Energy of a single-domain particle in a B-field

[HappyJazz]

Homework Statement

As seen here, http://homes.nano.aau.dk/ld/EOM15.pdf (last page):

"Now a 1-domain paricle is placed in a magnetic field B in the z direction. The magnetization M of the particle points in a direction with an angle θ to the z-axis. The particle has volume V.

Homework Equations

The Attempt at a Solution

I've solved the first part, determining the energy of a single-domain particle (no B-field) and a 2-domain particle (also no B-field). However, now that the 1-domain particle is placed in an external field the case is another.

I've set the energy equal to:

"magnetostatic energy" + "energy from the dipole / field interaction (-µ * B * number of magnetic dipoles * cos(theta))" + "anisotropic energy since the field is not parallel with the magnetization"

You can see the formula attached in the gif. However, it just looks wrong to me, and I feel I've somehow forgot something very important

 

[Jhero]

.





Your attempt at a solution is on the right track, but there are a few things that should be clarified. First of all, the formula you have attached is not complete. The energy of a single-domain particle in an external magnetic field should also include the Zeeman energy, which is the energy associated with the interaction between the magnetic moment of the particle and the external magnetic field. This can be expressed as -μ0*μ*B*cos(θ), where μ0 is the permeability of free space, μ is the magnetic moment of the particle, B is the magnetic field strength, and θ is the angle between the magnetic moment and the magnetic field.

Additionally, the magnetostatic energy should be calculated using the demagnetizing factor, which takes into account the shape and size of the particle. This can be expressed as -½*μ0*H*χ, where H is the applied magnetic field strength and χ is the demagnetizing factor.

Finally, the anisotropic energy term should also be included, as you have mentioned. This takes into account the anisotropy of the material, which affects the direction of the magnetic moment. This can be expressed as -K*V*sin^2(θ), where K is the anisotropy constant and V is the volume of the particle.

Therefore, the complete formula for the energy of a single-domain particle in an external magnetic field is:

E = -½*μ0*H*χ - μ0*μ*B*cos(θ) - K*V*sin^2(θ)

I hope this helps clarify any confusion you may have had. Good luck with your calculations!