Quantitative Determination of the Interaction Fields in Aggregates of Single-Domain Particles

The distribution of interaction fields in a substance composed of single domain particles may be determined from the anhysteretic magnetization characteristic of the bulk material. This characteristic as used here is the remanent induction vs applied field when, during application of the field, an alternating field decreasing slowly from well above the coercive force to zero is applied. It may be seen that when such a process is applied to an isolated single domain particle, the resulting magnetization will always be of the same sense as the applied dc field, even for almost negligible values of applied field. It follows that any group of independent single domain particles will also act in the same way even though there may be a distribution of coercive forces within the group: That is, for any applied dc field, all particles will be magnetized in one direction or the other after the application of the decreasing alternating bias field. This would imply an anhysteretic characteristic rising with infinite slope at the origin. A finite slope does not result if one merely adds a demagnetizing field, since this will only subtract from the applied field and any applied field will still produce saturation. The finite slope of the anhysteretic characteristic may be explained only by including the effects of the interaction fields. The interaction field acting on any particle is the sum of the fields from all the other particles and is determined by the geometrical arrangement of the particles independently of the applied field. Now the total dc field applied to any particle will be the sum of its interaction field and the external dc field. For any value of applied external field, all particles with interaction fields smaller than the applied external field will be magnetized in the same sense as the applied field after the application of the alternating bias field. The total net magnetization of a group of particles will therefore be the cumulative distribution function of the interaction fields and will be independent of the coercive force. The actual distribution of amplitudes of the interaction fields may therefore be readily measured. An expression is derived for the root mean square value of the interaction field at any point in an infinite aggregate of single domain particles. This expression states that the average interaction field may be determined from the volumetric packing factor of the particles and their remanent induction. The calculated interaction fields for an aggregate material is in close agreement with experimentally measured values.