 Thank you, so I'd like to thank the organizers So I don't have any pictures of me and Boris from the past, but we've never written the paper together But Boris played a big role in my career of publicizing my work about 15 years ago on low-temperature de-phasing So I'm quite grateful to him for that. So I'd like to tell you about a subject that hasn't been really discussed at this conference, ferromignete jossus injunctions So this is work supported by DOE and then recently we're working on Trying to make cryogenic memory with IARPA Northrop Grumman support So these are various pictures of my group. A lot of people here have contributed, but The work I'm going to focus on today was done by Bethany Nijelski and Eric Ingric That's my collaborator Bill Pratt without whom I wouldn't have been able to do any of this So let me just review proximity effect in superconductor normal systems superconductor ferromagnetic systems This is sort of the old-fashioned view where you don't worry too much about the details in superconductor normal You say that there are pair of correlations that extend into the normal over a distance than normal metal coherence length It can be very long at low temperature up to hundreds of nanometers micron in ferromagnet systems On the other hand you have extremely short correlations, and you have this oscillation The physics was actually explained by a myriacobi just to remind you the idea is if you take a Cooper pair from the superconductor It's a spin singlet you put that pair of electrons in the ferromagnet The two electrons have to go into different bands Just for the record real ferromagnets don't have this band structure, right? This is a theorists cartoon band structure. It looks just like a Zeeman split metal But for the physics we want to talk about this is this is what you need to do And so the point is the pair picks up a momentum q Which is just the difference between the Fermi wave vectors and the two bands where you can express it in terms of the exchange energy divided by the Fermi velocity And so you can also think of this this momentum as an oscillation of the pair correlation function And that oscillation well in 1d it would just oscillate forever if there were no defacing But in 3d there's a angular average that gives you an algebraic decay and then a diffusive system Of course you get an exponential decay and the oscillation length scale then of course is just the inverse of this q So it's a Fermi velocity divided by exchange energy And so you can see from this why why this distance is so short exchange energies and strong ferromagnets are large They can be of order an electron volt so you get extremely short length scale So just to review that the two differences in the systems are in normal metal you get Correlations over long distance, and they just monotonically decay in the ferromagnet you have correlations that Decay very quickly a very short length scale, and there's this oscillation So how do you see this oscillation in experiments? I will only talk about one of the ways and that is if you make a Josephson junction So you have two superconductors separated by a ferromagnet that Oscillation tells you that if you're in the right Range of thicknesses that you actually invert the sign of your of your current phase relation So you get what's called the pi state? It just means that in equilibrium the two superconductors have a pi phase difference between them so this was So by the way this I should just say the theory of this I didn't write down any of the people so this theory was done really around 1980 by people in Russia Sasha Buzden there was a paper before by Bulyevsky so this had been known about for a long time But experimentally it was difficult because this length scale was so short It was hard to controllably make samples to discover to Look at that physics systematically So the big breakthrough really occurred in 2001 of Larry Ryazanov and Chernigalovka In collaboration with Yon Arts and Leiden used a wheat ferromagnetic alloy. They used a copper nickel alloy The purpose was to decrease the exchange energy and hence increase this length scale from say a nanometer to several nanometers that makes the experiments much more feasible and these are actually data from their 2006 paper, but you can clearly see these these You know minima in the critical current and those signify the transition from the zero state to the pi state This is not a face sensitive measurement, but later face sensitive measurements were made It's it's definitely well established And then actually later this was done in strong ferromagnets. Also, this is worked by Mark Blamires group in Cambridge 2005 they did cobalt perma-loy Iron I think and you can see these oscillations occur over a very very short length scale Maybe not quite as many data points per oscillation, but I think we believe that that's what they're seeing So this physics I think is well understood and I'm This has not been the focus of my own work Although I will come back to this at the end of the talk as there turns out there's still some interesting things to do here So the focus of my work has been on this theoretical discovery in 2001 these two papers Where they basically said that you can take a conventional superconductor that has spin singlet pairs You can somehow convert them to spin triplet pairs using ferromagnets. I'll tell you in a little bit about a little more How that's done. I do want to also cite this 2007 paper by Uze and Buzdin because they're the ones who really suggested a Viable experimental geometry where this can be done controllably This is this is their experimental geometry where you have three ferromagnets and we'll talk about that and the basic Point behind all this theory is that if you have non-colonial magnetization you can convert pairs from spin singlet to spin triplet So as an experimentalist, how do you see that this is happening? so if you make Joseph's injunctions and you say Increase the distance of this middle ferromagnetic layer if you only have spin singlet Correlations the supercurrents going to drop extremely quickly I didn't bother to draw the oscillations here But the point is you'll have an extremely steep decay over that very short ferromagnetic Coherence length that has the exchange energy in the denominator if you are capable of converting spin singlets to spin triplets the triplets of course Don't they're not bothered by the ferromagnet because in particular let's say you have the up-up component of the triplet That means both electrons are in the same spin band and so for that component of pair correlations They view the ferromagnet just as a normal metal. So they have a long length scale So I've I've written the normal metal coherence length for the triplet of course in real life there are other processes such as Spin memory loss processes spin orbit scattering etc But we'll sweep those under the rug for now the point is there's a huge difference in principle between the very short length scale of the singlet And the much longer length scale of the triplet Okay, so I'll talk about I won't talk about all the work that's been done in the world I'll just talk about the work of our group Everything we've done is as in this standard sandwich style Joseph's injunctions of the current flows vertically. We have niobium on the bottom niobium on the top Don't worry about this gold. That's part of the fabrication process And then the ferromagnets are sandwiched in the middle and there can be multiple ferromagnetic layers as I showed you in the previous slide so I will skip all the shenanigans we went through trying to get reasonable results and just show you our reasonable results so we came up with this structure and There's you know, I could give you a long talk about how we came up with this but rather than do that Let me just compare our structure to the one suggested by Uze and Buzden and you'll see it's very similar We have two thin ferromagnets on either side. That's these two f prime f double prime We have something in the middle that's a thick ferromagnet It's actually a cobalt ruthenium cobalt and I'll tell you just a minute why we why we chose that The point is When you make the structure and you vary the thickness of the central ferromagnet if you don't have these two thin ferromagnets on the outside you just get a Very steep exponential decrease of the critical current as a function of the thickness of the cobalt So that's these black points that that was actually from an earlier paper If that doesn't look steep to you just look at the numbers here We're dropping critical current by four orders of magnitude as we go up to 20 to 25 Nanometers of cobalt, so it's a very very steep decrease now you add these two thin layers in this particular case This was Palladium nickel, but you can do it with other things too And you see that you get this What it what appears to be not decaying at all, but at least it's decaying on a very very slow length scale compared to this So by the time you get out to 20 nanometers cobalt you have a factor of a hundred or so enhancement of the critical current So that's the strong evidence for the for this been tripled if you'd like to see what happens when you fix the cobalt and vary the thickness of these two outer layers So we just sit along this blue line here and vary this thickness from zero up to four and beyond That's this graph. So you can see that So here's three different materials copper nickel Palladium nickel and actually just nickel So you can see as you increase you start at zero your way down here You increase the thickness it comes up and then at some point it goes back down again You know, it's going to go back down because the the the spin singlet will just die and that If you make that thing too thick, but somehow there's a conversion to spin triplet if you stay up here Then you get this very this very large enhancement. So how does this work? So obviously, I'm not going to go through Usa-Dell equations and greens functions for you But there's a there's a nice hand-waving argument due to Matthias Escherich that I'll just take you through So this is extremely hand-waving. We're not even going to write down the BCS wave function We're just going to write down the spin part So we're we start with a spin singlet now we look at this physics that I already talked about this FF at low type of Type of physics. So if you have your up down you pick up this This the center of mass a coordinate picks up this momentum q which is just kf at minus kf down But of course I could have also put the downspin on the right and the upspin on the left Which is this down upturn and then I pick up either the minus iqx instead So now you just rearrange using the Euler formula and you see you recover the spin singlet with cosine q x and you pick up the m equals zero triplet component with with sine q x now Don't get too excited because that m equals zero triplet component is also short-range it also oscillates So it's not it's not giving you any new physics to get the new physics You have to put a second ferromagnet in with its magnetization rotate it some angle theta And now you just take this this spin triplet component here and you realize that in the new basis It contains all three components So we've now generated two long-range components in this middle ferromagnet if I make this middle ferromagnet thick This m equals zero component will die out the spin singlet component dies out And I'm just left with these two long-range triplet components now. You might think I could just Slap another superconductor here and I'd be done that doesn't work because the niobium doesn't recognize these two components So you have to somehow convert back again In order to get the complete Joseph's injection. So that's why you have the third the third ferromagnet and So if I if I oh, sorry, let me just go back to this picture So if you look at this you see that you know why why does the nickel come up so quickly compared to say the plating nickel? That's because it has a larger exchange energy and therefore a shorter cf So you you do this phase rotation more quickly and then and you get the you get the big triplet component Okay, so I need to answer this other question. Why did we actually use that cobalt ruthenium cobalt? Why didn't we just use a straight ferromagnet? So that's a technical issue, but it's important one So I want to take a minute so you all know about front offer patterns You put a magnetic field transverse to the current direction and you should get this nice diffraction pattern but we were working with large area junctions at this time we did these measurements and Cobalt's a very strong magnet actually all these strong ferromagnets break up into domains And it turns out if you make a large area Joseph's injunction with a thick ferromagnet in it with lots of domains Your front offer pattern is a complete mess Now this is this is not noise in the sense that it's reproducible in a given sample if you don't go to too high field, of course But you can see there's lots of destructive interference if you're trying to do systematic Studies as a function of say ferromagnet thickness and you have data like this You're you're really out of luck So what we wanted to do is we wanted to get rid of the flux of the junction and my colleague bill Pratt knew about this trick That they that they use in the magnet some community when you take Ruthenium of just the right thickness say about 0.7 nanometers or so then you anti ferromagnetically couple that the The cobalt layers on either side so even if your sample is multi domain each domain at a time That you cancel the flux and so you recover a very nice front offer pattern So that's that was an important technical trick and it's what allowed us to get these Systematic data over a over a wide range. So in the rest of my talk I think all the triplet samples I talk about are going to have this actually I'm not going to do so much more triplet in this talk, but Let's see what's what's next. Oh, yeah so The next thing you'd like to do is you'd like to have some sort of control and the very first thing we thought about as well By all means we should try magnetizing the samples if you get all the magnetizations pointing in the same direction This triplet should go away because remember you need non-colonial magnetizations to develop the to get that basis rotation so You can imagine on this curve Let's say you've got a sample with triplet in it if you magnetize it You should somehow drop down to this other curve and see a big decrease So we asked our student to do that experiment and she did and these are her data I should just point out. This is this is not the measurement field. This is a magnetizing field All these measurements were done in zero field. So this was her sample in the virgin state She applied a field she took it back to zero measured a frown off her pattern plotted the peak Kept on doing that and low and behold She got an increase of a factor of 20 and the critical current So that that was a bit of a surprise because we thought that magnetizing it was going to make the effect go away But it turns out so my colleague Bill Pratt knew the answer to this also It turns out that these cobalt ruthenium cobalt synthetic anti ferromagnets have an interesting property They undergo what's called a spin-flop transition So this is an artist rendition of the domain structure in the virgin state of our fourth or ferromagnetic layers the two free nickel layers and This cobalt the two cobalt layers and this cobalt ruthenium cobalt These are supposed to be completely random pictures except for if you look carefully at the two blue ones You'll notice that they're anti ferromagnetically coupled everywhere. So there's an arrow to the right There's an arrow to the left Etc. So now we apply a big field say to your right We magnetize the two nickel samples the cobalt ruthenium cobalt Of course, it's trying to be anti parallel. You're putting a big field to the right You're forcing it this way so it's scissoring toward the field But now what happens when you take off the field it scissors back to 90 degrees away from the direction of the field. So you've done two things you've magnetized the nickel layer So you don't have all these random domains and you've optimized this angle of 90 degrees between the the outside nickel and the inside cobalt so that That seemed plausible. We decided that to confirm that we should probably do some some more sensitive measurements, so we sent samples to NIST where John and Gurus did SEMPA and Julie Borchers did polarized neutron reflection and that seemed to support this this interpretation Okay, so what do you do next? So these are sort of the next two things you'd like to do There's there's two more ways you can you can control the thing rather than just have a multi domain sample What you'd really like to do is have single domain samples where you can actually control the directions of all the magnetization So the two experiments you'd like to do. Let's say you have a sample like this where you've somehow managed to well actually this particular picture is a little tricky having these two Opposite I should probably put this to the right, but that's okay. It doesn't matter The point is here I've got 90 degrees between the magnetization directions of each adjacent layer that Optimizes the spin triplet because it's proportional to the sign of the angles between Adjacent magnetic layer magnetizations if I rotate this one so that it's parallel to say the middle one That should turn the triplet off. So this is an on-off experiment. It requires a 90 degree rotation The advantage is it only requires one junction because it's just an amplitude measurement But it does require two orthogonal field coils, which we didn't have for a long time We finally got that and then we're able to do this experiment So we have done this and I'm in the middle of writing the paper And if there's time I might show you those data if not, I won't worry about it The measurement that we actually chose to do first was this one So it turns out if you go through that that hand-waving derivation I showed you by Matthias Escherich It's very easy to show that depending on whether let's say I start from the bottom I rotate in one direction to get to here if I continue rotating in the same direction It turns out I get a zero junction if I rotate in the other way I get a pi junction and that just as a property of spin rotation matrices and so the Advantage of this measurement is you're just reversing the direction of one layer So you only need one magnet the disadvantage is of course It's you this is a phase measurement you need a squid you have to do an interference measurement And you have to have two junctions both of which are working nicely So we've actually done this experiment to and the data are in one of my students PhD thesis The data are not great and I get I may show them to you later But I'd rather what I'd like to do is show you something else Which is actually worked in my opinion better than either of these so I'm going to move away from spin triplet for a few minutes Maybe maybe the rest of the talk. We'll see how it goes return back to the spin singlet And it turns out even with the spin singlet you can also make a controllable junction It's not so obvious how you do that because you don't have this spin rotation here you have phase shifts that accumulate but I'll show you it turns out it's actually very straightforward and You'll see why it's actually easier than those other experiments. So let's reach. Let's return to this basic physics that again We talked about early in the talk Namely if you just have an SFS junction you get this oscillating and decaying Critical current is a function of the ferromagnetic layer layer thickness now. Let's say I make a spin valve Which is two magnetic layers and I have the option of having their magnetizations parallel or antiparallel Since I'm fixing the total thickness I'm just going to get rid of that decay and plot the oscillating part with a with just a constant amplitude and Just ask myself how much phase does a coup repair? Accumulate as it goes through the ferromagnets. So let's say through f1 The you know the up-down term accumulates phase relative to the down-up turn term When I go through the second for a magnet if its magnetization is parallel I continue to accumulate phase if it's antiparallel then I subtract phase So imagine that the thickness of the first one puts me here on this diagram Then in the parallel state the second one moves me to the right the antiparallel state it moves me back to the left So it turns out just with a single junction you can also get a you should be able to control whether you're in the Pi state of the zero state. I just emphasize the physics is very different from the triplet in the triplet case We're using spin rotations here We're using phase accumulation or subtraction So this is experiment we want to do we want to do a spin valve and you can see why maybe this one worked first This one only has two magnetic layers to control as opposed to the triplet which has three magnetic layers This one's just a little easier to control Okay, so the experiment we have to make a squid. So first we make small junctions That's not too hard to do using ebim lithography. We're making elliptical junctions We actually since we have a squid with two of these junctions what we'd like to do is make them elliptical with different aspect ratios This micrograph here actually shows junctions that are much larger than what we find they use the ones We find they used are typically a half micron wide by one and a quarter microns long It's typical aspect ratio what we do is we make one with a longer longer at bigger aspect ratio longer and skinnier And the other one that's a little shorter and fatter. Maybe it's easier to see over here This this shows two different squids There's a flux line running up the middle so you can put flux in the squid to measure the squid oscillation pattern the two junctions and Then the in-plane field in this direction is to switch the free layer. Oh, yeah one other thing I have to say we're using a hard magnetic layer a hard magnetic material and a soft material the soft material is permaloid The hard magnetic material is nickel Nickel is not so well behaved, but it's the best we have at the moment So the idea is with a small field We'll align everything with a big field and then with a small field We hope to rotate the permaloid and in particular the idea is we can switch the permaloid and the fatter junction first And then in the skinnier junction. This is just an artist's rendition of the same physics Showing the the two junctions in the squid and then the four different states Which we've we've labeled them already pi pi zero pi zero zero pi zero in Anticipation of what we're going to see and I'll try to convince you that the data Actually support that interpretation So what so going from pi pi to zero pi? We've just switched the permaloid layer in one of the junctions Then we switch the permaloid layer in the second junction Then we switch back the permaloid layer in the first junction and finally you get back to the initial state And this this just again to just make sure everybody understands what we're doing So here's the squid again if the two junctions are in the same state It doesn't matter if they're both zero or both pi you get constructive interference and the critical current of the squid versus applied flux If you switch one of the junctions, then you'll get destructive interference You switch both junctions you'll get constructive interference again. So that's what the experiment is meant to see So let's look at some data the data. I'm going to plot in a three-dimensional plot So I'm plotting critical current as a function of the flux through the squid. It's Listed in milliamps. It turns out the conversion is almost exactly one milliamp per flux quantum So you can just read this as flux and flux quanta This is the in-plane field we apply to try to flip the junctions So the protocol is we initialize everything with a field in the negative direction So we're in this state all magnets all magnetic layers all magnetizations are pointing to the left Now at around 30 ersted or so you see there's this big jump the critical current changes And you can also see there's a phase shift the position of the peak has shifted relative to here I'll interpret that tentatively as we flip the perma-loy layer in one junction and again I have to prove that later that that's actually what happens then we go to a slightly higher field 50 ersted again There's a big jump and a big phase shift So we interpret that as we've now flipped the second junction. So we're now Both junctions are in the zero state here. We come back in the negative direction. So we started zero in this state We come back at minus 35 ersted. There's a switch to yet another state I claim as we've switched the first junction back again And then finally up at around 90 or 100 ersted we get back to the to the initial state So just to summarize the observations First of all the critical current is periodic and flux with period fine Not as you expect we get magnetic transitions at these four fields both the amplitude and the phase change so that simple If I picture I drew for you was not completely correct then those of you who know what a squid looks like you notice that these Critical current oscillations here have a funny ratchet shape. I mean if you go back to the previous slide You know, you're used to seeing something like this It's an absolute value of a cosine curve and you'll notice that these These oscillations here and I see plus don't look anything like that cosine curve. First of all the modulation is not very deep Second of all it has a funny asymmetric shape. It's not cosine. It's ratchet That's a little bit confusing until you look back in the squid literature and it turns out this is all very well understood if you model the squid as Just having you know two junctions and two inductances It turns out that that idealized cosine curve you get only if you can ignore these inductances So if the product of the critical current times the inductance is very small compared to a flux quantum Then you just forget about the inductances and you have this simple squid model Once though so we we designed those squids actually for spin triplet experiments We use them for spin singlet our critical currents were 10 times higher. We were a little caught off guard So we have to deal with with deal with this and then the other thing is our geometry is asymmetric our geometry looks like this So the current going around the clockwise direction Actually has a much larger flux coupling than the current going counterclockwise. So the two inductances are unequal So it turns out when that's the case and then of course our two junctions the critical currents are switching So they're going to be unequal by necessity So it turns out in this case you get that the ic plus and the ic minus the critical currents in the two directions are not Equal in general they both oscillate with the period the flux quantum But the peaks are shifted with respect to each other and up equal in opposite directions so to do the analysis you actually have to go through a little bit of Curve fitting which we've done And everything is very consistent in fact we get we get very nice fits to all the data sets So here what I've done is I've taken a slice through those three-dimensional pictures at four different values of the magnetic field This was the initial state. This is after we had one switch This is after the second switch and then this is after the switch in the opposite direction The solid lines are fits to that simple squid model And as you can see the fits are excellent and all four fits give you a consistent set of in of inductances in the squid if you prefer you can plot what I call the average critical current which is just the The sum of the two in absolute value divided by two And here you get something that is doesn't have this funny asymmetry So this this symmetrizes the effect and you can see very easily that the peaks and valleys line up Which shows you conceptually that that you're getting pie face shifts each time you you go through one of these transitions So I think probably you don't want to see all the all the fitting parameters I just want to show you that if you do the four fits the inductance values You get are extremely self-consistent. You get very very small standard deviation For the two the two inductances, so it's about six picohenry's and 12 picohenry's for that for the two sides of the squid And then I'll go I'll jump through this stuff This is just to if somebody asked me I can prove to you that we actually did all the yeah We did all the fitting correctly So how much time would you like me to speak as opposed to questions three minutes? Okay, so let me just show you one more thing which will literally take three minutes So going back to here back to the spin triplet These data I won't show you because first of all they'll be published We'll submit them pretty soon, and it's a little bit long and complicated I would say the data decent, but they're not spectacular This one I'll show you just so you can see why I've been so frustrated doing this So it's exactly the same experiment. It's a squid experiment. Everything looks like the previous the previous few slides I showed you so we first We first got data like this so here again is the 3d plot. We're ramping up the set field So here you see these nice squid oscillations. They're quite a bit deeper Than before because the critical currents are much smaller here We're at 30 microamps instead of 300 microamps or 500 microamps, and then it's hard to see in the 3d picture But if you look top down you can see very clearly this beautiful pie phase shift here and then another pie phase shift there So we were jumping out of our seats with joy and then we applied the field in the opposite direction to get back to the initial state And we got this mess And that was extremely frustrating and we haven't been able to get it What we really wanted of course was to just reap you know We produce something like this in the opposite direction and I just couldn't bear to publish garbage data like this So these data have not been published. This is in my my students thesis a little bit frustrating Okay, so let me skip as I say we've done this experiment to maybe I just show one data set So here we're just trying to Rotate one magnet 90 degrees to turn the thing on and off and I'll just show you these data here We're measuring in zero field and we're applying this field and you can see the critical current is coming down down down It would have been nice if it had just dropped a zero there It's getting stuck on some probably in homogeneity due to roughness and then going the other way it comes It comes back up very nicely. So we have succeeded in doing that It just would have been nice if it had happened a little more abruptly. So I'm going to skip all those and just show you Go to the conclusions So the conclusions are there's long range spin triplet super currents are definitely there They require three for our magnetic layers. You can control the super current with the magnetic state We've done a Decent job or not so great a job depending on which experiment you talk about I didn't talk about this Crazy odd frequency firmly on pairing but given the number of theorists in the audience I'm sure we could start a large discussion of that Originally, I thought this was extremely exotic and then in recent years people have told me This is actually much more common than than was thought so I won't say much about it The the newest thing I showed you is that actually even the short range spin singlet super current can be controlled Using a spin valve junction and as you can imagine since I told you we're working on this for cryogenic memory That's that's probably going to be our memory device and if you're new to this topic and you'd like to read about it Matias Escherig wrote a nice a Nice overview of the topic in physics today in 2001. So again, happy birthday Boris and I'd be happy to take questions