Magnetic Domains The magnetic system I'm studyng is composed by a strip divided in two head-to-head domains, one larger than the other: as a consequence the system is unstable.

What is the reason if this instability? In other words, why the larger domains tends to expand? I think that a strip uniformly magnetized has a lower energy. But, what is the energy term minimized by the one-domain configuration with respect to the two-domains configuration?
Now, I switch on an external magnetic field, directed along the easy axis of the strip. If its amplitude is "small" the larger domains expands as before. In this case reducing the smaller domain increase the Zeeman energy term of the strip. So, again, what is the energy therm minimized here?
(In all my reasonings I'm not considering the energy stored in the domain wall between the two domain: is it a big negligence?)
Update: after running some simulations the energy term that decreases in the one-domain configuration (without the external field applied) is the demagnetizing energy. But I can't figure out why.
 A: You essentially have 2 bar magnets with their north poles held against each other. As we all know from playing with magnets as a kid this has an energy cost associated with it. 
This energy is going to be (to a first approximation) proportional to the total magnetic moment of each of the domains.
$$
E \propto m_1 m_2
$$
Magnetic moment is an extensive property, so it is proportional to the lengths of the domains, therefore
$$
E \propto l_1l_2
$$
We also no that the 2 lengths sum up to the total length of the bar, that is $l_1+l_2 = L$. putting this together, we have that the magnetic term energy will be proportional to 
$$
E \propto l_1(L-l_1)
$$
Which we minimise by setting $l_1=0$ or $L$. It is also not hard to see that the generalised force pushes in the direction of the smaller part. 
If you introduce an external field, then I would expect there to be some minimum size for the smaller partition at which point the Zeeman term balances the interaction term. 
Also a note about domain wall energy. Domain wall energy is generally the dominant term on a microscopic scale, but it scales with the area of the domain wall rather than the volume of the system, so in the thermodynamic limit its contribution goes to 0. Consequently whether it is relevant depends a great deal on what question you are asking. The reason you can neglect it in this instance is because (assuming that its area has been minimised) the contribution of the domain wall energy to the total energy is discrete and can't be varied continuously (you must have an integer number of domain walls) Consequently the domain wall energy does not lead to any generalised forces. 
