Distribution function of forces exerted by defects on domain walls in 50–50% NiFe

Abstract

Defects in ferromagnetic materials can exert forces on domain walls. For a given defect there is a maximum force fm which it can exert. For any greater force, the wall snaps free of the defect. At this point the average wall position has moved past the defect a distance z0, called the range of the defect. There is a linear relation between fm and z0 given by fm=k z0, where k is a spring constant. There is a distribution function n(z0) of defect ranges such that n(z0) dz0 gives the number of defects per unit volume having a range between z0 and z0+dz0. The number of defects per unit volume which can exert a maximum force between fm and fm+dfm is n(fm/k) (dfm/k). The distribution function for a particular sample (a tape-wound core of grain-oriented 50–50% NiFe) has been determined. It is given by n(z0)=z0−1Nexp(−z0/Z), where N≃1.6×1012 m−3 and Z=average range ≃ 70 μ. The spring constant k≃5×10−3 N/m. The maximum force averaged over the distribution is fm≃3.5×10−7 N. The total number of defects with which a steadily moving wall interacts at any one time is finite and is N0≃104. The defect density is estimated to be ≃2×1013 m−3. The results are checked by comparison with independent experimental and theoretical results and are found to be in satisfactory agreement provided that some experimental results are reinterpreted in the light of other experiments which observe the wall configuration rather than assuming it.