Why is a paramagnetic material attracted into a magnetic field?

Question

I want to start by saying I've seen this topic: Attraction and repulsion of Magnetic materials and its supposed duplicates and it hasn't helped me very much.

In the book Introduction to Electrodynamics by Griffiths, it says the following: "In general, when a sample is placed in a region of nonuniform field, the paramagnet is attracted into the field, whereas the diamagnet is repelled away." (section 6.14, p.273, 4th ed.)

I don't understand why this should be true. The book states that the reasons for paramagnetism and diamagnetism are due to quantum mechanics, but the book seems to imply there is a classical reason as well.

The only thing I can think of is the equation that in a nonuniform magnetic field, $F=\nabla(m \cdot B)$. Now if the $B$ field is getting weaker if you continue in the direction the field is in at that point (and stronger if you go the reverse direction), then for a paramagnetic material, with $m$ lined up with $B$ the direction of $F=\nabla(m \cdot B)$ is into the field, and for a diamagnetic field, $F=\nabla(m \cdot B)$ is away from the field. But I don't see any reason why the $B$ field gets weaker as you continue along the direction of the $B$ field.

Any help would be very appreciated.

Answer 1

I can give you a simplified picture:

The external magnetic field induces in the atoms of a diamagnetic material a current, which produces a magnetic field in the opposite direction (Lenz's law). Because of this effect, the diamagnet is repelled away.

The same effect takes place in a paramagnet, but here is another effect stronger: Due to the magnetic moment of the unpaired electrons in the material they accrue a total magnetisation in the direction of the external field.

This does not occur in diamagnetic material because there are no unpaired electrons.

I hope it helped.

Answer 2

I think there is some confusion here. The actual field direction does not play a role for diamagnetic or paramagnetic behavior. What is important is the field strength. What is actually ment by Griffith is: "The paramagnet is attracted into the region of higher field magnitude." In a simlified picture it goes into regions where the field lines are more dense, while a diamagnet lowers its energy by going into regions of lower field line density. You got it, hence, almost right already.