Re: [Phys-L] magnetic field reversals

[John Denker <jsd@av8n.com>]

On 10/05/2015 10:01 AM, Carl Mungan wrote:

> It seems somewhat common to find that bar magnets used in labs get 
> their magnetization reversed, so the actual poles are opposite the 
> ones painted on the bar. I am wondering why reversals are so common?
>
> If it’s because they get dropped or whatever, [1]

> why isn’t it more common to find that the net magnetization vector
> shifts by some angle relative to the axis of the bar, rather than
> shifting around by 180 degrees?   [2]

> Aren’t the domains small compared to the physical dimensions of the
> bar (say 1 cm in diameter)?        [3]


Starting with question 2:  You're not likely to see a bar-shaped
object with the field at some odd angle relative to the axis.
This can be understood in terms of basic energy considerations:
 a) Start with two cubes of unit size, widely separated, magnetized
  along the Z direction.  Bring them together to form a bar with 
  two units of length in the Z direction.  The energy is now /lower/.
  Bring in more and more cubes to increase the Z-length, and the 
  energy gets lower and lower.
 b) The energy is even lower if you form a very long chain and 
  bend it so it closes on itself, creating an endless loop.
 c) Start over.  Bring two cubes together side-by-side to form a
  bar in the X direction.  The energy is now /higher/.  Bring in
  more and more cubes to increase the X-width, and the energy
  gets higher and higher.
 d) The energy is even higher if you bring cubes together to
  form a slab in the XY plane.

In case (c) and (d) it is energetically favorable for half of the 
cubes to flip over, forming an ↑↓↑↓↑↓↑↓↑↓ array  In cases (a) and
(b) if you inadvertently install a few of the cubes upside-down,
it is energetically favorable for them to flip so they are all 
aligned the same.

This can be considered a /scaling/ argument, if you think of scaling
X, Y, and Z separately.  Y'all know how much I love scaling arguments.
  https://www.av8n.com/physics/scaling.htm

This suggests some obvious answers to question [1].  If you have 
N magnets, there are lots of ways of using N-1 of them to gang up
on the remaining one and forcing it to flip.  Mechanical banging
might help nucleate the transition, but is nowhere near sufficient
by itself.

As for question [3]: 
 -- In a needle geometry, it is energetically favorable to have one
  huge domain.
 -- In a slab geometry, it is energetically favorable to have lots
  of tiny domains.  The exact size depends on a tradeoff between the
  ultramicroscopic solid-state physics that favors alignment versus 
  the macroscopic energy of the magnetic field.  It also depends on
  gory details of the microstructure.  Steel is microcrystalline;
  it's never one big crystal.

======================
Tangential remark:

As always, when talking about issues of stability, the fundamental
idea is /entropy/.  Talking about "energetically favorable" situations
(as I have done here) is a bit of a sneaky trick.  It's OK in this 
case, since /system/ energy serves as a proxy for /global/ entropy 
in this situation.

In other situations you might need to use the Helmholtz free energy
or the Gibbs free enthalpy ... or (!) use the entropy directly.
  https://www.av8n.com/physics/thermo/spontaneous.html#sec-proxies

Everything I said here about "energetically favorable" situations 
is technically true AFAIK, but it might be considered dubious on 
pedagogical grounds, insofar as it could reinforce misconceptions 
about the fundamental role of energy versus the fundamental role 
of entropy.