In this lecture, I want to go through the different classes of magnetic materials and how they contribute to the magnetic nominees in crustal rocks will also go briefly through the two major types of instruments used for measuring the magnetic field. One of the most important things to remember, which is why I've put it in big, large lattice share is that all materials and every atom and every material responds in some way to an external magnetic field. The type of response that they have depends upon the class of magnetic materials they belong to. And there are in general, three different types or classes of magnetic materials. These are listed here as diamagnetic, paramagnetic, and ferromagnetic materials. We will go through each of these in turn, giving examples of the different types of minerals found in the earth. For each category. There is quite a lot of information on this slide. So bear with me as I go through it all. Perhaps the obvious way to categorise the behaviour of different magnetic materials is in terms of their response to an applied external magnetic field. The magnetic parameter susceptibility is probably the simplest of these observations. And you can see it defined here, and it is given the symbol chi. Again, susceptibility is simply the change of magnetization of material in response to an externally applied field. As we saw in our first lecture in SI units, both magnetization and field have the same units of amps per metre. So susceptibility itself is dimensionless. The figure on the right hand side of this slide shows our susceptibility. The differs for the three different classes of magnetic materials are listed on the last slide. The first class of magnetic materials are diamagnetic and shown here by the red line. You can see that for a positive applied field, a diamagnetic material produces a negative magnetization. Diamagnetic susceptibilities are therefore negative. And it implies that a diamagnetic material will be repelled from the stronger part of the field. This type of magnetic behaviour is perhaps contrary to our common experience, where we expect magnetic materials to be attracted to the stronger part of the magnetic field. For example, if we had a bar of iron, we put this close to a magnet. We would expect that the magnet will attract the iron bar. Diamagnetic responses are exactly opposite to this, and a diamagnetic material will be repelled from the magnet. The second class of magnetic materials are called paramagnetic. These have positive susceptibilities and so magnetised in the same direction as the applied field. These types of materials are relatively common and exhibit the sort of magnetic behaviour that we are familiar with. So for example, when we hold up a paperclip near a bar magnet, than the paperclip is attracted to the magnet. Both time magnetism and Para magnetism only exhibited in the presence of an external field. So when you remove the magnetic field or in the absence of a magnetic field, neither paramagnetic or diamagnetic materials exhibit any net magnetization. It's also important to understand that every material exhibits a diamagnetic response. And it is a fundamental property of all atoms on all matter. The diamagnetic response, however, is generally very weak. So that in that exhibit, any other type of magnetic response is feeble. Diamagnetic signal will be masked. The last category of magnetic materials are called ferromagnet. And unlike paramagnetic or diamagnetic materials, ferromagnet is capable of being permanently magnetised. That means that even in the absence of any external magnetic field, Ferro magnets will exhibit a net magnetization. You will notice another difference for ferromagnetic materials from the figure on the right. You can see that the magnetization, both paramagnetic and diamagnetic materials, varies linearly with the applied field. And this is true, except for exception large fields that are difficult to achieve in even the most sophisticated laboratories. However, the magnetization for ferromagnetic materials behave quite differently. And they're magnetization can be saturated even in relatively low fields that are easily produced using electromagnets. Some examples of materials from the different magnetic classes are shown on this slide. So common diamagnetic materials are water or silica. And chalk would be a good example of a diamagnetic mineral from a sedimentary rock. And also our biotin, Northside, common diamagnetic minerals found in igneous rocks exempts the paramagnetic materials are olivine, Garnett, Illuminate, which are all found in igneous rocks. And then side right? And pyrite, more usually found in sedimentary deposits. You will notice that the other thing up shown here in red is the temperature dependence of diamagnetic and paramagnetic materials. The diamagnetic materials, the susceptibility is independent of temperature. Whereas for paramagnetic materials, their susceptibility varies inversely with temperature. So in rock samples that have a mixture of minerals, the temperature dependence of susceptibility is often a good discriminator between the proportion of diamagnetic and paramagnetic minerals that are rock contains. Before we move on to look at ferromagnetic materials. Here as a reminder, an important summary of the properties of diamagnetic and paramagnetic materials. Or materials have a diamagnetic response to an applied field, although usually it's very weak. If material also has a paramagnetic response, this will almost certainly mask anytime magnetism, but it has diamagnetic susceptibility does not vary with temperature, but Para, magnetic susceptibility does. Neither diamagnetic or paramagnetic materials are capable of holding a permanent magnetization. As soon as you remove the external field, they will lose their magnetization. There are a couple of nice videos that I found online that illustrate the diamagnetic and paramagnetic responses to external fields. The first one I will show is the diamagnetic magnetization of water. In this experiment, they fill the plastic tube with water and then stuck this tube into a piece of polystyrene so that it easily floats in a bowl of water. They then bring a strong magnet near the tube. And as you will see, the tube diamagnetic water is then repelled by the magnetic field. Because it's a weak effect, the magnet has to be brought very close to the tube of water. It might appear that the experimenter is actually pushing the tube. But if you look closely, I think you can see that he really does not. Any demonstration of the effect of dye magnetism is not complete without showing this video of the levitating frog. This was an experiment done by the Russian scientist Andre game 20 years ago, where he placed a frog in a very strong magnetic field produced by a superconducting magnets. Because the frog's body is mostly water, it is repelled by the strong magnetic field and then appears to float freely in space. And before you go out catching frogs and attempt to do this at home, I have to say that it's not possible to reproduce this experiment without using extremely strong magnetic fields, much stronger than you can easily produce in your own home. This demonstration of the paramagnetic effect is perhaps more familiar to you, where you magnetise a chain of metallic objects by bringing them close to the magnetic field of a permanent magnet. When the magnetic field is present, each of the metallic items, in this case coins, becomes magnetised and they stick together like a chain of paperclips. When you remove them from the field, the coins are no longer magnetic and the chain collapses. If you try this at home, you should be aware that not all coins contain ferromagnetic metals. And you might actually be better off just using paperclips. The third class of magnetic materials that I want to tell you about our ferromagnetic materials. These materials distinguish themselves by being able to hold a permanent magnetization. That is, they exhibit a spontaneous magnetization, even with that, the presence of an external field. Unlike diamagnetic or paramagnetic materials whose susceptibility changes linearly for all reasonable fields that we subject them to. Ferromagnetic materials, saturate a magnetization evening relatively weak fields. Although the exact field required to saturate a ferromagnetic material can vary a lot from material to material. It's quite common, even amongst professional scientists to call any material capable of holding a permanent or spontaneous magnetization, a ferromagnet. However, this is not quite correct. There are whole range of magnetic materials that exhibit ferromagnetic behaviour that are not strictly speaking true Ferro magnets. I'll list number of these on the next slide. Ferromagnetic materials are able to hold a permanent magnetization by cooperative coupling between neighbouring atomic magnetic dipoles. In the slideshow, I represent a number of different classes of magnetic materials, all of which exhibit some degree of cooperation between atomic dipole magnetization on neighbouring atoms. Below each class, I have a blue arrow that shows the net magnetization for each type of alignment. In the case of true fair magnets seen here on the left-hand side of the slide. We have a number of atomic dipole moments are all aligned perfectly parallel to each other, all in the same direction. This alignment or cooperation between neighbouring atomic magnets means that they spontaneously exhibit a permanent magnetization. But you can also imagine cooperation between neighbouring atomic magnetic dipoles in which rather than being aligned parallel to each other, they are aligned anti-parallel. These types of materials are called anti ferromagnet. And as you might've guessed, although they are similar in terms of the underlying physical principles by which they are constructed. Because neighbouring dipoles are of similar size but antiparallel to each other, they will exhibit 0 net magnetization. The next category is called candid anti ferromagnet. In this case, we take the antiferromagnetic behaviour, but rather than the magnetic dipoles being perfectly antiparallel to each other, they are counted by a small angle with respect to their neighbours. This smoke counting of the magnetization produces a small net magnetization in the direction roughly perpendicular to the magnetic atomic dipoles. And the last column we see something called fairy magnets. Very magnets are somewhat similar to anti ferromagnet, except that the magnitude of the neighbouring atomic dipole moments are unequal. This results in a net magnetization parallel to the dipoles. In fact, very few minerals are true. Ferro magnets are most common. Magnetic minerals found on Earth will be very magnets. An example mineral of each of the different classes is given underneath each diagram. As you will have remembered from previous lectures, magnetite is one of the strongest and most common magnetic minerals found in Earth. And this is in fact, a very magnetic mineral. As we have seen, Pharaoh and ferromagnetic materials exhibit a non-linear change in magnetization with the applied field. And in fact, they saturate in relatively weak fields. That the property of such magnetic materials is that the variation of magnetization with field is only reversible for very small field values. We can trace out the characteristic response of Pharaoh and ferromagnetic materials to larger changes in the external field in something called a hysteresis loop. An example here, we start off from an unmagnetized state at point a at the origin of the graph and increase the field until the magnetization becomes saturated at point E. If we then reduce the field rather than retracing the curve from E back down to a, it takes another path to the point F. Point F is a 0 field state, but the sample has now become magnetised. In fact, the magnetization at point F is called its saturation magnetization. If we continue to reduce the field or in fact increase the field in the opposite direction. Then we will be able to reduce the magnetization of the sample to point O on the horizontal axis. The intensity of the backfield required to reduce the magnetization to 0 at 0 is called the samples coercive field. Is labelled here as minus hc. Beyond this, as we continue to increase the field further in the negative field direction, then we obtain a saturated magnetization state at point i. Now saturated in the opposite direction to that at point E. We can close the loop by reducing the field to 0 again and then increasing the field through to saturation. Tracing out the lower part of the loop from i to k two E. This type of loop is called a magnetic hysteresis loop. And the area inside this M H loop is a measure of the energy required to switch the magnetization back and forth between the two saturated states. At this point, it's worth showing you an animation we saw a few lectures ago, which might now make more sense to you. We have seen how Pharaoh or ferromagnetic materials exhibit spontaneous magnetism due to the cooperative forces between the neighbouring magnetic dipole moments. The fact that Pharaoh of ferromagnetic materials are not always magnetised to the saturated state is a consequence of their ability to form magnetic domains. First hypothesised by Pierre vice. Magnetic domains are regions within a magnetic material with the magnetization is saturated. But the direction of the magnetization can vary from one domain to another. The boundaries between domains are called domain walls. In a demagnetize state, domains are pointing in random directions as you magnetise them, the domains grow or rotate, so they point mostly in the same direction. We move on now to examine how these magnetic materials in rocks can produce crustal magnetic anomalies. As we have previously seen, magnetic anomalies represent one of the contributions to the observed magnetic field that's measured on the surface of the Earth. The magnetization of near surface rocks will either add or subtract the geometric field. And so will be seen as a relatively short wavelength variation compared to the large wavelength variation of the main Jian magnetic field that's generated in the core. Thus, when we look at the variation of the major magnetic field shown on the bottom left of this slide, we see changes only over distances of many hundreds to thousands of kilometres. And when we look at the crustal magnetization shown here on the right of the slide for survey over the UK, we see variations that occur over lengths of just tens to a few hundreds of kilometres. In fact, crustal magnetic anomalies will occur in a variety of relatively short wavelengths depending on the type of subsurface body that we are looking at. For example, we might expect to see a magnetic normally from a buried metal pipe. And this might provide an anomalous field with a wavelength of just a few metres. Iron-rich mineral deposits might create anomalies with wavelengths from hundreds of metres to a few kilometres. Was region geology might produce magnetic anomalies of tens to hundreds of kilometres. When we look at crustal anomalies on a global scale, we notice differences and the magnetization between oceanic and continental rocks. We have mentioned this in the previous lectures. And the Continental surfaces have complex magnetization patterns because the rocks have been twisted, rotated by tectonic activity over hundreds of millions of years. The oceanic floor, in contrast, has regular stride magnetic anomalies credit on a much newer surfaces near the spreading centres of the mid-oceanic ridges. The magnetic anomaly created by surface rocks will depend upon the type of magnetic minerals they contain plus the grain sizes, the magnetic minerals themselves. We've already seen that the main types of magnetic behaviour in rocks include diamagnetic, paramagnetic, and Pharaoh or ferromagnetic materials. But when we consider crustal magnetization, diamagnetic effects are far too weak to produce a significant contribution. When we think about crystalline accusations, then we need to consider two main contributions. Firstly, a remnant magnetization or a permanent magnetization due to stable magnetic recording from ferry or ferromagnetic minerals in the rocks. Secondly, and induced magnetization due to paramagnetic and super paramagnetic material. Remnant magnetization, then a permanent magnetization due to Pharaoh or ferromagnetic materials that will have become permanently magnetised as the rocks were formed. For example, as a lava flow cools in the Earth's magnetic field, it will become permanently magnetised in the direction of the earth's field at the time and location that the larva was extruded. And then induced magnetization or the component due to power magnetic minerals, or due to super paramagnetic grains of Pharaoh and very magnetic minerals. Component of the magnetization is induced by the ambient magnetic field. And so we'll be in a direction of the current local earth's field. These two components, the remnant and the induced magnetic anomaly field, will add together to form the net magnetic normally field. It is important to remember that magnetization is a vector quantity, so it has a magnitude and direction. When you add together the remnant and induce components, you must do this via a vector addition. In general, these two components will each have different magnitudes and directions. So for example, when a rock is formed, it will acquire a permanent magnetic magnetization direction of the magnetic field at that time. Then over geological time, the continent, the rock is attached to may have moved or rotated or twisted so that the permanent magnetization of the rock is no longer in the same direction as the local magnetic field. We then need to add to that the induced magnetization, which will of course always be in the direction of the present local gym magnetic field. But its magnitude will depend upon the magnetic susceptibility of the mineral that the rocks contain. The larger the magnetic susceptibility, the larger the induced component of the magnetization. In almost every case, induced and remanent magnetization will be in completely different directions. And just for your reference, this is a list of the magnetic susceptibilities of different common rock types. You can see that susceptibility can vary by several orders of magnitude. But in general, igneous rocks are have much larger susceptibilities and sedimentary rocks. And the last part of this lecture, I want to briefly look at the two different instruments used to measure variations in the magnetic field. These are called the proton magnetometer and flux Kate magnetometer. Both instruments of similar precisions of about one hundred thousandth of a nano Tesla, which is more than enough for most applications. For example, diurnal variations we might measure are likely to be a few tens of nano Teslas. And crustal magnetic anomalies will be about a few 100 nano Teslas are more. The most significant difference between the two types of magnetometers is that the proto magnetometer only measures intensity and not direction. Whereas the flux gate magnetometer measures both direction and intensity. I am going to describe the operating principles of each instrument very briefly here. And those of you doing the geophysics degree will get a much more detailed look at these next year. Firstly, the proton precession magnetometer. This instrument relies on the ability of atomic magnetic dipoles and a proton rich fluid to precess around the magnetic field line. Precession dynamics can be compared to the precession motion of a spinning top in a gravitational field, as shown in the figure on the bottom right of the slide. You may have played with such a spinning top with gyroscope. And you will know that if you place a spinning top on a surface and push its axis away from the vertical, it will precess about the gravitational field line. In the magnetic case, the precession occurs about the magnetic field line. The precession frequency f is directly proportional to the intensity of the external magnetic field, as shown here on the equation. The constant of proportionality is called the gyromagnetic ratio of a proton, which we won't describe further, divided by two pi. What this equation tells us is that if we can measure the frequency at which the atomic dipoles precess, and we can instantly determine the strength of the magnetic field. A schematic of a proton procession magnetometer instrument is shown here. It consists of a canister of proton, which fluid, such as hydrocarbon or water, around which a coil of wire is wound. The ends of this wire are attached to battery. When not connected to a battery, the output of the wire coil goes to a piece of electronics that can determine the frequency of the current in the wire. The proto magnetometer is used as follows. First of all, we close the switch to position one, which enables a current to flow through the quarter. Why the coil of wire is essentially a solenoid. And when a current flows through it, it produces a strong magnetic field parallel to the axis of the coil. This strong magnetic field aligns, or the atomic dipole moments in this protein-rich food be parallel to the axis of the coil. We then change the switch to location two. This switch is off the current to the coil of wire and know the only magnetic field present is that of the Earth's magnetic field. At this point, the atomic dipole moments start to precess around the magnetic field lines, and they do so in unison. This induces a current in the coil of wire, and the frequency of that current will be proportional to the intensity of the magnetic field, of the external magnetic field, as given by the equation on the previous slide. The precession of the atomic dipole moments continues only for a few seconds until thermal fluctuations start to randomise the motion of the atoms. Again, these few seconds are sufficient to be able to accurately determine the frequency of the induced current and hence the magnetic field intensity. The advantage of this instrument is threefold. Firstly, you do not have to accurately aligned instrument in order to get a good reading of the geom, magnetic field intensity. Secondly, it's an absolute instrument. By absolute, I mean that it does not need to be calibrated by any other system. In fact, because it's an absolute instrument, the proton magnetometer is often used to calibrate other types of magnetometers, such as fluctuate magnetometer, I'll describe in a few minutes. Thirdly, the instrument is not susceptible to thermal drift or drift over time. The disadvantage of a proton magnetometer is that it can only measure intensity, not direction. Also, it cannot continuously measure the magnetic field because you need to cycle through the sequence of applying a strong field and then measure the induced current for a couple of seconds. If we wanted to make measurements faster than about once every five seconds, and you would need to use another instrument, such as a flux Kate magnetometer. So here we have a simplified schematic of a flux geek magnetometer. A flux Kate magnetometer consists of two identical and parallel iron bars. That if a primary set of windings consisting of wire wrapped around each iron bar in opposite directions, as shown here in blue. The details of the operational principles are a bit more complicated than that of the proto magnetometer. But in essence, it depends upon an imbalance of the field experienced in each of the iron bars due to the some of the geom magnetic field plus the solenoid field, which is in an opposite direction in each of the iron bars. The important things to remember about flux gates are that firstly, only measure the component of the field parallel to the axis of the iron bars. In Praxis, each sensing head will have a set of three bar pairs arranged at right angles to each other. So they measure all three components of the external magnetic field. Secondly, it is a continuous instrument, so it's good for measuring rapid changes in the magnetic field. For example, when you need to make very frequent observations in an era magnetic survey where the instruments may be housed in a fast flying plane. If you use the proto magnetometer in an air magnetic survey, the several seconds between measurements might mean that you only had one observation per kilometre. Thirdly, a flux keeps magnetometer is not an absolute machine. So you need to calibrate the instrument frequently with an absolute instruments such as a proton magnetometer. And fourthly, and finally, the flux gate is sensitive to changes in temperature as well as shock noise. So you need to be much more careful handling the Fluctuate magnetometer. You may need to account for variations in temperature. And you need to be careful not to drop the instrument. Of proton and fluctuate magnetometers are very common on both the use for Jim magnetic surveys. They're both lightweight and they're both relatively cheap at about 10 thousand pounds or so each. And both of similar sensitivities. Probably the proton precession magnetometer is easy to use because you don't eat any special orientation of the instrument itself. And in fact, there's a proton precession magnetometers that we use in our practicals. In the next lecture, I will show you how to interpret the magnetic normally is measured using a proton magnetometer.