- #1

rogdal

- 14

- 2

- Homework Statement
- A magnetic dipole μ, which is located at the origin of a coordinate system, generates a magnetic field in its environment given by:

$$\vec{B}(\vec{r})=\frac{\mu_0}{4\pi}\frac{3(\vec{\mu}·\vec{r})\vec{r}-r^2\vec{\mu}}{r^5}$$

Calculate the magnetic field B generated by an atom with a magnetic moment μ ≃ μB (Bohr magneton) at the position of a neighbouring atom in iron. The typical first-neighbour distance r0 for Fe ferromagnets can be calculated knowing that Fe has a bcc lattice with a = 2.866 ̊A.

- Relevant Equations
- $$\vec{B}(\vec{r})=\frac{\mu_0}{4\pi}\frac{3(\vec{\mu}·\vec{r})\vec{r}-r^2\vec{\mu}}{r^5}$$

In a BCC lattice, ##r_0 = \frac{\sqrt{3}}{2}a##

I'm having a bit of trouble with this exercise because, even if I understand the physics of the dipole-dipole interaction in an ideal classical system, I don't get to know how to approach this problem. I've got a few doubts about how this system would work.

First of all, what would be the direction of the magnetic moment ##\vec{\mu}## of iron with respect to its lattice? I guess that by simplicity the direction [100] should be chosen, but I don't know if each atom's magnetic moment has the same direction.

Besides, now assuming ##\vec{\mu}## is fixed, the value of B wouldn't be the same in all the first neighbours positions, right? Since it depends on the dot product between the magnetic moment and the first neighbour's position, and this wouldn't be the same for the atom in the upper left corner and the one in the bottom right.

Do you know how to approach this exercise?

Thank you!

First of all, what would be the direction of the magnetic moment ##\vec{\mu}## of iron with respect to its lattice? I guess that by simplicity the direction [100] should be chosen, but I don't know if each atom's magnetic moment has the same direction.

Besides, now assuming ##\vec{\mu}## is fixed, the value of B wouldn't be the same in all the first neighbours positions, right? Since it depends on the dot product between the magnetic moment and the first neighbour's position, and this wouldn't be the same for the atom in the upper left corner and the one in the bottom right.

Do you know how to approach this exercise?

Thank you!