No, for a couple of reasons.
Ordinarily, the tendency of the electron spins (little magnets) to
line up with each other is more fragile than the tendency of the atoms
or molecules to form crystals. So the Curie temperature, at which the
magnetism vanishes (the spins start pointing randomly) is less than the
temperature at which the crystal melts. When the crystal is cooled down
again, the material can't remember which direction was magnetic North
and which was South, so the new magnetism has no memory of the
direction of the old magnetism.
There's a deep reason why for any magnetic pattern the exact
opposite pattern is equally likely to show up. One is just what you get
if you look at the other but with time running backwards. In thermal
equilibrium, there's on the average no difference between forward and
backward in time, so neither pattern can be more likely than the other.
In one case that we know of a liquid metal remains magnetic, in
the sense that the spins still line up into magnetic domains.
(www.edpsciences.org/articles/ euro/pdf/1998/19/44117.pdf ) However,
even then the direction of the magnetism will be quickly forgotten over
time in the liquid as the domains randomly rotate. In a solid, the
combination of the regular crystal pattern and random local deviations
from the regular pattern make the magnetic directions get stuck in
special directions. It takes a very long time in a good magnet for the
domains to flip around, so that's why we call those 'permanent'
One case that is particularly interesting is the magnet inside the
Earth that makes compasses line up. It's much more complicated than the
simple magnetic materials we talked about, because it is not close to
being in thermal equilibrium. Also, it's enormous, which tends to make
the typical times for it to change long. Nevertheless, the Earth's
magnetism too occasionally changes, leaving a record in the
longer-lived magnetism of rocks.
Mike and Tom
(published on 10/22/2007)