state and you bring it back so t-scale over u where the u is the intermediate state which costs energy of u in this case it's different because we have a multi-orbital intermediate state there are two kinds one is that the one with above all aligned with another one is not all aligned therefore the two intermediate state will differ by the Hoon's coupling so one of them will be uminot g and jh meaning that they are more aligned along the direction gaining the Hoon's coupling and the other is going to have less gain in the Hoon's coupling so we have to take into account this state effective three half state including all this intermediate state and then you project on to the three the half state as i said should include the higher state is equal to three half and that will allow the pseudo spin interaction because you see that delta jz is plus minus two this guy has a plus minus half and i got a plus minus three half from the higher state and that allows to have a the change of the two or minus two so that you can tell oh i need to have this intermediate state going through and then once you work it out then the step on the here will end up with only a set as set and then this type interaction here is going to be proportional to those two difference between the intermediate state this minus sign is important and if you spend Hoon's coupling is smaller than the u then you can see that this will generate the Hoon's coupling linear to the Hoon's coupling so without the Hoon's coupling this term is not not there so that's why i said two conditions so which are necessary one is the spin orbit coupling to generate this state effective half although we write s here this referred to the state effective halfway function here and then we'll just use it for from now on just call it s and another one is a multi orbital with the Hoon's coupling without it there is no guitar interaction so that's how you generate the guitar interaction so as i said if you have only p orbital mediated indirect hoping uh my local wave function is half here and going through back and forth i just to show you that though we've got the scsc here and then what do we do with x bond y bond actually that's rather straightforward and simple we use the symmetry so if you do the c3 symmetry c3 along the c axis c axis is out of play which is one one one in terms of local xyz coordinate the local is this octahedral coordinate xyz so if i do the c3 here then c3 along the one one one out of the plane then as said is going to change the sx and sx change the set that's a cyclic permutation of the spin rotating by 2 pi by 3 so then that's where the guitar interaction is actually coming up here and that one is back to this guineas old paper so 2005 so it's you can get them from most of this in this in these two papers so it's not in fact that this hemitonia itself exists even earlier than the 2009 you can go back to the 2005 of this triangle lattice the bond dependent interaction appears in this paper that i found that on a triangle lattice you can see this abc and written in this form here but you can rewrite them in terms of this form here and then you can see that there's a hydrogen bottom here and then there is this guitar interaction in a one bond and then other bond will have sx sx and then yy and so on so it's coming from much earlier than what we used to know okay now in real material of course we are not just having um p orbital mediated hoping we have direct hoping between the yeah i hear yes the other bond we'll have only at yy here oh that's precisely because this wave function is the same as same as this form in here so if i working on this i work on the z point right and then you work on the z point i end up with ising interaction on z point okay now i work on the x bond when i working on the x bond here um i'm not gonna it's basically your orbital is all rotated by c three so you rotate it and then you will find that the asset is changing as xs xs y so that's why this bond is going to be bond dependent ising interaction and that's precisely the same in here because this paper is on the triangle lattice i don't remember it's a deco or something but in any case and when lambdas you know we coupling is very large but it's a 3d stamp i think it was a 3d it's a cobalt tape here so it's a cobalt tape so it's a cobalt triangle lattice when lambda is big it again back to the z effective halfway function so i'm just showing that historically it was showing it much earlier than even 2009 that the one thing was okay and i'm just rewriting them in terms of this that in this form here will end up with heisenberg and then get type interaction here no one moment okay now in real material of course we are not just setting an indirect hoping we have direct hoping and direct hoping between the x y f y it's a single orbital moving back and forth and that's heisenberg interaction the first one that i introduced so then we have this heisenberg interaction which will be proportional to direct hoping t here differ from the in turn the going through the p orbitals okay and there is another interaction that's a gamma interaction that i just represent earlier there is another way to do it because it's a 90 degree edge sharing so these are not going to appear neither the nor the this gamma interaction is not going to appear in a 180 bond share so here we can do a two process one process is going through the p orbital but i don't have to come back through the p orbital but i can come back to the direct hoping the t so in this case the gamma interaction can be worked it out and then one can show that the in fact that this is going to be proportional to the hoping indirect hoping parameter t not and t and then proportional to the coupling so that one is going to be another bond dependent interaction because jet bond will take s x s y but the x bond will take x z and s y s y and s z and so on okay so here's this nxp model in the 2d outcome i'm just writing on jet bond here again this one bond here and then i just want to remind you that the x y z is this local coordinate jet is the direction to a p orbital where the n ion sitting or ligand chemistry in in that here is the one and then x is another another n ion here and then y is that one this becomes important because we might change the rotate we might rotate the x y z here towards the some abc coordinate which is crystallographic axis okay so we end up with this interaction now microscopic container three terms these are allowed by not only allowed by symmetry but also one can see which one is dominant in under what condition so we have a ket type interaction and gamma interaction and the heizen ball interaction which is bond independent but there are two bond dependent traction so this is another bond dependent interaction it's a jet jet jet bond will take eigen form of this but gamma interaction will take the x y form of this so sex s y as you rotate along the y bond and set bond this x y z will in fact change okay as i said here cyclic from x y z okay so i want to pay a little attention on the gamma interaction it says so i saw alphabeta alphabeta going along x y z bond again jet bond will take a sex s y ket type interaction is bond dependent eising interaction this is bond dependent x y interaction it's a highly frustrated and we don't know the solution yet and we'll just to show you a bit of between what happens between the two later on so when pd orbital this overlap dominate and that we think is the case for the ruthenium trichloride chloride chloride then the ket type interaction is a ferromagnetic i'll go back and show you the science uh because it's rather important later on that the um where that goes i got it too far away so if you have this p orbital dominate here you go here is a minus sign here and then of the rest of them is actually scarce absolute positive so this ket type interaction when the pd orbital dominate that's the only term that opens and it's a ferro isam ferro-ket type okay so it comes as a ferro-ket type interaction and then the gamma interaction is actually anti ferro in that case and then it's both of them are much bigger than the heisenberg interaction so that's where we end up with the ket type material with the non-ket type there are two kinds one is the gamma and there is a heisenberg there are two types of non-ket type interaction and there are also different okay so now before we go into the what they do yes no x y is also degenerate yes i'll repeat the question right so uh sree was asking whether i am assuming the uh among the t2z whether the x c and y is only degenerate and x y is non-degenerate in the local uh local basis uh they are actually all degenerate yes yes so the question is that whether that is only true when the otomix-vinovic coupling is the biggest that's true so if you are taking if you ignore the trigonal distortion like a small distortion which always a present in real material then uh those trigonal field will come in and x c and y is it was in this case the trigonal field is within the honeycomb so in fact uh it's not going to be x c y z which uh degenerate and x y is the split it that will happen in a tetragonal the the scare otromby or tetragonal situation in this situation it'll decouple it'll the degeneracy will appear again three uh three states will be split in a two one but they're going to be easy prime and a one g so that's split by the trigonal field and assuming this trigonal field is rather small which is a case in the ruthenium for example in the 4d otomix-vinovic coupling is about 400 m eb trigonal field is like a order of 10 m eb or something so in that situation you can still think about this is still degenerate yeah and trigonal field actually rather important later on because it allows them additional non-retail interest okay so before I go into the uh what they do just uh you know now we are working on the uh the three uh three interaction terms um Heisenberg Gitaev and the gamma and uh before we go into what are the phase diagram people zero phase diagram it's useful to go get back to the hidden symmetry because uh if you can change this Hamiltonian into some um some Heisenberg types so we know where the magnetic ordering appears so here is the phase diagram which are drawn in a circle here and uh the way that's oriented um you can see that the zeta is zero in the center and then moving towards the boundary of the circle is going to be set up high by two and the cosine zeta is the gamma and sine zeta take the j and k that means that in the center of the circle is a pure gamma and outside the boundary here is going to be k and Heisenberg okay Gitaev and Heisenberg is boundary here and then the at the middle angle the phi is going to take the ratio between the Gitaev and Heisenberg so here is an anti-ferro Heisenberg here is the anti-ferro gamma on the north pole here and then the uh to the left here is one of the ferro Heisenberg south pole here is one of the ferro Gitaev interactions now the dots are here is the where the two symmetry occurs so we know that Heisenberg here is the Heisenberg of course two Heisenberg point is again Heisenberg model so we know that anti-ferro-ferro appears on this left and right but if you look at zigzag here and then uh vortex here these are the hidden SU2 symmetric symmetric point so in other words if you do the force of lattice or six sub lattice transformation something like this uh it's a one of example of the t4 meaning force of lattice transformation from each of the side one two three four uh doing this transformation here will map to the uh this model uh become a SU2 Heisenberg so that will corresponds to this uh site here k equal minus 2j and gamma is zero is going to be SU2 symmetric again after this transformation and this transformation requires the force site that means magnetic order will have at least force site uh have to be repeated and that means that's exactly a zigzag order so that's how the zigzag appears zigzag here is going to be force site uh two blues and two red and that'll be my unit cell and then vortex state requires to have uh six sub lattice transformation and that's again k equal to gamma and that's the where the SU2 occurs so when the k type and gamma comes the same sign of each of them just kills the frustration to each other and then we are back to the SU2 symmetric Heisenberg so that'll be our order state so these are the place and then there's a stripy here you can do the dual transformation and that will be a stripy and that's exactly also mapped so there are few points other than the Heisenberg actual pure Heisenberg we know that magnetic order will appear so that he this metric will help us to identify full phase diagram and that's uh uh let's do that uh so here is again that's the big stars so the where we know that magnetic order should appear and then i'm going to lay out this with the 24 site ED calculation uh and you can see that indeed uh this is uh large space space is occupied by anti-ferro and then large space space anti occupied by ferro and then here is a zigzag and here is a stripy and here is 120 uh vortex state that appears so we know those are the magnetic order state and then the rest of them that does not seem to have magnetic order clearly within this 24 site cluster is this area uh here the the red color here and also before you look at that of course github here is not going to be a point it occupies small phase space and then plus github and ferro github here is going to be extremely narrow but we have this github spin like it does exist in our narrow phase space x here is going to be something very uh disordered and uh in fact most of the material that i have said uh is falling into here ferro github anti-ferro gamma i'm showing only our anti-ferro gamma here remember the cosine set up is a zero pi by two so we are taking only a positive gamma because that's more relevant to the actual situation okay so all this material with additional interaction which are allowed by the symmetry of course you can have stout nearest neighbor and so on second nearest neighbor and so on and they are going to be there too okay and i said that well this falling into you just said that this falling into the actual material but actual material you said that it was magnetically ordered at low temperature but at the same time i said well in this github and gamma range apparently there are some looks like some disorder state that are difficult to identify within a small size cluster so what happens there uh but it has to be magnetic order so one way to get the magnetic order is add a small trigonal distortion so if i add a small trigonal distortion which sree also asked question that in fact that there is additional interaction that are allowed which is the so-called gamma prime and you can see that effect of gamma prime is basically when the trigonal distortion have a small negative gamma prime then this window here lots of this disorder state will be replaced by this exact order so it's very sensitive to the magnetic order again in particular that's exact order okay so uh i will work on the github and gamma model now and why do we care well because as i said uh well the the actual situation dominant interaction is the ferro github and anti ferro gamma and then we'll have a small other interactions gamma prime isenberg and so on they'll generate to the magnetic ordering and then if we apply the magnetic field we may destroy some of this magnetic order and then reveal the phase step by this dominant interactions so now the question is what is the phase of the ferro github and anti ferro gamma models which i have addressed but let's look it up and see a bit of details there so i'm going to rotate my phase diagram here my circle has rotated because from the ferro github to our anti ferro gamma that will be my excess okay so i'm going to starting from ferro github and anti ferro gamma and see what is the phase between these two two frustrated interactions which they don't cancel each other because they come with the different signs okay all right so here's the two competing interactions competing cooperating i don't know yet which has two different signs so when they are equal sign again there is a hidden su2 so that develops six sites magnetic order called 120 water vortex so pure github model is github spinnaker pure gamma model is controversial so it's a hard problem that's so people have tried you can see the list is not complete because it stopped somewhere last year and there are more lists added up here except one of the studies by the variation of Monte Carlo where do they do find the github order most of others are presenting that it is some kind of disorder state i'd like to point out a nice walk by the classical spin by natash and yonis that this gamma model when you take it the large spin it's a classical spin leakage with the microscopic degeneracy of this growing as a system size and they also show that it is actually stable with a small quantum fluctuations so it's i found it's a very very nice paper and pleasant to read okay so just want to show you one of those i listed the many of them but one of them this is done by dmrg calculation by matias you can see that the ferro github to our anti ferro github and and going through the angle so here we set the angle of minus cosine pi it's going to be k and then sine pi will be a gamma and zero here correspond the ferro github and then one here which is the pi correspond anti ferro github pi by two here in the middle will correspond anti ferro gamma and you can see that this color here representing some kind of magnetic order you can see the magnetic order here zero absolute zero all the way before you hit the s u2 hidden s u2 appears in the middle here around the point 75 and that's where 120 appears but the other ones here if you look at the static structure factors of every momentum point that we can access we don't find anything much happens on the other hand there's a sharp jump here as if this is like a some kind of ripsy transition type which is kind of speculation there's a sharp occurs that means anti ferro github are different from anti ferro the ferro github spin like it is different from this gamma some some disorder state appears here these are dynamic structure factors in a different point the top left is going to be the ferro github and then bottom bottom right here is going to be anti ferro gamma you can see that there is not much of ordering they seem to have a small gap here but it's just dmig with us you know four six leg so of course we are missing not some momentum space and so we can tell if it's gapless or dark but in any case we have large disorder state and that was compounded by many others on this list here okay now we are going to turn it into this little more interesting like a magnetic field i'm going to add a magnetic field what happens on this disorder state maybe we just end up with some polarized state so magnetic order is going to destroy some magnetic order if i set the magnetic order and then we build a face again so here is again the circle which rotated and my x-axis is starting from the left with the ferro github to moving towards the center of the circle which is anti ferro gamma and that will be my x-axis as i said this is this is the kind of disorder so i'm going to just put the magnetic order zigzag magnetic order by adding some gamma prime so ferro gamma prime here we'll add some magnetic order here so and see what happens with that magnetic order in the field okay so and we know that the this is quite an isotropic so we are going to put the field and then rotate to the field and see what happens between the different direction of the field so here is one thing okay so here's our honeycomb again the different color represent x y z point and she axis is the one one one with respect to s x s y z that we have written up y j effective half x y z so this will be one one one axis so is the outer plane and then we are going to rotate this angle of the field and then put it into the direction of one one two minus two which is the axis so called and that is going to be parallel to the zigzag within the honeycomb okay it's a perpendicular to one of the point if you like all right and then the face diagram is like this angle has been five degrees here and here's a gamma over k this is non-github interaction but we have added additional github interaction which is gamma prime to set the magnetic order here which is the zigzag at the low field this is t equals zero so it's on the t the zero temperature face diagram and what we have found is that the uh at the fuel github here we have github spin leke and then we have a zigzag order set by this small trigonal distortion and then gamma over k is going to enhance this zigzag order but then as a functional field we have found that on top of this zigzag there is a large window of this disorder state that seems to survive before it polarized so white area is going to be polarized state and there seems to be a transition along these lines here this is again 24 side ed so it suffers from a sum of the finite size so one has to take that into account if i align the field along the axis along the in plane field here and in that case what we found is that in fact this large window of the disorder state disappears so we have this zigzag order sets in and then it just immediately polarizing to the polarized state when the field is in the plane in the plane of particular direction which is the direction parallel or perpendicular to one of the bond okay so here's the github spin leke yeah yeah yeah yes yeah sorry yeah the color corresponds to the expectation value of placket operator in fact so this is a negative and this is positive in fact the polarized state is also positive we just changed you know we just changed just removed it never larger than yeah uh yeah yeah so but here uh yeah so yes here is very large field by the way here is very tiny field so you can kill the zigzag with a very small in plane magnetic field but it'll take a lot of a lot of field to get it into this state and that's also consistent with the experiment in the retaining trichloride so a lot of things we know from this study so so we have found intermediate field disorder x when the gamma is finite and the in magnetic field is out of plane okay so that's something to bear in mind so after this there has been other studies so this is one of nice work by people here with and also Jungba is involved here infinite pencil product state with the field along the she-axis they have optimized this various initial state of all of this kind and what they found that the gamma again gamma over k here with a small gamma prime and set the zigzag over here and again the guitar spin like it is confined here and there's this x state which are separated from the guitar a different from the u d but i think that it is still there is a disorder state has found x here and they call the pneumatic paramagnet because it breaks the c3 rotational symmetry between x y z bond but it is again disorder state different from the polarized state so this is infinity system so hopefully that is telling us that there is a something interesting going on with a finite gamma and the magnetic field along the she-axis and there are many other studies that has been also pointed out the similar disorder state after that okay good so here's a summary of the t-co zero phase diagram again we have found that depending on the magnetic field direction so here's a gamma over k i'm specifically using now the non-guitar not a heisenberg but gamma interaction divided by guitar here is a ferro gamma is anti ferro different signs so that they are not canceling the frustration here the guitar spin like it seems to be confined in a very narrow window of the pure guitar limit field is like about two percent of field where you can be basically killed and then we have polarized things there's an unknown x-space that seems to be nicely sitting on top of magnetic order to polarize something robust is there and on the other hand if you apply the field along the axis in plane along the zigzag chain of the honeycomb shape then in fact that the gamma over k zigzag order is just to simply disappear and then go back to the polarized state i didn't put the sides here but this one here is much smaller like a point two here while here is one point something so you need a hundred tesla to look at this one here here we need the order of ten tesla you can kill it and then go into the polarizing okay so i put it here that's the we are going to now focus on this one here uh magnetic field in plane and then zigzag order and that strength of magnetic field if i increase we both go into the polarized state and that's a precisely experimental setup that has been done in many many laps so let's now connect to the experimental case of ruthenium trichloride and i just want to well i was trying to check the chat uh but hopefully peers can do it there are seven of them now so if i have any questions that i'll take it before i move to the ruthenium trichloride that's the only one view oh okay i just i didn't check you and uh your channel asks could you elaborate more how the magic power magnetic phase is different from the polarized phase um okay yeah so the actually a transition between the two appears to be the the polarized state so if you measure the bond energy so we have x bond y bond and z bond one can measure the energy of the bond it's so just take the hemitonia and take the part of hemitonia and measure the energy for expectation of hemitonia on that bond uh polarized state is where the bond energy is all equivalent okay along the c axis x bond y bond z bond all have the same energy which is expected because i put the field along the one on one it keep along the between the all three bond three bond that's sharing the same thing but the nematic paramagnet here it doesn't have a local magnetic order it's disappeared from the example but on the other hand the bond energy of the x bond y bond and z bond does different okay so in fact there are a couple of them here so some bond here is having higher energy than the other and then bond energy actually switches from the one to the other so the c three symmetry along the c axis is going to rotate x bond y bond and z bond but that's continuously broken in this nematic harmony hopefully that answers the question okay so that's what they have found okay yeah yes please yeah yeah um yeah so the temperature effect yes that's uh in fact now that was my y axis earlier but now let me put it this way which is out of the plane yeah so guitar spin like it is actually a 2d uh g2 so they are going to uh it's not well defined because you have topological defect which pro-reporating immediately so it's going to cross over to a some entangled state but it's not not the long range but it's maximally so maximally but in any case you have some guitar physics appears here zigzag order will have some some finite finite ordering t-nail t-nail will appears here and then this one will have some kind of so these two transition here will have some crossover at the finite temperature and they will survive all the way above this uh zigzag order so if i will be she filled in a finite temperature then i would expect that the above my zigzag order i'll see a physics of x space and that will probably represent some of the um continuum spectrums and other things yeah and here is going to be much more uh so here guitar spin the same thing and then zigzag order above the zigzag we probably will see a polarized state remain it depends on how far i am right because if i'm nearby i'll see some guitar but i know that gamma interaction is at least half of the guitar interaction we are somewhere far away here so actually she'll polarize think that's my under that's what i think um yeah okay so ruthenium trichloride how much time do i have where is the where i can see the time we are now approaching the last 20 minutes okay excellent okay so let's see if i can get to the symmetry part so okay ruthenium criteria um okay so idea of the ruthenium criteria is uh basically we know that iridium was a five press and that give us uh well four press which give a d five so we say well ruthenium is three press here which has to be similar and it's a better 2d material so that's where it comes from the proposal that this will be a one of the promising candidate um then we study like alpha ruthenium criteria and where that goes back it goes back to the chemistry it's uh it's uh coming from these papers of less common metal uh back to 18792 so it's made in fact long time ago um and they were calling less common but i was told from experimentalist that the ruthenium trichloride is abundant in the lab uh and uh there are lots of activities because it's easy to easy to easy to kill it the magnetic order with a small field can tesla in the lab with the in-plane field um so here's the pollinates uh all your data is a function of one over temperature and then y-axis is a logar isn't it so you can see that at the low temperature which is this right panel here uh is going to be the low temperature here and that's a very nice insulator so my colleague Yongjun was telling me it's hard to measure the conduct the resistivity at a low temperature because it shoots up so it's a very very good insulator um this is the 96 i found that this is the first paper and they were talking about semiconductor this is supposed to be semiconductor but we know that's a d5 so based on the band theory is supposed to be a metal there's no reason to be a semiconductor but that's what was believed in the 70s 90s is the pollini was the first one who suggests that this has a very earlier arpest data it's actually not on arpest is that arpest no i think it's only the it's a wave vector okay it's an arpest data wave vector is here it's it was a metal band maybe a multinsulator so that was a suggestion earlier data so back in when we just studied so this is Yongjun's one of the very early data shows the strong anisotropy between the ab and c-axis and that is understandable because gamma interaction is very anisotropic within versus the outer plane and therefore if the gamma is anti-peril we expect that it's a hot axis is along the c-axis in other words if i apply the field along the c-axis it's very hard to polarize okay and then there was some magnetic order appears at the low temperature you can see the two peaks the oboe peak is known to be a stacking pole so-called and this is the neutron data on the and there are some of nice peaks representing the magnetic order of the zigzag kind and then after that there has been many studies which confirms the similar magnetic order okay so magnetic ordering appears and what about oboe tc or inelastic as governed by some github interaction because github interaction is logistic despite it has magnetic order so all your studies of the Raman by in fact it's a canvas group and then we have lots of really nice work by the steven nugglers and they've seen the some of this inelastic neutron scattering showing some of this broad hump here which survive at a at a high finite temperature above the above the magnetic field which is a 15 k so here you can see a lot of this nice broad spectrum that is both inelastic here both below and above the above the magnetic ordering temperature so that sort of indicate that there is a strong frustrations and maybe it has some of the type contributions okay and then the field induced the spin naked was first studied by this group here you can see that I don't know the parameters because in the beginning we are all using a different rotation for a different interactions so it's hard to map into what parameter they are using but in any case as a function of field they have found that there is a some kind of intermediate state which you can see here much better so this is expectation value of this so-called plaqué operator around the hexagon product of the six-spin operator and they do have this negative plaqué and there's a sharp decrease here which they call maybe gap spin naked here before it polarizes so that's the kind of pictures okay now back to the thermal transport this was the what made a lot of attentions I don't have time go through all the details but I'll quickly review and remind you that the magnetic field they applied is mainly an in-plane here is in the beginning they had a out-of-plane component but it was a function of in-plane component H parallel here at sections is in-plane magnetic field here is exactly as we discussed which disappears around the seven tesla or something and there's a small window of the two teslas where something happens and then the polarized state occurs so here's a kappa thermal whole conductivity divided by temperature and you can see that the small window so-called half quantized half quantized integer half integer quantized values and that brought a lot of attentions okay so on the other hand that was challenged by other experimental groups one of them is again magnetic field is now they all plane in the a-axis with the a-axis there's a small window of quantum spin naked this is upon own screw and this one is here you can see that the whole conductivity here they just go through the half values half is somewhere here they go through here on the other hand it seems to be there's just some range of parameter space with a field they appears but again it's hard to see with your bare eyes both of them as represents despite the difference between the two there seem to have some indication of this quantum spin naked or some disorder state which I told you in theory we don't see them when you have magnetic field in the a-axis and in furthermore the upon own screw has this quantum spin like is not the guitar spin naked in fact that they are suggesting that there's some quantum oscillations here in the kappa x-axis longitudinal component with of you know moving up and down there are three peaks here and that represents some kind of different quantum spin naked from a guitar spin naked it's a lot of interest going on here okay and then that oscillation was again challenged by the hita-dakagi school here and you can see this quantum oscillation isn't they are representing these are two different samples made by different methods and this is the dmph as a function of the field and this one is a phase diagram it's a function of field and a temperature what they did is that this sharp peaks or oscillations or non-unit non how do you call it some some singular singularity looking behavior or non-monotonic behavior can be mapped into some of these phase transitions here and that was indicated by some kind of magnetic transitions which are probably something to do with the stacking of the system okay so i just want to uh summarize the current state between the theory and experiment in fact that as i said in the theory side fm-ferromagnetic attack with anti-ferroganma reason uh zigzag actually transitioned to a polarized state we don't find anything in the middle this is a t-co zero uh phase diagram uh zigzag to a polarized state when the field is along the a-axis and guitar spin leakage is confined in a very narrow area on the other hand this is the field and the temperature so i'm going to rotate to make the comparison so we are looking at only this side magnetic field here you can compare with this arrow here uh they found that there's something else the quantum spin leakage or something in the middle well we don't find anything in the middle unless field is out of plane so we are saying that this is out of plane field uh the gamma is our hard axis gamma generate the c-axis to be hard axis and that generates some kind of disorder state so in theory the disorder axis occurs in the c-axis and the recent experiment by this uh chinese groups here has shown that this zigzag is very hard to remove when you have a c-axis field and you can see that zigzag is actually decreasing here is this one exactly is the angle so as i move along the c-axis this actually requires a smaller field to destroy and then above this zigzag there is some kind of disorder state appears and y-axis is is not a linear field so you can see the top here is about 140 ks so it's a very high field consistent with the theoretical calculation okay so the possible origins maybe a sample dependence exchange interactions sample dependence was proposed well not the it's a presented actually reported by the japanese group here you can see that abc samples with the susceptibility chi here high temperature susceptibility is different between the samples means that exchange interaction is quite sensitive to the sample to a sample uh because it's low temperature is different magnetic on a magnetic order but high temperature susceptibility is mainly set by the exchange interactions and different samples seems to have a different interactions a sample is the one that shows the nice half quantization here and the other samples they don't like this samples for example they don't see uh any kappa xy it's actually just the zero here so it has a strong sample dependence uh kind of understood well expected because when you have strong spin over coupling they couple to the lattice small lattice change will generate the different exchange coupling strains so if you have a different stacking so it's a van der waals material so when you step the c-act when you stack the in plane out of the chi-axis the way they stacks they stacks and then slide stacks you know slide and depending on how they slide they can form a different space group one is called for example p3 112 and then these are c2m and there's a 3 bar which has a c2 symmetry and anyway so these are the different stacking you can see that and depending on the stacking in fact that the hooping parameter is different you can see some of this listed and kitayev is the one that in fact can even change the sign in this case for example here is is an anti-parallel so one has to be careful about what the space group of the actual bulk material is okay so and as far as I know most of people think it's a c2m but there are other stacking apparently happens depending on how you grow the sample so my suggestion will be that we need one given sample and then look at the full analysis like a look at the magnetic ordering directions and all of those will tell us exactly what magnetic exchange interaction that we have good all right do I have 10 minutes okay so 10 minutes okay okay so I'm going to go through quickly the my second question so about how to generate yes yes so I believe that there were yes so there are people who are working on the big question yes so the question was is there a way to generate the single layer extrapolate to do the single layer and exfoliation yes so the yes the answer is yes and there are people who have studied they can it's a wonderful so you can it's a like a graphene you can use a Scott Scott's tape to clean the single layer and that has been done people have been growing on the graphene for example and that case the graphene and luteinium cry 3 they hybridize and there's a hole or so there's a some doping that generates so you move away from insulator yeah so in that case I think people are still working on it let me put it that way yeah yes yeah so the question is so whether one can measure experimentally this flux of operator and if you do that and what was that in fact that I don't think we have measured experiment I don't know how to measure in the experimental just this itself I'm sorry oh this is a theory this is a theory data yeah and that theory was a kind of invoke the motivated the lots of experiment okay okay so maybe I have now nine minutes let me just quickly go through the symmetry of the problem it's I think this is something so okay so so far I've been talking about the spin off where it's effective half the question that was addressed earlier was that can we have a good type of interaction with the higher speed yes and if you do then how you generate them and how you estimate the strengths so examples of many of those in one we call diiodide and cronium triiodide and cobalt is as effective have there are many many now several candidates that appears but some of them include a higher space spin ask it I was theoretically studied by us currents at all here and they have shown that in fact this wp is now instead of product you can generate generate another operator here and one can show that they also commit to the metonia and generate the ultra short show range correlations but it's not exactly a solvable problem so the numerically it was studied because it's not exactly solvable that it might be a some kind of quantum spin liquid now the question is again how can we generate the bond-dependent traction bigger than spin half okay that's hard because remember that that there are two requirements one is the wounds coupling and they are just you know a coupling and they are not compatible each other so for example if I have a wounds coupling larger that is the case for a 3d sample so n equal 3 in that case the wounds coupling will make for example the a system here will have a easy to above so I'll have a spin s equal one state but since the wounds coupling much larger that means that my spin over coupling is much much smaller than there will be no mixtures of angular momentum and spin that's necessary to generate the bond-dependent traction so what do we do well actually we can use the heavy anions here because my anion ligand will be heavy like iodine with the spin over couplings about 800 med then you can see that the p o vitals will split into half and three half and one can go through this p o vitals and will generate the holes and one holes and two holes and there is software from this spin over coupling here so spin over coupling heavy anions is the what is going to generate the spin over coupling so the generator the bond-dependent traction so we work on it these are some hoping parameters that one can go through and we found that indirect hoping will generate the both gtive and the heisenberg in this case and they come with a ratio of minus two and that has something to do with the shape of the e g o vitals and direct hoping always exists and that will give us a heisenberg interaction which is positive here the heisenberg is negative here's a positive gtive is actually an anti-fair in this case so total hemitonia is anti-fair gtive and then heisenberg interaction which i hope that it's small because they come with two different signs but of course in real materials it's hard to tell up to the fourth order gamma is in fact zero so we are looking at these two nice in an ideal case again of course there are other interactions dot dot dot which expect to be small we have done the gd calculation for a spin one here and you can see that where heisenberg again generates the zigzag and anti-fair here but there is a middle one here they seem to survive to some kind of disorder state before we wrap up there's a question yeah in the chat and amegas could you explain how to capture the magnetic interaction in the honeycomb lattice specifically in both the anti-fair mageg and the ferro mageg and what about the zigzag phrase in the union boy right i don't quite understand the question what are you doing please wait how to capture the magnetic interactions in the honeycomb lattice anti-fair mageg and the ferro mageg phrases and what about the zigzag phrase so i think that's what i have gone through like you can capture the honeycomb lattice so magnetic patterns coming from three spin interactions so three different types heisenberg github and gondas and in the routinium criteria zigzag order will appear as if i have a ferro github interaction anti-ferro gamma in addition i can add a small and ferro magnetic while triangle distortion generate a small gamma prime and that will generate the zigzag order and the magnetic moment angle is even exactly the same as experimentally measured so many of those theories are rather nice except that a plane filled with some disorder state we don't find yeah so you go through that and yeah so these are some examples of the heavy anions like two minutes yeah two minutes so good so i'll just end up with some of those then yeah so this is the spin one triangles and we have a type heisenberg in triangle lattice this is the triangle lattice with a nickel surrounded by heavy anions the magnetic ordering pattern here will be most likely around the circle boundary of the circle because gamma is almost zero and you can see that heisenberg interaction with anti-ferro case is very unstable towards this so-called g2 phase and that g2 has a very interesting shape like this this is a unisys nice paper back in 2016 and the cronium triiodide might be another example where probably a ferromagnetic interaction is the largest but the github interaction might be there which might be subdominant second largest that's what i think and this one is the single layer 2d ferro magnet people have studied a lot about the anisotropy that occurs in the cronium triiodide and there is a some debate over the what the github interaction is large or not and so on i just put it this this is the way i see the material when that's how you know t2g and egs and so on that's my view of when you see these circles and there are debates over the strengths of the type of interaction but i'll leave that as an open question i have a few slides well more than few actually i think i have about six or a slide but i don't have time to get it into the estimate the type of interaction so i'll leave that five or six slides i'll probably have to skip it and i'll put it in a summary here um i don't think i have gone through the last part but that's okay so uh we have discussed or i discussed that the role of the non-github interactions in an ideal situation there are two non-github interactions one is isenberg that leads to the magnetic ordering as expected on the other hand there are another non-github interaction called gamma interaction and the ferro gamma near the ferro github they come different signs generate the disorder phase under the she-axis even without the field when gamma is large there is a very disorder state that is occupying large phase space even under the magnetic field they seem to survive much better than the github in this limit in this in this range of the parameter space second as i said under the in-plane magnetic field we found this exact transition to a classical polarized state of course this is not completely polarized due to the gamma interaction we'll see a partially polarized okay it's not going to be everything is like spin one immediately gamma interaction makes the magnetic ordering a magnetic size of moment would become a one in a very very large field so it's a partially polarized in the experimental situation but they are diabetically connected to the polarized state so i just will call it the polarized state okay and then outer planes it's at disorder state appears before you polarize so we think that's an interesting direction higher spin github interactions can be generated if you have a combination of influence coupling at the transition metal on the other hand spin over coupling in the ligand which surrounds the transition metals so we can use out of this you know we coupling and generate to the github interaction you know higher spin models or higher spin systems the one that i have not been able to touch due to the time limit was the proposal to estimate the github interactions for general spins i really want to talk about this but it's okay it's i don't even have a paper yet these are my proposal which will be written up soon you apply the magnetic field in a certain plane this is called bc plane instead of ac you apply anyone who is an experiment a list of please you know if you're interested please talk to me apply the magnetic field in the bc plane b is along the bone direction and then plane measure the spin x stations at our two momenta called m1 and mt these are related by broken meter symmetry so meter is broken due to the ligand so these are the symmetry of the lattice and symmetry of lattice is reflected in the symmetry of the hoping parameter that are allowed the hoping parameter fix my pseudo spin exchange interactions so these are all i cannot change anything out of this and there are two momenta these are related the by broken symmetry and you will see that these x stations that are m1 and mt will be different if there is a github interaction so this is a strong uh proposal i think it's a very simple one example here for example these are the brilliant zone which do i have any brilliant zone here yeah here is a better example so here's my brilliant zone here m1 and m3 these two are related by broken meter of the bc plane and this x station enters and that x station enters is different if i have a few in the bc plane with the angle of some finite angle of the set up don't put it in the c axis not in the a axis one has to break the c3 so you have to put it in a certain angle with the angle of the set up and this change between the two and it's different between the two measures the github minus the gamma actually measures the k minus gamma but higher spin case is even nicer because gamma interaction is almost zero therefore this difference will immediately tell us the github interaction so that's my last proposal yes that's my last proposal and i will leave this summary here and then thank you for your attention okay good yeah so there are exactly solvable models so other than the github interaction for example the one that appears like yawoli model for example in that case one can have exactly solvable but it's kind of rediscovered the github because it says to symmetry was another github interaction but in any case there are other models that are exactly solvable most of them are a bit artificial to my mind because they include the six spin interactions and so on it's not just quadratic so it's difficult to realize probably in the actual system but theoretically it's a beautiful beautiful theories so yes they do and the the other question about the higher spins yes there is a single ion on isotropy that becomes finite which become constant because it's something secure in skin half but bigger than half there's a single ion on isotropy which is going to affect the in plane and outer plane in plane outer plane on isotropy that will be responsible for the in and outer plane and the g factor difference because gamma is now almost negligible but this experiment that i propose is independent of the single ion on isotropy because single ion on isotropy is a local so it doesn't depend on the broken meter symmetry that i'm using unfortunately i didn't have chance to go through this but yeah but it's there and it's it's negligible it's not negligible in us in bigger than half but you need a trigonal distortion to generate the single ion on isotropy so but in real material they are always present okay there are no for the questions okay here go yeah here go ahead real life question okay go ahead the effect of phonons can you repeat the question yeah so the question is what is the effect of phonons brilliant question um it's uh very important because whenever we have a strong spin of a couple again spin is coupled to orbital orbital is fixed in the lattice so the spin of spin lattice coupling i think it's important um and uh well and that probably you can look at the Raman sketching and so on have to see that of course how important in what sense is i i'm not sure because i know it's there it's very important whether that is important to destroy the spin liquid or not i am not very sure about that yeah the yeah spin over coupling is atomic spin over coupling yeah so the repeat to the question uh what type of spin over coupling uh am i using is that like intrinsic uh like a rash bar or something you said right yeah yeah so rash bar spin over coupling for example it's going to it's going to be a crossing so you have to break inversion to get the rash bar spin over coupling you can derive the rash bar spin over coupling with the atomic spin over coupling which is a local site lambda l that is angular momentum and spin just like hydrogen atoms you can think about of course they're very small but it's a local atomic spin over coupling if you add an inversion symmetry broken you can in fact uh derive the rash bar spin over coupling so we are not going that far we are actually even fundamentally before that we have just atomic spin over coupling that occurs in the extra transition metal uh together with the hoon's coupling that for a j effective half or you have atomic spin over coupling which is present uh at the heavy ligand which on an ions so we are just using our most simple spin over coupling one more question coming up regarding the x-phase the x-phase with the gamma and the ketayev so um you you find the phases using exact diagonalization okay so up to 18 sites yep so it could 24 sites okay up to 24 sites it could be that this x-phase cannot commensurate with the 24 sites that's a very good question again but we have uh yeah so once okay so question was for online people question was that this x-phase that I call disordered was found using a a finite size cluster which is a 24 site so if I have a magnetic order which has not been commensurate with a lattice uh you may miss it and I think it's an excellent question um so the earlier study that we did was a 24 site ed but then there are other studies which are in infinite tensor product state and that one is uh uh I believe going definitely beyond the 24 site and they do still find the part that is called the magnetic parameter and yeah so that I would say more um confident than the 24 site any more questions we can have more questions but bear in mind it will reduce your coffee time I think maybe it will hold it and we will reconvene in 18 minutes for on the trip across talk thank you