 to this course on nanostructured materials, synthesis properties, self assembly and applications. We are in module 4 lecture 7 and we are discussing magnetic properties of nanostructured materials. This is the second lecture of three lectures we will be discussing on magnetic properties of nanostructured materials. In the previous lecture on magnetic properties, we looked at basic magnetic properties like what is ferromagnetism, what is diamagnetism, what is a magnetic moment, what are the units of these magnetic quantities and how magnetic domains are formed, what are the energy involved in domain formation and what is the technique to look at magnetic domains in a solid and that technique is the magneto optical curve effect using which you can identify different stripe like structures or circular structures which give you the shape of the magnetic domains present in the magnetic material. Now, these properties what we discussed in the previous lecture are generally applicable to any magnetic material, they need not be nanostructured materials, they can be bulk materials as micron sized with micron sized particles or larger particles and now we will discuss how these properties these magnetic properties will change when these materials are in the nano dimensions. So, when you have particles of small size say 20, 30 nanometers or even smaller, how does the magnetic properties of those materials compare with their bulk materials that is those materials having micron sized particles. So, we will be discussing mainly the magnetic properties of nano sized materials in this lecture and the subsequent lecture to complete our three lectures on magnetic properties of nanostructured materials, this is the lecture 7 of module 4. So, another quantity one has to understand when one wants to differentiate between the magnetism of bulk ferromagnets and how the magnetization changes as a function of field and how this will depend on the size of the particle is of interest to us. So, magnetic hysteresis plots can be obtained if you measure the magnetization M of any material as a function of the applied magnetic field H. So, imagine that you are having 0 magnetic field then the magnetization is 0. So, you are here and if you increase the magnetic field the magnetization will increase. So, initially it will increase from the origin it will go like that and then it will reach a saturation which is called the MS or saturation magnetization that is given by extrapolating this line to the y axis and this value of magnetization is the saturation magnetization. Now, ideally in a normal ferromagnet you will see this kind of a hysteresis loop and as you change the magnetic field it increases reaches a maximum then you decrease the magnetic field the magnetization will start decreasing. However, it will not come to 0 from where you started but will intercept the y axis at some position and this point where the magnetization cuts the y axis is called the remnant magnetization. Now, the field applied at this point is 0. So, you are having a net magnetization which is remaining even in the absence of a magnetic field and hence it is called a remnant magnetization. This is a property of anything which is ferromagnetic or ferrimagnetic and it is because of the magnetic domains present in the magnetic material and the alignment of the magnetic vectors within those domains. Now, if you change the magnetic field in the opposite direction. So, you are increasing the magnetic field in the negative direction then the magnetization will further decrease till it hits the x axis at a particular field. So, you are making the field negative or which means the field has a direction which is opposite to the original direction of the magnetic field. So, this field which you are now applying is in the opposite direction and has a magnitude h c when the net magnetization goes to 0. That field at which the magnetization is really 0 is called the h c or the coercive field. So, what we learn from this hysteresis loop typical for ferromagnetic materials is that you will get a saturation magnetization you will get a remnant magnetization when the field goes to 0 when you are doing the cyclic loop and when you take the field further in the other direction you will get a net magnetization is equal to 0 only at a field which is h c and is opposite in direction to the original field applied and then you further increase the field in the direction in the negative direction and the magnetization changes sign. So, it goes in the negative direction and reaches a saturation which will be equivalent to the magnetic saturation magnetization in the opposite direction. So, here whatever will be the value you get a negative value that means a magnetization in the opposite direction with a similar magnitude and then if you again retrace the path you increase the magnetic field you will again see an increase in the magnetization. So, this particular loop of magnetization as a function of magnetic field is called a hysteresis loop and is typical for ferromagnetic or ferrimagnetic systems and the area under the loop tells you about the material about how hard is the magnet or how soft is the magnet. So, something which we say is magnetically hard what does it mean something to be magnetically hard means it is difficult to magnetize that sample that means you have to give a very high magnetic field to reach saturation magnetization. So, if you have high M R and high critical field that means very difficult for the magnet to lose its magnetization. So, high H C means you have to go to very high magnetic fields before the magnetization goes down to 0. So, basically the area of the loop will increase when something is magnetically very hard and not only that this breadth of this loop will be very high because H C will be very high means the breadth of the loop will be very high. So, typically a permanent magnet has a ferromagnetic substance will have will be magnetically very hard it will have a high remnant magnetic field and it will also have a high coercive field something which is magnetically soft will have a low remnant magnetization and a low coercive field and this area under the loop will be very small. So, such a material can be easily demagnetized a hard material cannot be easily demagnetized whereas a soft material can be easily demagnetized. So, if you look at the hysteresis loop again carefully the red line shows that initially you started with 0 you reach the maximum which is possible magnetization and here we are calling it in plotting in terms of the flux density which is related to the magnetization. So, you can plot the flux density also and so you have a remnant flux density B R and then you have a coercive field and this kind of plot shows you a ferromagnetic substance and this if you look at this plot what is what is the type of magnetic dipoles that you have what is the orientation of the dipoles at different stages of this plot can be seen here especially the red plot the initial magnetization when you started from 0 magnetization the material was not pulled earlier. So, first time when you magnetically pull the material you apply a magnetic field you go through these steps. So, you see initially at 0 field there is 0 magnetization because all these vectors are in different orientations. Now, when you increase the magnetic field then some of these dipoles become gain in strength you see this region is becoming larger here there are four quadrants all the four quadrants are equal the vectors are pointing in different directions the net magnetization is 0 or the net magnetic flux density is 0 when you are here then you see some of the quadrants being higher in energy and hence you have a net magnetization or a net magnetic field intensity flux density and that region grows in area and so this region is increasing till you come here and all out of four domains you had four domains here you had four domains here here also you had four domains, but very small domains some of them and one large domain here now you have again only three domains and one large domain out of the three finally, you have only one domain only one vector you have you can see very large vector in one direction, but the magnetic field is in this direction. So, this vector is yet not aligned with this direction, but all the vectors within different domains have now become one and you have one magnetic domain. So, this is a single domain particle though the magnetic vector is not aligned with the magnetic field now if you increase the field further then this direction of this vector also becomes aligned with the magnetic field. So, that is the maximum that is the final stage that is when all the small domains had converted to one domain and the vector in that domain has aligned with the applied magnetic field and that is the maximum magnetization you get if you increase the field further there will be no further change because this moment cannot grow any further there are no new domains to be added to it and so the net magnetization becomes constant and this is the explanation of this red curve here. So, you can see different stages how the magnetic dipole vectors are changing and the domains are changing as a function of the applied magnetic field. Now, you can have different types of hysteresis so you see you can have a hysteresis loop which is very small area here the area is large then you can have a hysteresis loop where you can have nearly very sharp change in the magnetization or magnetic flux density and or you can have a smooth change in the magnetic flux density. So, there are different types of magnetization as shown by these three here the remnants is very low here the remnants is very high this also has a very high remnants, but you reach saturation very fast the moment you cross this field you immediately reach saturation. So, this is a rectangular type of loop this is normal loop and this is very good for storage you can apply a particular field immediately all the dipoles are aligned you apply a field in the opposite direction all the dipoles will get misaligned and you will get a resultant flux density to be 0. So, quick switching can occur in this kind of system here it is slightly slow because it varies with the magnetic field it does not change suddenly in this case there is very low remnants although the induction or the magnetic magnetization is high now in this case there is a 0 remnants. So, this is not a particular ferromagnetic material because the remnants is nearly 0 and this is a linear type flat loop and this is typical for powder based material there is hardly any remnants it is nearly 0 remnants and this is a non-linear loop for mixtures you can see that you have a ferromagnetic component shown by the hysteresis loop, but the component it reaches saturation, but it never reaches saturation it never becomes flat you see it is continuing to increase with increase in field strength. So, it is a kind of a non-linear loop because there is the change in the magnetic field is not directly proportional to the field. Now, we come to the exact problem of magnetism in nano materials what is super paramagnetism many of these magnets when you decrease the size of the particle to the nano dimension you will get super paramagnetism. So, in nano structures the thermal energy is insufficient to overcome the spin-spin coupling energy which exists between the magnetic dipoles at room temperature. So, they are unable to change their position. So, you would not have that kind of energy to overcome the spin-spin exchange coupling energy at room temperature and if you cannot overcome that then you will have a random distribution of the magnetic vectors and that is what happens in super paramagnets where you have a random orientation of the magnetic spin inside the particles and this kind of a random spin leads to 0 remnant magnetization and 0 coercerivity which is like a paramagnetic behavior. So, not like a ferromagnetic behavior in a ferromagnetic behavior you must you will have a remanence and you will also have a coerce field that means the plot will not go through 0. Whereas, whenever you have a 0 remanence and 0 coerce field the line will go through the origin that means the you need no energy to bring back the sample from its magnetized form to the 0 form where there is no magnetization. So, that kind of result where you have a net magnet remnant magnetization is 0 and 0 coerce field that is kind of a paramagnetic behavior since it is a particle and not a ion or molecule. Hence, we call a super paramagnet that means several molecules or ions together form one magnetic vector which is disoriented or has random oriented inside the particle. So, that you can see here in this plot the difference between a large particle and a small particle what happens is if you have two position two vectorial directions. Suppose this one indicated by mu has a vector which is pointing upwards and here it is pointing downwards and if you cannot go from here to there then that means you will have some net magnetization and this is ferromagnetization when the energy exchange energy is greater than k t. Now, you have if you have a plot energy plot here is the thermal energy as a function of say orientation of the spins here you can consider this to be a magnetic moment and if you are in this stability zone that means the energy is minimum here for one direction and the energy is minimum here for the other direction of the magnetic vector you want to go from this direction to this direction you have to overcome this energy barrier now this energy barrier for a large particle is large. So, this is the total energy barrier you have to give this energy if you want to change your spin from this direction to this direction in a small particle in a nano particle this energy difference is much smaller and so it is easy for the moment to change its this magnetic vector to change its direction by giving this kind of energy. So, now if at room temperature the thermal energy has a value of this nature which is less than the value required by the large particle, but this energy is sufficiently more than the energy required to change the magnetic vector in a small particle then you will automatically have this change in the spins. So, you can do this spin flipping by the normal temperature at normal temperature and you will have both possibilities in your system and so this spin fluctuation then leads to super paramagnetism. So, whenever the energy required this value is called u and this value whenever it is less than k t where k t is the energy that is the thermal energy then you can have spin fluctuation and then it will result in super paramagnetism. So, what will it look like in when you plot the magnetization how will the hysteresis loop look like. So, for a large particle where you have plot magnetization on the y axis and the applied magnetic field in o r state in the x axis you see that there is a loop although the loop is not closed here if you go to higher fields this loop may close, but you can see that there is an area under the curve when you plot magnetization versus magnetic field this is for large particles. Now, for same material if you decrease the size of the particle. So, suppose these particles are around 50 nanometers and these particles are around 10 to 12 nanometers these small particles do not show this hysteresis loop, but they show a plot which goes through the zero which is like there is no remnants and the coercive field is zero and this is typical for a super paramagnet. So, it behaves like a paramagnet although it is a particle with several moments, but the moments are flipping among themselves and so resultant is a behavior like a paramagnet. So, this particular plot shows you how a super paramagnet behaves in a magnetic field and these two plots clearly differentiate the change in the magnetic property of a magnetic material when you decrease the size of the particle. So, this is one of the most important aspects of the magnetic properties of nano structures the property of super paramagnetism when you decrease the size of a magnetic material which shows a hysteresis loop when the particle size is large, but the same material when you lower the size of the particle to nano dimensions then it does not show the hysteresis loop, but the magnetization plot versus field goes through the origin showing no remnants and no coercive field. So, this way and when will this happen this will happen whenever the energy required to flip the two vectors is lower than the thermal energy. So, that is the key point that the energy to change from one vectorial direction to another vectorial direction is much smaller than the available thermal energy then you will see this kind of super paramagnet super paramagnetism which is highly prevalent in magnetic materials and is a function of the size of the particle. Now, in super paramagnetism the smaller the size then you have a temperature which is called a blocking temperature that means that as it is behaving as you are lowering the temperature the magnetization should increase in a paramagnet like in any ferromagnet also the magnetization increases as you are lowering the temperature, but in a super paramagnet below a certain temperature the magnetization will start decreasing. Now, that temperature is called the blocking temperature. So, the blocking temperature changes as a function of size smaller the size of the particle smaller will be the blocking temperature. So, the temperature at which the behavior of the paramagnet instead of going to a ferromagnet where it the magnetization should increase further instead of that it starts decreasing that temperature is called the blocking temperature and the blocking temperature will change according to the size of the particle. So, the smaller the size smaller is the blocking temperature and this actually is due to the fact that the thermal energy is much larger than the anisotropic energy barrier that is u we discussed and smaller the size of the particle this u will become even smaller and thus magnetization will be easily flipped. So, the blocking temperature gets lowered with the size of the particle apart from that there will be no hysteresis in super paramagnets there will be no remanence remanence or no remanent magnetization there will be no coercivity or no coercive field the h c will be 0 the m r which is the remanent magnetization will be 0 and the large particle a magnetic moment in each particle will be there. So, the magnetic moment of each particle will be like the collection of the magnetic moments of the dipoles which are present in the particle. So, it will have a larger magnetic moment. So, if you see the plot here which we mentioned initially you see you have these the length of the arrows may be taken as the magnitude of the moment. Now, these are very small as you the as you are changing the field you see this arrow is growing and it is becoming larger and larger. So, here the length of the arrow is much higher that means the magnitude of the magnetic vector is higher and so that is that will always be found in this kind of material super paramagnets where you will have a large magnetic moment in each particle and also there will be a fast response to the applied field. That means if you apply a field the moment will be there and if you remove the field the moment will not be there it will be having a large response quick response to the applied magnetic field and the magnitude of the magnetic moment will be larger in this each particle and that is why it is called super paramagnets. Because normal paramagnet will have some magnetic moment but when you have a particle with several of these moments aligned together to act as a single moment then this single moment will have a much larger value and that is why this property is called super paramagnetism. Now, there are some other quantities which one relates to these kind of super paramagnets one is of course the blocking temperature that is the temperature where it the paramagnet should have become the ferromagnet but the magnetization instead of increasing starts decreasing. So, that is the temperature which is the blocking temperature then you have the magnitude of the magnetic moment which will be much larger and that also defines a super paramagnet and then there are other quantities like the relaxation time how much time it is required to achieve zero magnetization after removing the external field. So, you apply a field and then remove the field how much time will the moment require for it to become again zero the magnetic moment to go to zero because in the absence of the magnetic field any paramagnet and hence a super paramagnet should also have a zero magnetization but it will take some time to achieve that zero magnetization that is called the relaxation time tau and that is given by this expression tau equal to tau naught exponential capital K multiplied by v by small k t the small k is here the Boltzmann constant and capital K is something to do with the material it is called the anisotropy energy and it changes from material to material. So, for example, the anisotropy energy if it is very large then it will take much more time for the magnetization to decay to zero because it is exponentially related to the capital K which is the anisotropy energy and the anisotropy energy for iron oxide which is a good magnetic material. So, if you reduce the size of iron oxide particles make nanoparticles of iron oxide then you can observe that it will show super paramagnetism and it will show a relaxation time tau which is related to this equation and where capital K has a value of nearly 20,000 joules per meter cube there is a value of capital K and v is the volume of the particle. So, that means smaller the volume smaller will be the relaxation time because it is exponentially related and of course, higher the temperature smaller will be the time. So, if you increase the temperature then it will relax faster this understandable because we are increasing the thermal energy. So, K t is increasing and so K t is in the denominator of the exponential and hence higher the value of t lower will be the relaxation time it will relax faster. So, this gives you the equation between relaxation time and the material property which is the anisotropy energy which is different for different materials and for a very good magnet like iron oxide that value is very high is nearly 20,000 and of course, this will vary whether it is Fe 2 or 3 Fe 3 or 4 or iron metal etcetera. Then the blocking temperature which is also very important that is the temperature where the paramagnet becomes a super paramagnet that blocking temperature is also related to this anisotropy energy. So, larger the anisotropy energy larger is the blocking temperature and so the blocking temperature and the relaxation time are more or less related in this manner that is if you keep other things constant then the material with a high anisotropy energy will have a high blocking temperature and will also have a large relaxation time. So, blocking temperature and relaxation time are that way related. So, this I already defined that what is this blocking temperature it is the transition temperature where you should be getting ferromagnetism, but you start getting super paramagnetism from a ferromagnetic material as it is going from a paramagnet to become a ferromagnet, but it becomes a super paramagnet and that is the blocking temperature and it depends on different materials. Now, the applications of super paramagnetic materials why are they very important in nano technology super paramagnetic iron oxide. So, iron oxide is ferromagnetic when we make small particles of iron oxide they become super paramagnetic and these super paramagnetic iron oxide in short we call them SPIO they are used as MRI contrast agents what is MRI contrast agent when you do imaging of your body like the cat scan and you can do imaging of the spinal cord and all that using what is called magnetic resonance. You do you apply a magnetic resonance principles where you have a magnetic field and you apply radio frequency and this is known in many applications in medicine of course, also in chemistry and biology where you use NMR techniques this is a kind of NMR, but it is imaging you are imaging some signals and this is not spectroscopy. So, NMR is a spectroscopic tool whereas MRI is an imaging tool where you want to see some place some part of the body where the magnetic field can be mapped. So, MRI machines image places with differences in magnetic fields and to make a good contrast you need to add some MRI contrast agents that is which create the differences in magnetic fields locally such that you can see them better using an MRI machine. So, in that case the super paramagnetic iron oxide particles are very important they are given to in the body it is transmitted normally coated with dextran or siloxanes or polyethylene glycol it is coated with these materials inside the iron oxide which is of a very small size because it has to be super paramagnetic. So, the idea is you you do not want ferromagnetic iron oxide you want super paramagnetic iron oxide that means you want nano sized iron oxide and these nano sized iron oxide when it is coated with some of these is sold in the market as different commercial names are there. For example, you have ferridex which is dextran coated ferram oxide that means iron oxide and it targets the liver and so if you want to do MRI of the liver that means you want to see the different parts of the liver this can be used and this is already marketed by certain commercial companies. There are other kind of drugs or MRI contrast agents to be more specific based on iron oxide all of them are based on iron oxide because iron oxide is biocompatible. So, you cannot use any nano particle you have to use nano particles which are biocompatible our body will not reject such particles and so iron oxide is one such magnetic particle which the body does not reject and so iron oxide nano particles are being used as MRI contrast agents because they show the property of super paramagnetism. So, if you make iron oxide you have to make it in very small size such that they are nanometers in dimensions and then because you want to avoid some other reactions you coated with certain polymers or some other chemicals as given here like dextran, siloxanes etcetera and then you introduce into the body and these particles are transported to specific places because of the coatings. The coatings kind of functionalize these particles to take them to certain positions in the body like the liver or the lymph node etcetera and there they create a contrast which the MRI machine can see much more easily without these contrast agents also you can see, but the contrast will not be good hence clarity will be less. So, this MRI contrast agents can be seen we will see them now this is just magnetic materials these are not MRI contrast particles there is nothing coated on the magnetic particles, but it is to show that I can agglomerate magnetic particles such that I can write alphabets out of them. So, you have written A B C etcetera with magnetic particles they have been brought close together and assembled in a fashion that they look like different letters in the of our alphabets, but they are basically nanoparticles having size of around 10 20 nanometers and which have been assembled by some technique in this fashion to write down. So, it is possible to assemble magnetic nanoparticles, but what is the application now we will look at the application how do you make these assemblies like I said you can assemble them in a particular manner say I want in a linear manner like this or I want in a curve like that how do you plan these kind of assembly of nanoparticles which are magnetic in nature. So, this is one process where you create magnetic chains. So, magnetic nano chain synthesis how do you do this in the laboratory that is of importance. So, what people have done they have taken some magnetic nanoparticles. So, these black spheres are taken are magnetic nanoparticles and can be iron oxide and then it is put into a solution of a some chemicals which can be polymerized. So, you add like glycidyl methacrylate and divinyl benzene dvb. So, GMA and dvb are these and then you also add two to azo bis isobutyronitrile which is called here as a n it is normally called as a i b n a for azo and i for isobutyronitrile. So, b n so these three reagents can be added. So, you have this and then you add them together with the magnetic nanoparticles and you apply a magnetic field. So, you bring a magnet close to each. So, the magnet will align these particles and once they are aligned this mixture of these three the monomers of these will polymerize. So, you have a precipitation polymerization technique. So, you want them to polymerize and this polymerizes at around 80 degree Celsius. So, you once in the presence of the magnet these particles are made into chains then the polymerization occurs and when the polymerization occurs they form this kind of a p pods p pod like nano chains p pod means you have those piece with its cover and they form a well defined cover on top of these particles. So, this is a methodology for synthesis of nano chains. Now, this is one methodology there are many other methodologies by which nano chains can be created and here the method is what is called precipitation polymerization technique and it uses these kind of polymerizing agents and monomers to form polymers at a particular temperature. So, these are iron oxide it is one dimensional. So, it is 1 d Fe 3 O 4 because it is chains. So, it is one dimensional. So, 1 d Fe 3 O 4 chains with a p pod like a polymer which is covering it on top. So, this is a very interesting method of making a self assembled or a chain of a magnetic nanoparticles specifically of iron oxide and can be used for several applications. This is the real picture in the presence of a magnetic field. So, you have these particles and in the presence of zero field. So, at zero gauze all the particles are agglomerated you see there is no particular orientation that means no nano chain formation here. When you apply the magnetic field of 150 gauze then you start seeing some chains being formed here. So, this is like the previous plot here we are shown it schematically that you apply a magnetic field and this is what should happen when you have these particles which we can now see through our eye that means through an electron microscope. You can see that when there is no magnetic field there is no alignment when you apply a magnetic field there is some alignment when you increase the strength of the field then you get much longer chains. So, from 150 gauze if you are going to 400 gauze you see the number of long chains are increasing and hence for you increase it further to 800 gauze you see still longer chains. So, it tells you that the methodology which we described earlier bringing a magnetic field to align this particles is working and you can get aligned particles like long chains as a function of magnetic field. So, zero magnetic field no chains small magnetic field small chains and they increase the strength of the magnetic field you increase the length of the chains of this magnetic nanoparticles. So, this is very interesting for applications now if you measure the property of these chains. So, depending on different amount of monomers. So, you want to because you want to polymerize on top of this you want this polymer. So, if you add different amount of monomers the amount of polymerization will be different and. So, the magnetization will also be different because if it is uncovered you will see some magnetization if you cover it with a polymer then the effect of magnetization will decrease. So, that one can study when you do the real experiment of measuring the magnetization using either a VSM which is a vibrating sample magnetometer or a squid where you can measure magnetization in both of them you can do magnetization as a function of field. And when you do that study on these magnetic nano chains you see this super paramagnetic behavior this is what I described earlier that any super paramagnet will show a behavior where it will go through the origin that means the remnant field should be 0 and the coercive field will be 0. So, all the three compositions made with three different amounts of monomers show the same super paramagnetic behavior which we explained earlier is the super paramagnetic behavior. There is no hysteresis which one expects in a ferromagnetic material like iron Fe 3 O 4, but Fe 3 O 4 here is in very small size in nano sized and hence it shows a super paramagnetic behavior. What is the difference in the three plots the difference in these three plots is the amount of coating one has because you have added different amount of monomers the amount of coating has changed. So, this is very small a is very small amount of polymerization which has taken place and so you see the magnetization is higher because the iron oxide can feel the applied magnetic field and its magnetization is high. When you add more amount of the monomer then more of the chains are covered with the polymer. So, the magnetization decreases from A to B and then if you add further increase of the monomer the magnetization decreases further to C. So, effectively with the change with the thickness of the polymer around the particles if you increase this polymer which is forming by increasing the amount of monomer you are adding you will decrease the magnetization and that is what is happening. So, you can get control magnetization of these chains by controlling the amount of monomer that you are adding in the system before you heat it at 80 degrees to polymerize. So, you can vary the amount of magnetization all the three cases which we discussed show super paramagnetism, but the amount of magnetization changes with the amount of monomer that you are adding in the system. So, this is a good control of the super paramagnetism in this system. Now, finally one more thing probably the last point I want to discuss today is about nano composite magnets. How you can change the magnetization? If you have materials with two different types of magnetization. So, suppose something is a hard magnet and something is a soft magnet. So, what is a hard magnet we discussed earlier in a hard magnet the remnant magnetization will be high the coercive field will be high and the area under the hysteresis loop will be very high. So, that will be a hard magnet and in a soft magnet all these things will be smaller the coercive field will be smaller the remnant magnetization will be smaller and the area under the hysteresis loop will be smaller. So, if you have a mixture of two materials one is a hard magnet and one is a soft magnet then what is found is that you can alter the net magnetization effectively. So, if you make nano composites of magnets take hard and soft magnets and make a composite a mixture of two different magnets. For example, this is a high resolution transmission electro micro graph and it is quite high resolution as you see the scale is 3 nanometers. So, you are seeing a very very small regions in these samples and you have a region which you can identify using energy dispersive x-ray analysis in a TEM you can find out the composition that this part of the material this material has this part is having a formula one iron is to one platinum. So, it is an alloy particle of iron is to platinum and this is also iron platinum whereas, this part you can see it has a different kind of contrast and different kind of lattice fringes. So, this different as the lines you are seeing here are called lattice fringes and they tell you about the crystal structure the difference in the planes atomic planes in the material. So, from that we can identify that this is iron platinum one from their lattice fringes second by doing energy dispersive x-ray analysis on this part of the sample. You can find out that this is iron platinum one is to one and this part we can find out that this is iron platinum three is to one ratio and they are two different types of materials this is a hard magnet because it has a high remnant field if you take pure iron platinum particles it is a hard magnet. If you take pure iron three platinum it is a soft magnet and a combination of the two because in this particle which is probably around 15 and this whole particle is around 15 to 20 nanometers in this side and 15 to 20 nanometers in this side. So, the whole particle is around 15 by 15 nanometer has got many such small regions which are different in their properties. So, this part will have a different property because it is Fe 3 P T and this part is a different property because it is Fe P T. So, this is hard magnet type this is soft magnet type and together they are existing and what is the result the result is whenever you have a combination of this permanent magnetic field like given by a hard magnet and magnetization due to a soft magnet then you will get much larger magnetization as compared to traditional single phase materials and why is that why do you get much higher magnetization in such composites because they are interacting between each other by exchange coupling. So, when you have hard and soft particles within the same material you can have this kind of a magnetic exchange and you can have much larger magnetization than the single phase materials and how was this kind of a composite made what you do is you start with a mixture of iron oxide and iron platinum alloy. So, these are 4 nanometer 4 nanometer or 8 nanometer 4 nanometer you can mix them with different sized particles of iron platinum and iron oxide and then you anneal them. Now, you can see them differently these are particles of iron platinum alloy the small particles 4 nanometers these large particles are iron oxide particles 12 nanometers of course, here you have 8 and 4 nanometers. So, you can have different mixtures and once you anneal them that means you heat them then these form this kind of a composite having iron platinum and iron 3 platinum type of domains which are in the composite material and this kind of nano composite magnets are more interesting because they are better than permanent magnets because the soft and the hard components this the hard iron platinum grain and the soft iron 3 platinum grain interact with through magnetic exchange and you get very good magnetization. So, these are some of the properties one can change when one talks of magnetic properties of nano materials and one can do tremendous amount of application using these nano composites or just nano particles covered with polymers in drug delivery in MRI contrast agents and in other magnetic applications which we will do some more applications we will do in our next lecture. So, today we end the second lecture of our 3 lectures on magnetic properties of nano structures and this was the 7th lecture of module 4 we have 5 more lectures remaining one more lecture on magnetic properties which will be our next lecture. Thank you very much.