Magnetization
If you ask the average person what "magnetism" is, they will likely talk about refrigerator magnets or compass needles—things that seem to have no obvious connection to moving charges. Yet, all magnetic phenomena are ultimately due to electric charges in motion.
If you look at matter on an atomic scale, you find tiny currents: electrons orbiting nuclei and spinning on their axes. These microscopic current loops act as magnetic dipoles. When an external magnetic field is applied, these dipoles align or shift, causing the material to become magnetized.
1. Diamagnets, Paramagnets, Ferromagnets
Unlike electric polarization, where induced dipoles almost always line up with the electric field, magnetic response is more varied. We classify materials based on how their internal dipoles respond to an external field $\mathbf{B}$:
- I. Paramagnets: Materials containing unpaired electrons (like Aluminum or Oxygen). Their atomic dipoles try to align parallel to the external field. However, they are constantly jostled by thermal energy, so the alignment is usually very weak. They are weakly attracted to magnets.
- II. Diamagnets: Materials where the orbital motion of electrons shifts to create a field opposite to the external field. This effect is present in all matter (like Water or Copper) but is usually masked if paramagnetism is present. They are weakly repelled by magnets.
- III. Ferromagnets: Materials like Iron where quantum mechanical effects lock neighboring dipoles together into "domains." They retain their magnetization even after the external field is removed.
Note: Ferromagnetism is theoretically more complex than the other two. We will focus on Paramagnetism and Diamagnetism here, and return to Ferromagnets later in Linear and Nonlinear Media.
2. Torques and Forces on Magnetic Dipoles
To understand Paramagnetism, consider a single magnetic dipole $\mathbf{m}$ placed in a uniform magnetic field $\mathbf{B}$. The field exerts a torque on the current loop, twisting it to line up with the field direction.
The Battle Against Heat
If the torque lines them up, why aren't all paramagnets incredibly strong magnets? The answer is
Thermal Energy.
The atoms in a material are constantly vibrating and colliding due to heat (Temperature). This random
thermal motion kicks the dipoles around, scrambling their orientation. The magnetization we observe is a
statistical balance: the magnetic field tries to order them, and heat tries to disorder them.
(Force on a dipole in a non-uniform field)
3. Effect of a Magnetic Field on Atomic Orbits
While electron spin and torque explain paramagnetism, what explains Diamagnetism?
Electrons revolve around the nucleus, creating an orbital dipole moment. When a magnetic field is applied perpendicular to the orbit, the magnetic force $-e(\mathbf{v} \times \mathbf{B})$ acts radially. This changes the centripetal force, causing the electron to speed up or slow down.
Be careful with signs! The Right Hand Rule applies to current ($I$) or positive charge. Because the
electron has a negative charge ($-e$), the current flows opposite to the velocity
($\mathbf{v}$).
Consequently, the magnetic force direction is opposite to what you would get for a positive charge.
This leads to the specific result that the induced field opposes the external field.
According to Lenz's law, this change creates an induced dipole moment $\Delta \mathbf{m}$ that is always opposite to the direction of $\mathbf{B}$. This effect exists in all matter, though it is often masked by stronger paramagnetism.
4. Magnetization (M)
To treat these effects macroscopically, we don't want to track billions of atomic dipoles. Instead, we define a vector field called Magnetization, $\mathbf{M}$.
$\mathbf{M}$ is defined as the magnetic dipole moment per unit volume. It plays a role analogous to Polarization $\mathbf{P}$ in electrostatics.
If a material has a magnetization $\mathbf{M}$, it creates a magnetic field of its own. We calculate this field using the method of Bound Currents, which we will explore in the next section.