Orientation of Magnetic Dipoles

Does a magnetic dipole (in a permanent magnet) tend to align with the B-field or with the H-field?

The current loop (Ampère) model of the magnetic dipole suggests the former, while the magnetic-monopole (Gilbert) model suggests the latter.

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$$\vec{H}=\frac{\vec{B}}{\mu_0}-\vec{M}$$ And since dipole moment is always colinear with itself, aligning with B-field is equivalent to aligning with H-field.

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(A) If you put a B-field in free space and a small magnet in the field, it rotates so that the magnetic moment is parallel to the B-field (U=-m⋅B, so potential energy is minimized when m and B are parallel).

(B) Inside a bar magnet, the B-field points parallel to the m's inside the magnet, while the H-field points in the opposite direction to the m's.

(If the bar magnet is a very very long, narrow cylinder, polarized along its axis, then the H field is almost 0, so $B/\mu_0$ is almost equal to M.)

Based on (A) and (B), you might think that the magnetic field tends to stabilize a bar magnet, but in reality it's the exact opposite -- they call it a "demagnetizing field" for a reason. The magnetic field wants to flip the magnets around and stop the alignment of magnetic moments. The bar magnet maintains its magnetization despite its own magnetic field, rather than because of it. (The more important factor is that the bar magnet wants to minimize electron kinetic energy, which is related to spin-alignment via the Pauli exclusion principle.) The demagnetizing field is the main reason domains form in magnets.

Most magnetism is associated with electron spins. These are true intrinsic point dipoles: Neither current loops nor magnetic-monopole-pairs. It turns out that H is almost always more helpful than B for understanding the behavior of magnetic materials, but I don't think there's any fundamental reason for that, it's just the result when you work everything out very carefully.

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