 I am continuing in lecture 24 studies with neutron reflectometry technique. In the last lecture I discussed with you how we could interpret the alloy composition in a nickel-aluminium multilayer, though we use PNR but there it was more of physical density. Before I go on to polarized neutron reflectometry studies which is the most interesting thing for the condensed matter researchers, I must briefly mention you neutron reflectometry for liquid-liquid interfaces. This is a branch of studies which has gained popularity in last I should say 20 years or so where we study the interface between two liquids or interface between liquid and air with various chemicals like we can study interfaces of a liquid possibly with surfactants sticking out from them. I use this example because we have studied myself form from surfactants in science technique. So similar studies in reflectometry for these interfaces are very much popular presently and such studies have become so much in demand that there are dedicated neutron reflectometers of an unpolarized neutron reflectometer where you can have physical density profiles for proteins on liquids or polymers on some kind of interfaces. I will use only one example to highlight the role of these studies. This study I have chosen is with liquid-liquid interface with neutrons. Such interfaces can also be studied with x-rays and have been done also. But in case of neutrons the interesting thing is that I discussed with you earlier that we can play with the D2 OH2 ratio in the solution or if it is water then in the water background or the water substrate on which we make spray these chemicals so that I can get a very good contrast that is the advantage. So here I am just showing you one example of nitrile reflectivity data for WIC, poly cation, PDMA, EMA, poly dimethyl amine methanolic that is one polymer and spreading of such polymers are important for biological samples because polyethylene oxide brushes and how they interpenetrate this is important these studies are important because protein spread or protein unfolding on such medium are of interest for biological studies. So here this example deals only with an example of PDMA, EMA and PEO brushes and this study highlights how these brushes they interpenetrate actually they have been stabilized with a hydrating solution at pH 5, pH 5 and pH 10 so depending on the pH value we know that pH is the negative logarithm of hydrogen density and pH 7 is a neutral solution so pH 10 is alkaline and pH 5 will be acidic that is the thing and we have just showing two data unpolarized reflectometry but if you look at this schematic or the cartoon on the right hand side you can see that there are two possible configurations at the interface for PDMA, EMA and PEO one is that they don't interpenetrate they don't mix and the other one if they mix that the brushes interpenetrate the first data at pH 5 you can see that the fit without penetration this one and with penetration have been attempted and the fit with penetration interpenetration of the brushes gives a better fit and that means at pH 5 for these two brushes spread on a hydrating solution allows the interpenetration but when we go to pH 10 of course under a pressure of 6 bar this whole experiment was done under the pressure of 6 bar then it switches from interpenetration to no penetration here the experimental data for interpenetration this one and no interpenetration compact fit so this one gives a much better fit so it supports this picture and this is not correct here this is not accepted so this is an example while by measuring scattering length density profile this is what we measure in all neutron and x-ray reflectometry experiments as I showed you earlier the scattering density profile is a nuclear density if it is an unpolarized beam and for so we call it NSLD and in case of x-ray it is electron scattering length density or ESLD and if the system is magnetized or it has got magnetic moment then this NSLD for neutrons we also add one magnetic scattering length density I will get into it right now so this is the only example I am using where organic and biological samples at the interfaces and their properties with respect to their spreading into each other penetration into one of one medium to another medium can be studied using a neutron reflectometry or rather neutron reflectivity now I will get into polarized neutron reflectometry or beams with polarized so polarized neutron reflectometry PNR is polarized neutron reflectometry so as the name suggests that this PNR needs a beam which is polarized now this can be done in two modes one with no polarization analysis and with polarization analysis so I will first talk about without polarization analysis and then with polarization analysis let me just show you the experimental setups this is the one at Zluva this setup is at NCNR NIST you can see that there is a polarizer in both the cases there is a polarizer in both the instruments and after the instrument there is place for analyzer here also there is an iron silicon analyzer so for without polarization analysis we have what we measure is r plus and r minus so if this is the sample with this is the magnetization direction then I have two reflectivities one the neutron parallel to the magnetization in the sample and the other one is antiparallel to the magnetization in the sample and there r plus and r minus now if you remember I had earlier also discussed this that this nuclear potential for r plus it is getting added by one V magnetic and for r minus this is minus V magnetic so now we have twice pi h square by m the potential the step potential rho B coherent this is the density B coherent plus minus a magnetic scattering length which gives me Vm and this is either plus or minus and then because of that we have also the critical angles which are different because V dictates the critical angle of reflection for that particular neutron so if I see the reflectivity I will share with you if this is plus then this will be minus the critical angles are different and this polar let me just remind you that this polarizers are often super mirrors super mirrors these are the as I showed you like in nist the iron silicon super mirror and as I explained to earlier super mirrors reflectivity one is it has got a large critical angle over simplified picture but it is somewhat like this for once spin of neutrons and much smaller critical angle for another spin of neutrons and this is if I take a reflection at an angle which is between these two critical angles then I can get a fully polarized beam so this is the principle of polarization and in the reflected beam say with using the same principle if I put an analyzer analyzer of the same super mirror at an angle which is again between these two critical angles then I will get only one particular spin reflected into the beam and the other will be transmitted so I can find out what is if it is a plus one plus reflectivity then R plus is given by R plus plus plus minus both because we don't analyze when there is no polarization analysis but if we want to do the analysis then I will get two reflections it's non-spin flip because plus goes as plus and spin flip plus goes as minus I will come to it later so this is a general assembly of a reflectometer with the analyzer in place in both these things typically in the reflected beam we need to put a polarization analyzer to know the non-spin flip and spin flip so now first we are just measuring R plus and R minus that means we don't do any spin analysis of the reflected beam we just impinge a beam which is either parallel to the magnetization in the sample or anti-parallel R minus and we measure them now as I told you earlier that that V in a matrix form has got two components one is the plus component one is the minus component so V plus and V minus equal to B coherent plus BN and V coherent minus BN and similarly as I wrote earlier also earlier the critical angle was lambda square root of rho B coherent by pi for unpolarized beam now for the polarized beam I have got two critical angle which are described right now this is the expression for them so now we also have to consider the Schrodinger equation for propagation of these waves and they are actually two equations one for the up neutron which is due to the standard form of the Schrodinger equation where V plus is the potential which is mentioned here another one is for the anti-parallel neutron which is given by E minus V minus A so you can see the solutions are different and the critical angles will be different for the solution so again now also I use parrots formalism as I wrote earlier parrots formalism to calculate the model reflectivity pattern for up and down neutrons and then fit do the fitting in our case we use genetic algorithm but there are other fitting techniques which are used and we get the solution in form of reflectivity as a function of angle for the two polarizations so it's just an experimental example I am showing you it's a nickel film this nickel film is magnetic and we know that nickel has a magnetic moment of around 0.54 Bohr magneton per atom so I have shown here the plot of the reflectivity profile of the two spins R plus and R minus reflected from the film and we often we also take records to a plot of asymmetry parameter asymmetry parameter is this it is R plus Q minus R minus Q divided by R plus Q plus R minus Q so this asymmetry parameter joins the two reflectivity profiles at one and also joins the fit to both of them as I show here so we have fitted it using parrots formalism for the two spin components and this is the joint fit which shows that oscillation these oscillations are due to kissing oscillation these are kissing oscillations and you can see the asymmetry parameters and the fit and from the fit we could get the magnetic moment density in this medium so when we don't do polarization analysis what we get is magnetic moment density in the medium that is what we get so this at the measure at a mesoscopic lens scale so now with this much of introduction to experiments that are possible without polarization analysis of the reflected beam I use two examples to highlight the findings of such one is that this is a cobalt film which was deposited by electron beam technique electron beam deposition technique and this is a cobalt now interestingly this is first before I take you to the neutron reflectometry or polarized neutron reflectometry usually for most of the samples we first carry out an X error because X error 1 it is possible to get very accurate result for the physical density because it is a high intensity technique we have also used X tm or cross sectional tm high resolution tm to get the crystallographic structure at the interfaces so never a study is complete but interesting enough unless we marry several techniques together surely pnr is an excellent tool but I want to highlight this point that to get interesting result we need to combine several techniques together here from the external data we calculate and you can see the kizig oscillations so these kizig oscillations are coming because of the thickness of the film thickness of the film as I harping again and again and fit to the data gives me the physical density profile and gives us a signature of something which needs to be probed further what are those signatures one if you look at the density profile that I have fitted for the cobalt film what I would expect for a film such a single film film is somewhat like this if I consider the substrate density profile is this in some unit the cobalt film should look in density somewhat like this because at the if I consider this side substrate this side air because we have seen generally that the density at the surface is less and after some point it goes to near bulk density similarly due to interpretation or mixing between the surface I mean between the substrate and the film there is a lowering of intensity at the interfaces but here what I found by XORR is something very interesting what we found here actually not just this structure I will go back to the we find a high density layer high density layer high density layer density layer at two interfaces one is at the substrate film interface the other one at the substrate air interface this is something not expected and then XTM we did XTM in this region and this is the region which I have highlighted here and the first Fourier transform of the XTM pattern over here this mean FCC structure this is also an interesting phenomena because this is high density this is FCC whereas cobalt is a ferromagnet which is HCP bulk cobalt is HCP this cobalt is FCC at the interface and it has got an interface density almost one and half times that of bulk density and FCC structure from XTM so then we took this sample to a neutron reflectometer that oak reach now this will tell us this FCC cobalt cobalt and its its magnetism so one is a physical density profile that I will obtain from nuclear scattering length density in the same manner I obtained in XRR through electron scattering length density so please see the neutron or polarized neutron reflectivity data this is the physical density it clearly shows the fits are here for the plus and minus polarized neutrons this is the asymmetry parameter over a very large Q range almost up to 0.25 angstrom inverse and you can see that the high density layer so XRR and PNR they are able to identify this high density layer and its density turns out to be similar to what we found from XRR values so this is the physical density now the magnetism we have done we have found out the magnetic density profile also from the reflectometry rate of X plus R plus and R minus this is the asymmetry parameter here interestingly the bulk of the cobalt has a positive scattering length density that means it is ferromagnetic and the magnetic moment density profile shows that but this high density layer if I look at the high density layer at the interfaces they are non-magnetic so these experiments they allow us to identify a non-magnetic FCC cobalt layer at the interface this has been reported here so FCC and non-magnetic cobalt layer is an interesting observation because it is known that under high pressure cobalt goes to non-magnetic high density phase but here in this thin film at ambient pressure they were I mean when you use the film for the reflectometry experiment there at ambient pressure this same phase is obtained so at the interface we conjectured that due to grain boundary migration grains some grains got pressurized and they turned into this FCC high density cobalt in this specific film which otherwise not seen in bulk at ambient pressure so this is one very interesting result using magnetic moment density from thin films another interesting thing is coupling between a superconductor and a ferromagnet this is an ideal sample for polarized electron reflectometry reason being we know that super conductors are ideal diamagnets if you remember superconductors conductors ideal diamagnets that means they repel any magnetic field and generally you are familiar with this picture if there is a superconducting material with a magnetic field when you go at T less than superconducting transition temperature it will for a type 1 superconductor it will repel out the magnetic flux that's why a superconductor is known as an ideal diamagnet and in measuring magnetic moment density we should be able to identify here the magnetism in a superconductor but now here we have gone into little more interesting aspect what do we have here in this experiment that I am explaining to you we have got a trial layer so we have got YBCO formula given here it's familiar to you this is an insulator SRTIO3 STO and this is a ferromagnet LSMO Lantanamstronchium MNO3 now this is a tunneling geometry that means if I show you then you will be familiar with this I hope you are familiar with tunneling so I have got a superconductor I have got an insulator and then I have got a ferromagnet so we have a superconductor and a ferromagnet separated by a layer of insulating STO that's your tunneling geometry now we are familiar with the fact that in case of superconductors we have tunneling of cooper pairs of cooper pairs pairs so what are cooper pairs in VCS theory we know that electrons with opposite spin on the Fermi surface these are Fermi surface they couple with each other so we have got a spin zero cooper pair and it is known that if I have a superconductor another superconductor with an insulator in between we can have two kinds of tunneling one is single particle tunneling known as gaver tunneling we also have a cooper pair tunneling where it might go from here to here and based on these many experiments and many devices like squid or bill so in this case we have a bill uh trial layer where we have this tunnel we have invoked this tunneling geometry they are laser beam deposited and they are oxide so high tc superconductor then insulator and then a ferromagnet this superconductor has a superconducting transition temperature of around 65 kelvin we determined it from bulk measurements and also it has got cool temperature of around 290 kelvin that has also been obtained by bulk measurements interestingly in this case what we found from extra diffraction this is an extra diffraction pattern that nice layered structures do form x t m tells us but this is a highly 00l oriented structure 00l oriented structure that you can see from the peaks that we obtained we call it ysl ysl trial layer you can see 0034567 you get so many of the orders of bright peaks in 00l index same for ysl and if we make films of ybco and lsmo and ybco, stu and lsmo we get similar peaks so because of the what was the crystalline matching between these layers we get highly oriented films there is a reason for me telling you this because this superconductor ybco is a d wave superconductor superconductor so as I told you earlier I mentioned to you that other conventional superconductors are s equal to zero and it has got a spherical symmetry of the cooper pair but here because a d wave superconductor d wave superconductor there the band gap that there is a gap superconducting gap at the surface of the at the fermi surface position this gap is anisotropy anisotropy and this is s equal to zero and p is the wave function the cooper pair wave function so you can have dx square minus y square and that looks like this and dxy will xy will x and xz will look with lobes like this so the symmetry of the wave function for the cooper pair is not spherical here it is like this and directionality in the deposited film should have something to say about the cooper pair tunneling and also the gap that you see in various directions now let me get into the experiment of polarizing electron reflectometry so it's a highly oriented yttrium barium copper oxide srtio3 lsm of film in which we have created a tunneling junction and we want to see how the magnetization is affected by the superconducting transition temperature