 Yeah, so first of all, I would like to thank the organizers for the invitation and the great honor to speak here in Trieste This talk will tie in a little bit to the previous talks We're talking about strain how to apply strain in an experimental way and two examples I will talk about our strontium ruthenate and iron cell night So first of all, I would like to acknowledge all the people involved in these projects This is mostly the team around Andy Mackenzie's group at the Max Planck Institute for chemical physics of solids in Dresden and For strontium ruthenate. We had lots of theoretical support by Thomas Gaffidi and Stephen Simon from Oxford Some of the samples are grown by Alexandra Gibbs And we also had a lot of input from Yoshi Mino from Kyoto University For iron cell night, we had a very nice collaboration with Suguru Hoso and Takasadashi Boushi Will give us samples and important input to the theory So a brief outline. So first I want to motivate the story a little bit We look at tuning and condensed matter why we should look at uniaxial strain and What we classically use as tuning parameters for example for quantum phase transition here I've brought up Classical system e-turbium rhodium 2 silicon 2 which if you tune down to very low temperatures You have anti ferromagnetic order which can be suppressed by applying a magnetic field Along the c-direction of the system and then you have here a quantum critical point Which is indicated by this large kind of funnel shaped Resistivity exponent that's close to one so linear resistivity over a wide range of the phase diagram Another classical tuning parameter and condensed matter is of course chemical composition and here shown is the phase diagram of high-temperature Cucarates and what we can see here is by changing the chemical composition We can go from anti ferromagnetic order to a wide range of metallic behavior to strange metal behavior and Possibly also tuning to two different quantum critical points here within the superconducting phase And we've seen already in the morning a little bit that if you apply pressure to iron cell and night you can Influence the nematic order you can induce a magnetic order here and you have a Change of the superconductivity on a wine temperature scale by applying pressure and Now looking a little bit what happens with uniaxial pressure or strain here is a tight binding calculation of strong subruthanate 214 and what we see here is that basically a lot of materials if we look at here That is the Fermi surface in the AB plane if we apply hydrostatic pressure We will see a very small change and if we apply a comparable uniaxial pressure we can often see dramatic changes to the Fermi surface and shown here below our band structure calculations where we see that for a Strain of 0.75 percent we can drive this system already to a lifts its transition And this is not achievable with hydrostatic pressure under normal experimental conditions Furthermore if we compare the Experimental accessible strain this corresponds to a Zeeman energy of more than 100 tesla and it's a very clean Tuning parameter we can apply it in situ down to 100 milli Kelvin also in high Fields and it's also a continuous parameter Now coming to a little bit the experimental setup. How can you actually apply strain to single crystals? The standard way is basically you take a sample and you would clamp it between two end valves Then that allows you at least to apply pressure But if you want to actually strain it it would be better if you can go in both directions And what we tried in our first iteration is attach the sample to a piezoelectric actuator Which allows you to apply tension and compression to the sample and Then if you take into account the system when you cool it down you have a relatively large differential thermal contraction between the sample and the surrounding Instrument then you can take three piezoelectric actuators, and then you compensate this differential thermal expansion Now going a little bit further. We also want to restrict any movement in the other directions to have really uniaxial pressure So we integrated some linear flexures here and have the sample glued to this movable anvil in the center of the device Now to create more Symmetric conditions to the sample we basically add small clamps on top and Then this is shown here basically a sketch of how the actual sample is mounted So we have a long straight bar we use here for example electrical contacts to measure the resistivity The sample is attached with a small amount of epoxy to the sample plates and more details of the setup in this reference Now a little bit. What can we actually achieve with our devices? So if we then apply a voltage to the inner stack that is shown here the stack expands We can reach compression if we have a voltage to the outer stacks We basically pull this back and achieve tension to the sample and Here is one of our devices the body is shown here is made out of titanium in this setup We can reach strains up to approximately 1% in a temperature range between 300 and 100 mili Kelvin And the samples are millimeter sized single crystals And currently what we can measure is for example AC susceptibility in a very crude way by attaching just a Susceptometer coil on top of the sample. We can also measure resistivity As AC specific heat and are trying now to integrate scanning Hall probe measurements into the setup Now coming a little bit to the first example of Stront's Ruthenade Where we're trying to probe the superconductivity with uniaxial strain So a brief introduction to Stront's Ruthenade here on the left hand side is shown the tetragonal crystal structure Which is analogous to the high temperature superconductors The electronic structure in this material is nearly two-dimensional and Several of the 4d ruthenium orbitals contribute to the Fermi surfaces The material is at low temperatures a very nice Fermi liquid behavior, which is shown here in the t-squared resistivity The anisotropy is quite high So if we compare the resistivity along the c-axis to the ab plane we get a ratio of about 1400 Now shown here on the left hand side are the three Fermi surfaces in the ab plane And Experimentally these have been very well characterized using various quantum oscillation methods It's relatively clear and uncontroversial that is an unconventional superconductor This is shown here for example in measurements of tc versus An amount of disorder for different samples And so basically as soon as you reach a disorder level that's above one micro ohm centimeter The sample is not superconducting anymore and that limits a little bit the research in this material Because for example for thin films you cannot reach currently samples with residual resistances less than 10 micro ohm centimeters And early on from thermodynamic measurements, but most importantly from the nmr night shift It was kind of clear that it's a special type of superconductor He has shown the night shift as we go through the superconducting transition Compared to the normal prediction of a spin singlet superconductor and essentially you see a constant night shift in the ab plane When cooling the sample down So this was indication that it's not a spin singlet superconductor and further experiments that kind of show that The potential order parameters of odd parity is shown here. These are muon spin resonance experiments for both In the ab plane and along the c axis and we see for both directions kind of Exactly as we enter the superconducting state An internal field that the muons feel and this field has a range of approximately 0.5 Gauss So this shows really the time reversal symmetry in this material is broken in the superconducting state And further evidence for this time reversal symmetry breaking comes here from polar curl rotation measurements Where as shown here is basically the electrical resistivity which drops here at tc and at exactly the same time We see an increase in the curl rotation. This is on a very small scale But the magnitude of the effect is comparable to other spin triplet superconductors like uranium platinum 3 And further experiments kind of hinting at odd parity pairing come from Josephine interferometry experiments But this is as far as I know not as reproducible On the other hand, there's also some evidence that the system is not a simple odd parity superconductor shown here is the Face diagram where if we apply a field along the ab plane the transition becomes first order And that is of course an hint for pauli limiting which is incompatible with the proposed spin triplet superconductivity And furthermore from the The basically predicted state where we have internal fields. We would also see Currents in the sample and here are measurements of scanning quit squid experiments where we see here the data and that is Drawn here the expected signal of these currents and their approximately effect of 1000 below the prediction So at this point, it's kind of clear from the experimental side We have more or less some evidence for some evidence against it And we're trying now to explore this a little bit with uniaxial strain and our hypothesis is basically for Px plus ip y wave function if we look at the low strain region What should happen is that we break The tetragonal symmetry of the system and then if we apply anisotropic strain We should see a small cusp in tc over strain and renormalized bend structure calculations show that the cusp at zero strain should have Magnitude of approximately 300 millikelvin per percent of strain And furthermore from the band structure calculations We hope to reach at higher strain the van Hof singularity Which is indicated here by a large increase of the density of states and Furthermore if we look a little bit at the orbital limits in the simplest case here If we consider the upper critical field this proportional to 1 over the coherence length And this is in principle Kind of an average of the gap times the density of states squared And if we hold others all other things equal in the system we Kind of expect that the upper critical field scales as tc squared And now considering that here are shown two brilliant zones if we have pot parity pairing That requires that the gap exactly when these two Points touch is zero and so here exactly the firm reverse velocity is small So from the symmetry argument we would expect that hc2 actually decreases And these are we coupling renormalization group Calculations which kind of support this very basic symmetry argument shown here is basically what happens to the ratio of hc2 over tc squared For applied strain for a p-wave scenario where the ratio actually goes down where the Here we have a very strong increase for a dx squared minus y squared order parameter And Basically Trying to reach high compressions in stront's ruthenate has already be done in chemical ways. And here's shown up as results of chemical substituted stront's Ruthenate and from these we know that the van Hofstingularity is approximately 14 millilevel Below the Fermi level and for substitution levels of about 20 percent who can reach this And similarly here with biaxial strain thin films you can reach the van Hofstingularity by basically Applying stront's ruthenate compared on other substrate materials In both cases though the high amount of disorder only allows to study the electronic properties But not the superconduct defeat t in this material And similarly it has early on been shown that you can increase tc For example by including small amounts of ruthenium or by applying uniaxial pressure between anvils Which is shown here for different kind of uniaxial pressures We see an increase in tc, but of course the the onset is very broad So you can't really distinguish different types of superconductivity from this measurement So coming a little to our results now of the ac susceptibility We have the sample here now under compression and we're measuring the ac susceptibility By putting a coil on top This is the unstrained sample where we see a very nice sharp transition around 1.5 kelvin And by increasing the compression now we see that the transition moves up Gets a little bit broader which is due to strain and homogeneity along the axis of our sample And then going further we can increase this and at approximately 0.6 percent We see now a change in the behavior We see now this very sharp onset here And by going even further we see that the onset doesn't move but we see a decrease at Lower temperatures again So if we put all that together into a phase diagram We see here for different samples that we can More than double the critical temperature of this material If we look closer around zero strain we see a more or less broad quadratic behavior And at high strain we see basically for all samples kind of a finite range Where we really say we have reached the maximum tc in this material And for higher compression going beyond we see the steep decrease of tc And so comparing that to kind of the same range the predicted range We think we really have reached now basically the van Hof singularity at this compression And very recent results of the same setup have integrated a squinting squint setup And what is shown here is basically this is the setup also using the same strain system And putting a small scanning squint center into the center And here is shown a map a local map of tc of the material in the unstrained state And we see on a scale of 50 microns we have a lot of inhomogeneities and ruthenium inclusions But still looking at different spots here we can try to resolve The tc versus strain dependence for the different points And then comparing that to kind of the predicted casp magnitude We can try adding kind of the linear term And fitting that to the data of all the different observed points here We see clearly that the prediction really does not match the kind of combined data So if there is a casp in this material then it's an order of magnitude lower than the prediction And we also looked now at critical fields This is now shown here for the system right at the van Hof singularity with tc of 3.4 kelvin What we see is that we increased the critical field along the ab plane by a factor of approximately 2 point over a factor of 20 And if we compare that basically with previous data We see here that we have an enhancement of hc2 over tc2 of about 3.6 So this clearly shows it's more compatible with a spin singlet scenario If we have the material under strong uniaxial strain And if we look at the phase diagram under magnetic fields This also reminiscent of the three kelvin phase around ruthenium inclusions that have been found earlier Yeah, so we can conclude a little bit for Strontium ruthenate That with uniaxial strain we can enhance tc up to 3.4 kelvin The peak in tc corresponds to a lift transition And that our hc2 data suggests that we have spin singlet pairing at the peak And also kind of the first order of behavior here is indicative of a Pauli limiting in this material And furthermore the three kelvin phase is probably a strain effect Yeah, coming now a little bit now to our very recent results on iron cell night Here we're trying with uniaxial strain to probe the pneumatic properties of this material A short introduction in the morning we heard a lot about this already What's important for us is shown here is the tetragonal crystal structure at high temperatures Which becomes orthorhombic at about 90 kelvin And here on the right hand side is shown the phase diagram from thermal expansion measurements Where basically if you take the material and measure the orthorhombic A-axis You see a strong decrease along the one direction and basically an increase along the other direction And if you don't apply any kind of external pressure or force Then you have a lot of twinned state in your material And of course this spontaneous breaking of the rotational symmetry is An indicator for pneumatic behavior Here's shown the evolution of the fermion surfaces This is mostly from ARPIS data What happens is basically that the whole like in the center and the electron likes At the boundary of the brilliant zone become Distorted we have here an ellipsoid and here these peanut shapes And we have comparatively here so a shortening of the B-axis a lengthening of the A-axis And what makes the electronic structure complicated as we saw already is that All d orbitals contribute to the electronic structure And further evidence for the pneumaticity comes from illustrious activity measurements Here is shown the 2M66 coefficient, which is basically kind of The susceptibility to the orthorhombic transition and we see this Divergence here towards the structural transition temperature, which goes with a Curie Weiss kind of behavior Now a little bit the motivation for our experience First of all we wanted to look a little bit into the dependence of TC with applied strain And furthermore if the pneumatic order parameter has a special symmetry Maybe we can couple to that with applying strain For example if we strain a sample along the crystallographic 110 direction This is basically the B2G strain And this shear component should then couple to the order parameter Furthermore we wanted to look also a little bit in the wider phase diagram at the resistance which we can hopefully experimentally access And for this very ductile material we had to modify our setup a little bit You cannot really compress iron cell knighted So what we did we developed a platform technique Where here the actual strain from the piezo device is put into a small titanium platform And we glued the sample into the center of the platform And here are shown FEA simulations which show that we have a relatively homogeneously strained region in the center of the device And we calibrated that by an optical method which is shown here Where we measure the displacement and compare that to the strain in the platform And then here is shown kind of the experimental setup Where we have here kind of the side view of the platform Where the sample is glued onto the titanium with a thin amount of epoxy Our samples are between 10 and 25 microns thick And are grown via chemical vapor transport And here is shown a setup where we have basically the sample glued to the center of the platform And electrical contacts are done via sputtered gold and silver epoxy on top And then in the actual experiment we control and basically determine the strain By a simple plate capacitor method Now looking a little bit okay what are expectations for the order parameters In a very simple two order perimeter Ginsberg-Landau treatment If we have nematic order and strain and apply stress And we have no coupling between the two of them What we expect is basically for applied stress that the strain in the sample just linearly increases And we have no no coupling to the nematicity Now if we kind of let them couple a little bit What we expect is that instead of the lower ordering temperature We have now for in both a single transition temperature And for any applied stress we also have a non-zero order parameter at high temperatures as well When we break already the symmetry And here we assumed basically in linear coupling in first order And now this kind of very simple picture Would lead to a phase diagram that looks like here If we could hold actually the local strain fixed What we expect is like a ferromagnetic in field If we apply a small field we would see here this crossover at higher temperatures And going at lower temperatures we would expect the first order transition Now the sample can build twin boundaries and domains And so what we can in our experiment only do is we can hold the average strain constant By gluing it to the platform And so what we expect is that we actually have a transition here And by applying strain we enter this domain phase So here we have the first order transition On both sides on compression and tension And we hope to kind of explore this phase diagram Yeah and we did this with electrical resistance measurements First we focus a little bit at the region near TS And here we perform temperature sweeps And this is kind of the raw data And we see here this kind of kink like feature in the resistivity And if we apply now either tension or compression We see that the transition gets much broader very quickly But also in both directions moves towards lower temperatures And to identify the transition We looked a little bit at the first and second derivative And then applied a Gaussian fit to the derivative of the electrical resistance And with this we're trying to create a phase diagram And here is shown the structural transition temperature That under strain applied along the 110 direction This is not coupling then to the pneumatic order Or the orthorhombicity And here we just see a very shallow slope With a linear behavior along the whole applied strain range And then if we apply strain along the 110 direction That is along the orthorhombic distortion Then we see here this approximately quadratic behavior For the three different samples And we also see that the width of the transition Increases a little bit by applying higher strain And we further look into the elasto resistance By applying strain sweeps here right below the Structural transition temperature And what we can see here is basically that By going down in temperature Now we're entering the twin region Here we have a very nice linear behavior of the resistivity Which can be shown here in the first derivative Where we basically go from this kind of quadratic behavior Above the structural transition temperature To a linear behavior within the phase So in principle we can access directly the resistance anisotropy Where we can either have the sample in the state Where everything is along the A direction Or where we measure the resistance Along the B direction of the sample And from this if we compare that a little bit To previous measurements of x-ray data From iron cell light we have scaled this Here and shown as a guide to the iron We see that is quite comparable to the data previously published Now coming to lower temperatures We looked at domains And what we did here this is within the phase Going down in temperature and then sweeping the strain And what we see here is not really a hysteretic behavior But what we think is that we're kind of annealing Out domain wall boundaries And basically if we go further out We see always a decrease in temperature Until we exit the phase So it's not really that the amount of domains Is the dominating scattering factor here About the amount of domain walls And if we go down in temperature and further out We can also see kind of this closing Of the hysteretic behavior So here we have a fully detuned sample And coming now to the last Measurements at low temperatures Here we look at the superconducting transition This is here different cuts at low temperatures Into the resistivity data And we see basically here very nicely that In the twin region we have an absolutely Dynia behavior of TC with applied strain Along the 110 direction With a slope of approximately 1 Kelvin per percent So that measures in principle not the B2G But the basically the perpendicular The A1G response of the superconductivity to strain Here and with this I would like to conclude For iron cell night With our platform technique We can apply compressive strains up to 0.6 percent Now with also ductile materials We can probe with strain in both directions And we see signatures of the structural Transition temperature We can map out the elastor resistance Look at domain wall contributions And see a very large response of TC With applied strain Here and with this I would like to summarize We have a uniaxial strain setup Which is kind of a new tuning parameter And condensed matter We can apply this to very hard bulk materials And reach large changes in the electronic structure We can now also apply this to very thin and ductile materials And in transruthanate We can tune TC over a wide range And our HC2 data suggests That we have spin singlet pairing When we reach the high TC state And furthermore We are now exploring also iron cell night And trying to map out the phase diagram And access basically the whole region Where the sample is twinned And also go beyond the twinned region And with this I would like to thank you for your attention