The true cause of magnetostriction
  The cause of magnetostriction is revealed by analyzing this phenomenon in a polydomain crystal of Fe. It is based on the two fundamentals: (a) magnetization is a rearrangement of spins by rearrangement of the crystal structure, and (b) the {\alpha}-Fe has a tetragonal rather than cubic structure. The magnetostriction results from bringing the shorter tetragonal axis to coincide with, or closer to the direction of the applied magnetic field. It is not rooted in the alleged deformation of crystal unit cell. 
Yuri Mnyukh
physics.gen-ph