Hi there. So today I want to talk about magnetic nanoparticles. So first of all, let's define what we mean by a magnetic nanoparticle. Well, a magnetic nanoparticle is a particle that's typically less than 100 nanometers in diameter, and they're a class of nanoparticle that can be manipulated using magnetic fields.
They're often made of ferrite, which is iron oxides, or metals like nickel, iron, or cobalt. And they're usually coated or passivated. with something like a silica shell or ligand or surfactant. And this helps to prevent clumping or agglomeration of the nanoparticles. And it also functionalizes the surface for whatever application that you want.
And of course the type of coating that you would pick to put on your nanoparticle depends on what you're going to do with it. Now in the last lecture I talked about basic magnetism that you might have learned about in your introductory physics courses. So this is the magnetization curve, or the hysteresis curve, for a ferromagnetic material that we talked about in the last lecture. So there's a couple of parameters that you can deduce from looking at your curve here, and I'd like to talk about them because they can be pretty important in some of the nanoparticle applications.
So the first is the coercivity. And the coercivity of the material is related to the width of the magnetization curve, basically where it is at point C and A. F here, that width.
Alright, it tells you what the magnetic field strength is that has to be applied in order to bring the magnetization of that material back to zero. Now this is important in applications like data storage, for example. You want the coercivity to be large enough that your bit doesn't flip spontaneously.
In other words, if this is a very narrow curve, then a small stray magnetic field might cause your bit to flip and your data to be then lost or overwritten. However, you want the coercivity to be small enough that it doesn't cost you too much energy to write that bit in the first place. So that's an important property. Another parameter from the magnetization curve is the remnants. And that's the value of the magnetization of the material when the external magnetic field strength is zero.
So that would be at points B and E here on your curve. Now, magnetic... recording applications, since we're already talking about it, they require a large remnants, but other applications like magnetic nanoparticles for cancer treatment would prefer this value to be as small as possible.
Now when it comes to magnetic nanoparticles, size really does matter a lot. Okay, so let's talk about this plot here. The blue curve here that you can see shows the size dependence of the coercivity of a particle.
with the radius plotted on the horizontal axis. And you can see that this is a ferromagnetic material in the bulk. So as it approaches large radius or infinite radius, you can see it approaches an asymptote or a limit here. All right.
So that means that it's going to have a magnetic field even in the absence of an externally applied magnetic field. So it's a ferromagnetic material in the bulk. It has a non-zero coercivity. And then as you start to shrink the nanoparticle down, you can see...
that the coercivity goes up, okay, until it comes to a peak right here. Now, that is due to the fact that it's becoming a single magnetic domain. So you can see that in a large particle, you have a large number of domains, and they're all kind of oriented randomly. And then as you shrink it down, there's fewer and fewer domains until it just becomes the one domain, all right? Now, as you continue to shrink it down, then the coercivity actually falls to zero here.
and then it makes the transition to being called a superparamagnetic material. And we'll talk more about that. So why does this happen? Well, this is partly because as you shrink the particle down, the number of magnetic domains in the material shrinks until it's a single domain particle, as we discussed. And the critical diameter of that particle, when this happens, depends upon a lot of different factors.
So as you change the type of material and maybe even the shape of the nanoparticle that you've got, then that value is going to change. Some of the reasons that it might change is because the value of the magnetic saturation of the material changes, among other properties. Now, it's really all about why this happens and what's going on here is really all about the free energy calculation.
And there's two main competing effects. And those two competing effects are the demagnetizing field and the exchange interaction. So what does that mean?
Well, The demagnetizing field or the stray field is the magnetic field that's generated by the magnetization of a magnet. Electric and magnetic fields have an energy density or cost to them, if you will. So this is true even in vacuum. So if you have an electric or a magnetic field moving through the vacuum of space, you might remember from introductory physics that there's an energy per unit volume or an energy density associated with just that field that's proportional to some constants times the... the magnetic field or the electric field squared.
So the total energy associated with the demagnetizing field is found then by taking the integral over the volume of the magnet. So what that means is that as the size increases, that means that there's a greater energy and hence a greater energy cost associated with the demagnetizing field. And this is the principal reason why magnetic domains form in bulk materials.
If you have a bunch of magnetic moments scattered throughout the material oriented randomly, then your net magnetic field is going to be pretty close to zero. And since you're integrating over the volume and the magnetic field, if the vector points basically to zero, the cost associated with that demagnetizing field is also pretty close to zero. Now quantum mechanics is responsible for the exchange interaction, which is our second competing effect. And quantum mechanics tells us...
that it's energetically favorable for nearest neighbor atoms in ferromagnetic materials to have parallel magnetic moments. So quantum mechanics wants neighboring atoms to have aligned magnetic moments and hence one domain basically in the whole material. So this is because in certain materials and it also depends upon the crystalline structure and how close the neighboring atoms are among other things but basically Quantum effects matter here because the wave functions of the neighboring particles overlap, and so the particles can influence or the atoms can influence one another. And the formation of a domain wall where, for example, neighboring atoms would have magnetic moments that are not aligned, so here you have atom A pointing one way and out of B pointing another, right?
That costs energy in terms of the exchange interaction. And so it would prefer to be this way where the energy is minimized due to the exchange interaction. And so forming that domain wall between those two atoms costs energy. Okay, so here's what happens actually when you take a bulk ferromagnet and you place it in an external magnetic field.
Initially those, if it's not a permanent magnet, they'll be, the domains will be randomly oriented. They'll be pointing in lots of different directions. And then what happens is when you place it. inside of a magnetic field, an external magnetic field, there's going to be a torque according to the equation mu cross B where mu is your magnetic moment and B is your external magnetic field and it's going to want to rotate those things. Now the energy is equal to the negative dot product of the magnetic moment with the external magnetic field which means since it's the negative dot product that that energy will be lowest when the magnetic moment and the magnetic field are aligned in most cases.
that provides sort of a potential well that it can fall into. So what that does is the size of the domains with the magnetic moments that are aligned with the field already or close to align with the field, those are going to grow. That growth starts at the edge or the domain wall where the exchange interaction would already prefer those neighboring atoms to be aligned in their magnetic moments. And so it's true that the magnetic moment will rotate in the presence of a magnetic field, but it's not like it happens all throughout domains that aren't aligned at once.
It's going to start at the domain wall and rotate around to align and propagate outward as it happens. Okay, so that's how a sample can become a permanent magnet, because then if you take away the external magnetic field, we have a coercivity for that. and then it's going to remain kind of aligned with the field even in the absence of that external field. Now what happens in nanoparticles is at a critical threshold in the nanoscale particle, the energy is minimized when one domain will grow to encompass the entire particle. At that threshold value, at that threshold critical size, the energy cost associated with the demagnetizing field isn't very high because your particle is pretty small.
Okay. So let's look at this curve now with that new knowledge that we've gained in this discussion. When the coercivity falls to zero, it becomes what's called a superparamagnetic particle.
The susceptibility, the magnetic susceptibility, is still larger than a typical paramagnetic material. Because it is a ferromagnet in the bulk, right? So it's going to have that susceptibility that's larger.
For example, if you had an iron oxide, it already has a larger susceptibility than something like an aluminum. Okay? So the susceptibility is larger than a typical paramagnetic material, and so it responds very strongly to externally applied magnetic fields.
And yet, it's actually a small enough particle that edge effects and thermal effects are going to cause that thing to go back to a randomly oriented magnetic moment when the field goes to zero. So it acts like a paramagnetic material in that in the absence of a field, they're not all going to be rotated to align, to be aligned with the field. See, it goes back to a random orientation of your magnetic moment.
Okay, so when the applied field vanishes, the particles no longer behave as magnetic materials and this can be really useful in a wide variety of applications. It can also be a problem for a wide variety of applications as we'll discuss in a moment. Okay, so particle size thresholds for common ferromagnetic materials.
This is a plot taken from the introductory introduction to nanoscience and nanotechnology by Horniak and other authors. So here's a bar plot and it plots the nanoparticle diameter where these things happen, various transitions happen for different particles. You can see that for different types of materials the sizes are going to vary, sometimes by quite a lot.
If you look at this plot, the dark gray corresponds to the range of sizes where it's a single domain particle, but not yet a superparamagnetic material. So up here at the top you can see that transition happens at about 100 nanometers and it drops down all the way to about say 50 nanometers for some materials. So in the range of 50 to 100 nanometers you're getting that transition from being a multi-domain particle to a single domain particle.
Now then as the particle size continues to decrease they'll eventually be a threshold or critical value of the diameter. where it will transition to being a superparamagnet. And so that happens in the range of, say, all the way up to 30 nanometers, all the way down to about 10 or 5 nanometers.
That transition happens. Now, this property, like I said, superparamagnetism, which does sound a little bit like supercalifragilisticexpialidocious, it looks like you're just going to break into song, but anyway, the property can be really useful in a lot of biomedical applications. like contrast agents for MRIs, targeted drug delivery, hyperthermia to kill cancer cells, et cetera. However, it does establish a limit, the superparamagnetic limit, which is a great title, by the way, on the storage density of hard disk drives. Basically, it's going to place a minimum size on the magnetic storage particles because, of course, if it's a superparamagnetic particle in the absence of an external field, you're going to lose your data.
And so that can cause a lot of problems. Now another fun application of superparamagnetic nanoparticles is ferrofluids. So ferrofluids are colloidal suspensions of magnetic nanoparticles.
They behave like fluids. Even in the presence of magnetic fields, they're going to flow. And I've posted a really awesome video, external video, that you can see it's very zen-like, it's got music, and it sort of shows the art of ferrofluids, if you will.
And they're going to flow in response to these magnetic forces in preferred directions. Now the ferrofluids often consist of iron oxide nanoparticles coated with a surfactant to prevent the agglomeration, and then they're suspended in either water or oil. They lose their magnetic properties when the applied field is zero, and then they act like a normal fluid.
So... I hope you enjoyed that and if you have any questions as always let me know and thanks for your attention and time