In a 180 domain Bloch wall, it is known that exchange energy can be decreased if we allow the 180 changes in spin direction to take place gradually over N atoms, thereby minimizing the angle between adjacent spins [ since exchange energy in a ferromagnetic is a minimum only when adjacent spins are parallel]. However crystal anisotropy energy within the wall is higher than it is in the adjoining domains since the spins within the wall are pointing away from the easy direction and so anisotropy energy tries to make the wall thin, in order to reduce the number of spins pointing in non-easy direction.

Accordingly, anisotropy energy within the wall should be directly proportional to the domain wall width/thickness and exchange energy should be inversely proportional to the wall width, since larger is the width lesser is the exchange energy and larger is the anisotropy. Right? However, the formula for wall width given in books completely contradicts this. Below I have attached wall width formula from two different books [B.D.Culity and David Gills] According to the formula, wall width is directly proportional to the exchange energy and inversely to the anisotropy...

PLEASE DISCUSS ON THIS.