# Let's make some single-domain magnetic nanoparticles

• etotheipi
In summary, the conversation discusses the energy and stability of a spherical single-domain nanoparticle, and aims to find the critical radius for forming a second domain. The stray field energy is expected to scale with the radius cubed, while the domain wall energy is expected to scale with the radius squared. The Ising model and super-paramagnetic iron oxide are mentioned as possible tools for further exploration of this topic. Additionally, the use of single domain particles in magnetic recording is suggested as a potential source of relevant information.
etotheipi
Might be interesting, to determine how small a spherical single-domain nanoparticle needs to be in order for it to be stable against forming more domains. The energy of such a nanoparticle (occupying a spherical region ##\Omega##) will be$$E_1 = -\frac{\mu_0}{2}\int_{\Omega} \boldsymbol{M}_0 \cdot \boldsymbol{H} d\tau = \frac{\mu_0}{2} \int_{\Omega} \boldsymbol{M}_0 \cdot \nabla U d\tau$$where ##\boldsymbol{H} = - \nabla U## where ##\nabla^2 U = \nabla \cdot \boldsymbol{M}_0##. [This stray field energy we expect to scale ##\propto r^3##]. Let's then consider forming a second domain, and forming a domain wall [at some energy cost] along the equatorial plane. Then, in one hemisphere the magnetisation is ##\mathbf{M}_0##, and in the other ##-\mathbf{M}_0##. Denoting ##\Omega = \Omega_1 \cup \Omega_2##,$$E_2 = \underbrace{\frac{\mu_0}{2} \sum_{i=1}^{2} \int_{\Omega_i} (-1)^i \boldsymbol{M}_0 \cdot \nabla U d\tau}_{\text{stray field}} + \underbrace{E_{\text{bloch}}}_{\text{domain wall}}$$To be stable against forming a second domain, it's required that ##E_2 > E_1##. Forming more domains reduces stray field but at the cost of increasing domain wall energy, so the aim is to find that critical radius.

I would like some help to flesh out this calculation! Firstly, I expect the domain wall energy to scale ##\propto r^2## as the domain wall area, but how can I determine an explicit expression for this? Also, what approximations are justified, in order to simplify the determination of the stray field energy? Thanks!

How about doing something in 1D first? I am not at all expert here but aren't you going to end up with the Ising model or similar? This is a very interesting question but by no means a new one.

etotheipi
I didn't even know what the Ising model was until about 1 minute and 30 seconds ago, but it does look cool. I'm sure Professor Tong has written some notes about them, somewhere [EDIT: yes, he has, under 'statistical field theory' ]. I'm not familiar with this field so I don't know what tools are available or what models already exist. But open to suggestions

What do you mean by trying something in 1D first?

anorlunda
Check the Ising model stuff. I know the questions were usually regarding phase transitions (order-disorder). The 1D models are just a string of interacting spins with some temperature maybe? This led to much of Ken Wilsons renormalization group. Enough here to last a lifetime! Wish I knew more.

etotheipi
Okay cool, thanks, looks like I've got a bit of reading to do... better go and make a cup of tea first

hutchphd
etotheipi said:
I would like some help to flesh out this calculation!
This seems like an interesting calculation. In MRI we use super-paramagnetic iron oxide which consists of iron oxide particles that are small enough to consist of a single domain. So you can use the size of those as a check

nasu, anorlunda, Motore and 2 others
Single domain particles were used in the magnetic coatings of the old magnetic tapes. You can find a lot of relating info by looking up magnetic recording. And iron oxide was the most common material too.

## 1. What are single-domain magnetic nanoparticles?

Single-domain magnetic nanoparticles are tiny particles made of a single magnetic domain, meaning that all the magnetic moments within the particle are aligned in the same direction. This gives them unique magnetic properties that make them useful in various scientific and technological applications.

## 2. How are single-domain magnetic nanoparticles made?

Single-domain magnetic nanoparticles can be made through a variety of methods, including chemical synthesis, thermal decomposition, and physical vapor deposition. These methods involve manipulating the size, shape, and composition of the particles to control their magnetic properties.

## 3. What are the potential applications of single-domain magnetic nanoparticles?

Single-domain magnetic nanoparticles have a wide range of potential applications in fields such as biomedicine, data storage, and environmental remediation. They can be used as contrast agents in medical imaging, as building blocks for magnetic data storage devices, and as catalysts for environmental remediation processes.

## 4. What are the advantages of using single-domain magnetic nanoparticles?

Single-domain magnetic nanoparticles have several advantages over other types of magnetic nanoparticles. They have a higher magnetic moment, meaning they are more responsive to external magnetic fields, and they have a more uniform magnetic behavior, making them more predictable and controllable in applications.

## 5. What are the challenges in working with single-domain magnetic nanoparticles?

One of the main challenges in working with single-domain magnetic nanoparticles is their tendency to agglomerate, or clump together. This can affect their magnetic properties and make them difficult to disperse in a solution. Additionally, the synthesis and characterization of single-domain magnetic nanoparticles can be complex and require specialized equipment and expertise.

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