 In this particular module and lecture I am going to talk to you mostly about magnetic materials and being the first lecture in this series on magnetic materials I am going to consciously confine myself only to discussing the basic principles involved in magnetism. I am not going to draw any particular example as we have done in other cases. So in the next few lectures we will go into some of the special cases and find out how the magnetic properties evolve in materials both in bulk and thin films and in nano structures. So in today's talk mostly I would like to confine with some basic definitions and some understanding that is needed to view different class of magnetic materials. So I just want you to confine only to some of the basic definitions of magnetism and let us see in the next few lectures how we can go about defining a various class of magnetic materials. So in this talk I will try to tell you the importance of the magnetic structure in a molecule in a material as you would see here these are all very good cartoons of different materials how they respond and give face contrast when it is under the influence of a magnetic field. As you can see here the cartoon here on the right hand bottom is actually a classic example of bubble memory material where you can see all the stripes of this magnetic bubbles or magnetic stripes very clearly defined and they present a domain picture. Similarly on the right hand side top you can see the different range of magnetic stripes that are present those in blue denotes a different magnetic environment those in orange they show a different magnetic environment. Similarly in thin films you can see the face contrast between a ferromagnetic and a anti ferromagnetic stripe and because of this face contrast we can try to understand what is the level of interaction or how the nano magnetic domains evolve in different structures and here again you can see how the magnetic ferromagnetic domains are distributed in a given magnetic material. So before we understand how this intrinsic property develops in a material we will look at some basic definitions I should also say that it is very difficult to singularly isolate magnetism and discuss only magnetic property without discussing a correlated property. As a result magnetism and electricity is one which goes hand in hand when you think about electrical property you also look into the magnetic property because it is basically the charge and the spin of electron that we are looking at therefore when you look at magnetic property sometimes the importance of that study may have to do with the electrical property of those materials. Therefore when we think about the importance of magnetic material again the example of giant magneto resistance comes vividly to our memory and here is the classical example of how magnetic information can help us order the electrical property in nanostructures and this is a topic which I will be dealing in detail in module 5 under electrical properties of materials and this is one of the most fascinating magnetic nanostructure which has affected today our hard drive and whatever we handle our gadgets in terms of pen drive or iPod all this has to do with the discovery of giant magneto resistance where you are talking about simple arrangement of three layers only nano layers and these are all of the order of 3 to 5 nanometer in thickness and how these ferromagnetic anti-ferromagnetic or non-magnetic layers are arranged and depending on the arrangement either in a parallel fashion or in an anti-parallel fashion the whole idea of a hard disk drive or in other words the read head can be engineered. So in today's life as of now in 20th century we are handling this spin valve nanostructures which has nothing but to do with alignment of these magnetic nanostructures either in a ferromagnetic fashion or in a non-anti-ferromagnetic fashion. So when we study this magnetic property we should understand this globally affects almost every spectrum of application in today's life. Mother nature has also gifted us with lot of magnetic materials which are available but some of these materials as such have proven to be a great help in practical applications. For example, we have just come out of the age of using audio tapes we are now more into other recording media like iPod and other things where digitally we record we know more record using tapes but till 1990 audio tapes were very famous and gamma ferrite which is one form of ion oxide has been used as the tape material which is a very magnetic material and again in today's nano biological applications we have magnetite that is Fe3O4 which is being used it is a very magnetic material having Tc force 75 to 485. Then we can also look at other examples of different phases of ion oxide hydroxide which are also showing interesting properties for example alpha FeOOH actually is a AFM anti-ferromagnetic material but the other phase is a very magnetic compound with a Tc of 180. So you can see a range of oxides and apart from this oxides we also have our traditional ferromagnetic elements like ion, cobalt and nickel showing strong ferromagnetism and ferromagnetism is above room temperature. So these are all some of the classic examples of naturally occurring mineral oxides and metals and alloys which are intrinsically magnetic and having this as the base thousands of materials have been prepared with similar stoichiometry. Now let us look at magnetic materials as an empirical approach and try to see how we can distinguish one from the other then we can categories what sort of a magnetic material we can talk about and depending on the nature of magnetism we can also group them for different applications. First of all some of the terminologies that we use very frequently in magnetic materials is magnetization M. Material with the net magnetic moment is magnetized and the magnetization is the magnetic moment per unit volume within the material. So that gives the strength of your magnetization M and that depends on the net magnetic moment in a given area and also it depends individually on the size of magnetization and the number of such dipoles. So magnetization that way depends on the number density of the magnetic dipole moments within the material. So if it is more crowded then we are talking about more density therefore more magnetization. So we also talk about the magnitude of the magnetic dipole not just on the density as we saw but also on the magnitude of the magnetic dipole because sometimes they can as we would see in the next few slides sometimes they may be reverse and in one case the magnitude of the dipole may be smaller but it will still result in a net magnetization and then the alignment of this magnetic dipoles will also cause the net magnetization therefore we talk about arrangement apart from the magnitude and the density. So the arrangement of the magnetic dipoles will tell whether there will be a net resultant magnetization or not. Magnetization in materials generally can be categorized to two things one is unpad electron spins or it could be due to orbital motion of electrons within the material to a lesser extent. So what is predominant is the number of unpad electrons but we should also understand there is a spin orbital contribution spin orbit coupling and because of the orbital motion of electrons also there is a intrinsic moment that is induced but this is of a lesser extent. So two contributions from the material itself apart from the dipoles. So how do we measure the strength of a material? Now we need to have external force by which we can gauge whether the material is good or not. So in general we can generate a magnetic field and this magnetic field actually is generated by a solenoid and solenoid is nothing but you wrap up any material say glass or even a ceramic tube you can just wind it with a conducting coil and then that electric current passing through this conducting coil will give you a flux or a magnetic field and that is how you can generate a uniform flux density within the coil. So the number of turns that you make with this conducting coil will determine what sort of strength that you employ. So you pass current and this is the length and the number of turns of this conducting wire will give you the strength of the magnetic field therefore you can generally create a electromagnet based on the number of coils so this is not impossible for you to generate in a lab scale. So flux density actually can be in vacuum within the coil so it increases in proportion to the electric current as we saw and also it increases in proportion to the number of turns per unit length in the coil so that would give you the strength of your electromagnet. Now once you keep a specimen inside the solenoid then the response of this material to the solenoid will actually determine the magnetization. So generally the orbital and spin magnetic moments within the atoms respond to the applied magnetic field and the flux lines are actually perturbed by the specimen. So how the flux is either let to pass through the material or it ripples the flux determines what sort of material you have for example if you have a material which does not have any magnetic response then you simply see the flux passing through the material and therefore the flux lines are not perturbed. But if the material has a considerable magnetic moment then it tends to concentrate the flux lines for example materials containing high concentration of magnetic atoms like iron and cobalt then you would see that it is actually putting force on the flux lines. Now there are some materials which totally ripple the flux line and this is your flux axis this is the direction in which you apply the flux but you would see totally the flux is rippled and in that case you actually categorize that material as diamagnetic material which will tend to ripple the flux lines example water protein fat. These are all molecules which will not allow magnetic field to easily penetrate through although higher fields can do damage these molecules and a classic example of a situation where the material is actually not a diamagnet but in a superconducting state it behaves like a diamagnet is the high temperature superconductivity and one of the possible application that we would see in detail in the next module is the magnetically levitated train where the issue of diamagnetism actually brings about a total ripple of this flux lines. Flux density B within material can be determined by both the geometry and the current in solenoid magnetic properties of the material and the geometry of the material. So two three things are interdependent one the solenoid itself will determine what sort of flux density you have then the magnetic property of the material and then the geometry of the material. So B if it is your flux density then you talk about mu U H which is due to your magnetic field and then mu U mu 0 M which is due to the magnetic material itself. So two things are interconnected and your mu 0 is nothing but the permeability of free space. So in case there is no magnetization if the material is not magnetic then your flux density is equal to mu 0 H but if the material is magnetic then the other parameter also will come into picture. So measuring the magnetic moment of the specimen we can actually pass the material through the solenoid and measure the voltage generated across the coil and the voltage is actually proportional to the moment on specimen. So that is the way we measure the strength of the magnetic moment and we can also use large coil to apply magnetic field to the specimen. We can also try to do this same measurement using either furnace for high temperature applications or a cryostat for low temperature applications and today using this principle many equipments have come into picture. Now the way the material respond is actually linked to the susceptibility a value which is actually dependent on both magnetization as well as H. So we will come to the definition of susceptibility which is usually denoted as chi. Generally magnetization changes in magnitude as H is varied so this is what you call as a linear response. So as you increase the field then the magnetization also keeps increasing and the magnet of the response is measured by chi and therefore diamagnetic materials will have a very weak negative response because there is no net moment and they have a small negative magnetic susceptibility. So susceptibility per se can be defined as chi is equal to M by H or sometimes it is defined as a difference in magnetization over difference in H. So this would actually give you chi or sometimes it is also taken from the slope as we as we see from this expression. So chi can be derived from a simple M versus H curve. There is a variety of ways that M responds to this H. So the response can be based on the type of material that you have or M the chi can actually vary or magnetization can vary with temperature. Response can sometimes depend on the previous history of the magnetic field strength and the directions applied to the material. In case of thin films it is heavily direction dependent. Perpendicular to the film it will show a very different behavior in the axis of the film it will show a very different behavior. Therefore this angle dependent magnetization is much more exemplified in single crystals and in thin films. But in bulk usually this dependency is not highlighted much. So in general magnetic materials show a non-linear response if they are really magnetic and suppose your temperature T1 is less than T2 less than T3 and T5 for example. So at high temperatures significantly you would see a response like this whereas at low temperatures you would see a very clear magnetic behavior and therefore they are always non-linear with respect to temperature. So we can say that M versus H behavior is usually a non-linear behavior and only at small values of H they are usually linear where you can see at any point at low values of H they are linear otherwise they are mostly non-linear and M also intrinsically tends to saturate at high fields and at low temperature. As you would see here at low temperature that is T1 the saturation is at a much lower H whereas in the case of high temperatures saturation takes a very large field. So this is one of the manifestation of a non-linear response and therefore if you actually make a curve of a plot of 1 over chi as a function of temperature for a low field magnetic susceptibility you would actually see a linear dependence as you would see from this and this is nothing but the Curie-Weis law. And if it is ferromagnetic material then this nature of this linearity will change if it is anti-ferromagnetic material or diamagnetic material the nature of this 1 over chi versus temperature plot will actually vary. So from this we can easily verify what set of a contribution that we are getting. Typical magnetic material would actually give a hysteresis where two parameters are very interesting to follow one is saturation magnetization it is when you take the virgin sample and then you try to increase the field then it gets saturated and on removal of the field actually it will not take the same path as that of the MS rather it would keep going down where this is your MR that is remnant magnetization and to completely revert it to zero magnetic moment then you need a field which is called as HC which in other words called critical field or coercivity and that coercive field is the strength of how much the magnetic moment is aligned. If it is quickly reversing then you can say that the pairing of these moments are very weak. So the strength of the magnetic interaction that is going within the sample is actually highlighted based on the nature of the loop. So just by looking at a magnetic hysteresis it is possible for us to gauge whether it is a strongly correlated spin or very weakly correlated or whether it is paramagnetic or non-magnetic all this can be verified using magnetic hysteresis. For example, if a material is a strong ferromagnet which has a very good saturation magnetization then the disappearance of this MS against the temperature will decide the curie temperature in other words that is the critical ordering of ferromagnetic behavior beyond which the aligned spins will be diluted and it will go into a paramagnetic state. So if your MS is disappearing as a function of temperature you call that field as a critical temperature for a curie temperature. So, M depends on the previous state of the magnetization and then remnant magnetization the spins will be diluted and it will go into a paramagnetic state. So, if your m s is m s is disappearing as a function of temperature you call that field as a critical temperature for a curie temperature. So, m depends on the previous state of the magnetization and then remnant magnetization remains when applied field is actually removed therefore, we need to apply a field coercive field in opposite direction to reduce m to 0 and that is what we saw from the previous slide. Now magnetization also can be traced as a function of temperature and if your remnant magnetization is this at temperature 0 then as a function of temperature you can try to trace what is your remnant magnetization and at the point when your m r is actually going to 0 then you call this as your T c. Heating a magnetized material generally decreases its magnetization and remnant magnetization is reduced to 0 above curie temperature. So, this is one of the way you can determine your curie temperature by plotting m r versus T and heating a sample above its curie temperature is a way to demagnetize a sample. So, especially for permanent magnets if you heat it beyond the curie temperature then it completely loses its magnetic property and the only way to again bring it back to a permanent magnetic magnet behavior is to again chill the whole sample in a external magnetic field otherwise they remain demagnetized and that is actually called as thermal demagnetization. Now let us look little bit into the microscopic picture of the magnetic materials and see what is intrinsically happening within a material when it has a moment. So, we will look little bit into the experimental evidences and try to make some conclusion on the different types of magnetization that comes in materials. One is a paramagnetic gas and paramagnetic gas is one where it is like a classical gas of molecules each with a magnetic dipole moment. So, in zero field the gas would have almost zero magnetization mainly because these magnetic dipoles are actually very randomly oriented therefore there is no net resultant spin. So, we can compare this to a classical gas of molecules and paramagnetic gas usually they will align when an applied field is employed and this would tend to orient the dipole moment and therefore this paramagnetic gas would attain a magnetization. Again as you would see from this cartoon it is not a perfectly aligned system, but there is a net alignment giving some amount of magnetization. Very high fields can actually be used to saturate it, but this is not the real feature of your magnetic material because typically if it is a magnetic material you should actually see a coercivity, but in a paramagnetic gas you once you remove the magnetic field you would actually see a zero coercivity and that is the sign that this paramagnetic samples cannot be saturated and therefore it would actually require a very high saturation field in order to saturate it. Heating the gas would tend to disorder the moments and hence decrease the magnetization and therefore the paramagnetic gas the interaction energy with the applied field is actually dependent on a term e is equal to minus m b cos theta where your theta is the angle made between the magnetization of your paramagnetic sample with the applied field axis. So if you can really overcome this factor then the interaction energy will be maximum. So the dipole interaction with b actually will determine whether you can get a net magnetic moment and the examples of such paramagnetic species are ferrous sulphate crystals, ionic solutions of magnetic moments usually they display this paramagnetic behavior. This can the paramagnetism per se can be interpreted based on two models one is a classical model where you do not really bring in spin-spin interaction where you consider each one as an independent molecule therefore it is based on the field that you are applying and the cos theta dependence of the magnetic moment to the field which will actually bring about the net magnetization or it is based on a Brilloine function which is usually a quantum model where we are considering the spin-spin interaction two spins and how they interact the coupling between two spins in the presence of the field will give a net magnetization therefore the paramagnetism study of paramagnetism itself is a quite a challenge therefore it can be viewed with the two different models and we can evaluate the behavior of a typical paramagnetism. When we come to ferromagnetism this is purely viewed based on a quantum mechanical exchange interaction and materials that retain magnetization even in zero field so there should be net polarization of this dipoles in and absence of the magnetic field therefore the quantum mechanical exchange interactions favors parallel alignment of moments examples are the magnetic elements like iron cobalt and also nickel the exchange interaction therefore depends on the correlation length how closely they are placed and once they are in optimum distance when there is a exchange involved then this will result into a bigger cluster and therefore there will be a net magnetic moment. Now if you try to trace the behavior of this magnetization as a function of temperature you would see that at lower temperatures these moments are aligned parallely and therefore there is a strong correlation thermal energy in such cases can be used to overcome those exchange interactions and once you keep heating the sample now these aligned moments can get disoriented and as a result the magnetic moment can be removed and then we get into a state where you have this T c therefore Q d temperature is a measure of exchange interaction strength and exchange interactions are therefore much stronger than dipole-dipole interactions this is just as a comparison the strength of this exchange interactions are therefore much stronger and we can actually view this ferromagnetic arrangement in two different ways one totally as a quantum mechanical system where you only talk about spin-spin interaction in the presence of a field. So all these neighboring spins they do interact and therefore there is a net moment that is evolved from a unordered state to a ordered state and that is actually coming through the external field it can also be viewed as a ways field where you do not take into picture the spin-spin interaction you just force whatever be the state of the moment you just force it using a vice field a vice field means the external field actually takes care of overcoming all the other barriers therefore you let the external field do the job so this is called a vice field so there are two ways we can bring about a ordered system from a unordered state. So the physical reason for this quantum mechanical spin-spin interaction that has no simple classical analog but in the mean field approach or the vice approach the ferromagnetism simply we assume that a magnetic field can line up the magnetic moments and therefore it is generally called as orientation polarization where you just use a external field to align the samples when in ferromagnetic compounds when you try to influence the material which is already having a net polarization of magnetic dipoles then you develop into another situation called domains magnetic domains and that is the strength of a ferromagnetic material so when you apply a field immediately all the neighboring spins will actually in one sense percolate together to form a domain and this domain will have a net moment of this order and there can be other moments also but those are actually aligned in different directions. So a domain picture evolves where not necessarily all the domains have to be oriented in the same axis where the magnetic field is applied. So each domain is magnetized in a different direction domain structure therefore minimizes energy due to stray fields and what happens to such a domain when you try to increase the field along a particular direction for example it is in this direction then this particular domain which was originally in this size will start growing bigger and the other domains will start easing out in other words they will coalesce with this bigger domain so as to form a domain picture like this. So applying a field changes the domain structure so you can actually manipulate and how easily that this domain structure can be altered depends on the strength of the magnetic material. So domains with magnetization in the direction of the field grow other domains shrink and as a result when you try to overcome this energy then you almost coalesce all the domains together into one single domain in other words you call this as a single domain behavior where no other domains are there and everything is aligned in the field of its axis of your magnetic field. So applying very strong moments then you can actually revert it into a single domain and that is what we see from the typical hysteresis we are talking about this situation somewhere here where all the domains have come into this form and therefore when we remove the magnetic field then it does not mean that all the domains have to come back to its initial state it can take a different domain pattern and as a result you will get a net magnetic hysteresis. Now we will also see how this domains can rotate and we will make correlation with the nature of the hysteresis loop in the next slide. So in the previous slide we said as we reverse the field the magnetic hysteresis develops and we also said that the domain does not need to reverse back to its initial state and this is one curve a qualitative measurement picture which will give you an idea about how the domains rotate as a function of field as you would see here these are the magnetic domains and once you apply initial field there is a area where the slope changes at this point and this is nothing but your pinning point or it is called flux pinning where the magnetic dipoles are reluctant to move with the field as a result a boundary is created here and this wall is reluctant to move. But once you start increasing the magnetic field strength then you can see that this wall has moved here and as a result a bigger domain has developed and once this pinning is actually overcome then as you increase the field then you can see that a bigger domain can emerge out of field. So once a domain picture evolves then you can keep rotating the domain according to the field direction and that is what you would see here we have also seen this picture in the earlier slide and once this pinning is overcome then the domain actually grows in size and then it would also become a single domain at the saturation. So this is the way the domains actually form and they dissolve into a one single domain picture. Now the single domains have a strength and the single domain also have a dimension it roughly the single domains have a dimension of 100 nanometers but suppose you make a particle which is less than the single domain particle less than this domain size then you call that as a single domain we will look at that situation in one of the few next slides and what would happen when we are trying to rotate this domain two things can happen one this can get frozen over a period of time where the domains are actually turning and they would go into a opposite phase in this case the net moment is in this direction in this case it is in this direction but along this dimension you see that the dipoles are rotating and this measure is actually called a needle wall or this is called as a anti ferromagnetic block where you have reversal of the spin and this takes this much of energy for the moments to rotate thus therefore this domain wall is called as needle wall and in some cases you can experience another situation where it is up spin but the domain is actually not rotating but it is actually minimizing at a point where the moment will get reversed to opposite direction and therefore that strength where it is neither completely aligned or completely inverted and this measure is called as block wall depending on that you can look for different shape of hysteresis and this is one such shape which is a typical hard magnet where you will almost get a rectangular hysteresis loop and this is seen for hard magnets where you have a very large coercivity and very high remanence because this is your saturation and saturation and remanence ratio saturate MS by MR will be almost close to 1 in such case you can call this as a hard magnet but in a soft magnet you would usually see that the saturation is somewhere here and your remanence is somewhere here and therefore your MS by MR is going to be very less than 1 and in such case you categorize this as soft magnet usually the magnet of a soft magnet would be of the order of 0.5 MS by MR ratio would be 0.5 therefore you can find out what set of a domain movement is in your material and what is the strength and the coercive force that is involved in such materials. Now in the ferromagnetic materials you actually come across different cases ferromagnetic material in general can be classified into different states and that depends on the way the domains rotate for example this is animation which unfortunately I am not able to access but therefore I would just give this link as a reference where you get a very good animation of a rare phenomena in a ferromagnetic material which is called magnetostriction magnetostriction actually comes where your domains actually rotate with your field and as a result what would happen you can see the blue and reds dipoles magnetic dipoles they actually rotate in this form and then then you go this way and then it will go this way so when it actually goes from this to this you actually have a shrinkage in volume and then expansion of your sample size sample will become larger in this dimension and sample when it actually is orienting the dipoles are orienting this form there is a natural contraction of your sample and therefore we can say in the presence of applied magnetic field depending on the field direction and because the magnetic dipoles are rotating there will be a expansion or contraction of your sample size and that is what we call it as magnetostriction which is a phenomena that happens peculiar of a ferromagnet. Suppose the easy magnetization axis easy axis of magnetization otherwise coincides with the direction of the applied field then you would actually expect a rectangular loop like this this is the situation when the easy axis of magnetization is overlapping with the direction of your applied field then you would see a rectangular loop of this form. In case the easy axis of magnetization is perpendicular to the field axis then you would see a linear loop therefore in that case the ferromagnetic loop will be more like this and in other words you call this as a hard axis you can clearly see that this is the hard axis of magnetization and suppose this is a single crystal one would be intelligent to immediately change the direction of the field then from a hard axis you can immediately see such a rectangular axis for a magnetic material therefore the easy axis of magnetization which is intrinsic of your crystal lattice or the way the moments are arranged in your crystallographic plane will determine whether you will get a rectangular loop or a linear loop. So this is one way that the ferromagnetic compounds evolve and if two adjacent domains magnetizing or magnetizing opposite direction and are always separated by a transitive layer which we call it as a block wall in such case you would actually see a block wall movement for example in this case you can see the dipole in this direction where there is a blue top and a red bottom dipole fashion and in this case you can see it is a red on the top blue on the right. So this is one dipole domain and this is another domain and in between this there is a block wall and in such cases you would see a step wise shift in the magnetic hysteresis which we call it as a pinning or this is due to the block wall movement. So this block wall movement can actually go in both directions both in the left and the right then this will become very evident that there is a block wall. So in magnetic domain walls you can actually measure the wall thickness where there is a canting of spin. Spin is actually canted from this place to this place therefore you can even measure this canting where which we call it as a domain thickness or wall thickness T and this is typically of the order of 100 nanometer this wall thickness. For a single domain particle actually you do not have domains okay particles smaller than T this T. If the particles are smaller than 100 nanometers generally we say that it is a single domain behavior which we can easily calculate from a given formula. Now from a anti ferromagnetic situation we can immediately turn down to see what if the neighboring spins are correlated but they are correlated in opposite direction. In some materials this exchange interactions actually favor a anti parallel alignment and only then the system is stable. So in such cases you experience a anti ferromagnetic behavior and they will have a very low chi. They will almost resemble that of a diamagnetic material because diamagnetic material shows negative chi but this will be almost as close to a diamagnet but with sufficient chi which gives an idea that it is a anti ferromagnetic metal. Most of the metal oxides are anti ferromagnetic in nature. Now we can actually try to overcome this picture of a anti ferromagnetism by thermal energy to overcome this exchange interaction. So what you try to do as you did in the case of ferromagnetism you can try to decouple this exchange interaction using heat or thermal and therefore you can break down this magnetic order which is called as nil temperature and this nil temperature is just the complementary to curie temperature. So in both cases thermal effects can actually defreeze such exchange correlations and there is another interesting situation where you have a anti ferromagnetism but this is not a anti ferromagnetism because one of these two are exchange coupled but the magnitude of this dipole is less compared to the magnitude of this dipole. Therefore there will be a net resultant magnetization as in the case of magnetite or mahemite. So these are compounds for example magnetite is your Fe3O4. This is not a ferromagnet per se but it is a ferrimagnet and different sized moments on each sub lattice is noticed in this sort of ferrimagnets. Now when we come to single domain particles as I told you if you escape that domain wall thickness then you can call this as a single domain picture and in that case single domain magnetization can also introduce a interesting small particle magnetism and this is actually understood based on stoner wolf earth particle where if it is ellipsoid type of a particle like this where your magnetization is actually oriented by a factor theta with respect to the easy axis of magnetization then the magnetic anisotropy energy favors magnetization along certain axis relative to the crystal size. So this can become a very interesting issue if we can try to understand how this single particle magnetism works. Uniaxial single particles are actually uniaxial single domain particle and the way they make angle theta with respect to the easy axis of magnetization gives you an anisotropic energy magneto crystalline anisotropy energy and that is actually correlated to sin square theta. So where k is actually a constant dependent on the material therefore your magneto crystalline anisotropy ea is proportional to sin square theta and in that case you would see this sin function will vary as a function of theta and what can happen in such cases the particle can actually get trapped in one of this wells. At low temperature this magnetic moment of the particle can be trapped in one of these wells and therefore these particle moment is actually blocked. So in order to derelease this one this blocked particle then you need to heat it and then it goes into a paramagnetic situation. So at high temperatures this magnetic moment can be over which is trapped can be overcome and then we can try to unblock this this moment using thermal energy and therefore we come across another interesting situation in terms of single domain magnetism where we talk something about blocking temperature. The magnetic blocking temperature T b is the temperature below which the moment is blocked therefore there is a critical temperature beyond which this blocking can be removed below that the moments are nearly frozen which we call it as blocking temperature and this depends on the particle size and to some extent particle shape also. Larger particles have higher blocking temperature the longer the observation time the more likely it is that the moment will be absorbed to flip. So if you increase the your field strength sometimes this blocking can be removed that is the effect of applied field on the single domain particle. So as you would see here that applying the field along the easy axis favors moment aligned with the field above the blocking temperature this results in moments spending more time in the lower well and when you go to still higher temperature then particle exhibits time average magnetization in the direction of field. So this brings you to another situation where this is not exactly paramagnetism but you come to a state of a super paramagnetism. So super paramagnetism is not paramagnetic behavior whereas where it is a magnetic dipole but it is within the single domain picture and in that it can display some of the paramagnetic features. So these are termed as super paramagnetic behavior and in the absence of field the moments are aligned in different direction and you can successfully try to rotate these moments close to the axis of your field and therefore unblocked particles can respond to a field known as super paramagnetism. So how do the paramagnetic and super paramagnetic particles behave this is the typical fashion. So response of a super paramagnet to applied field is actually described by Langouin model qualitatively they are similar to paramagnets and at room temperature super paramagnetic materials have much greater magnetic susceptibility than paramagnetic material. So typically this is a way that we can distinguish between a paramagnetic and a super paramagnetic particle as you can see here there is almost no saturation whereas in the super paramagnetic case it may confuse you to be a ferromagnetic but necessarily if you try to open this area then you would see that it lacks coercivity therefore you can call this as a super paramagnetic situation and not a true ferromagnetic signal. So super paramagnets are often they are ideal for applications where a high magnetic susceptibility is required and zero magnetic remnants is required. So when you actually take the field of it should immediately go back the moment should go back to zero and therefore this can be used for many applications and as a result super paramagnets are used in variety of biomedical applications than the typical paramagnets. So we have sort of seen a varied situation depending on how the dipole magnetic dipole Oren's itself to the applied magnetic field we have seen the case of paramagnetic gas we have seen example of how a ferromagnetic cluster will evolve with the domain structure and how anti ferromagnets differ from ferromagnets and also we have seen a case of ferrimagnetism and as a special case the super paramagnetic behavior. So all these are embedded in the so called magnetic materials and we would see in the next few lectures examples of how to analyze the true magnetic response something may give a hysteresis but it may lack the ferromagnetic order. So how to distinguish experimentally and what are all the ways we can study the magnetic behavior in materials specially we will take examples from oxides and thin films and try to look at the various response to magnetic field.