Single‐domain critical sizes for coercivity and remanence

Abstract

It is usually assumed that magnetic parameters such as coercivity and saturation remanence are single‐domain (SD) over the same size range. In reality, there is a different SD size range for each parameter. We define critical sizes LSDcoerc for coercivity and LSDrem for remanence. In general, LSDcoerc ≤ LSDrem. Up to L = LSDrem, the saturation remanent state is single‐domain. If a sufficiently large reverse field is applied, a conventional SD state would reverse by uniform rotation. However, the mode of reversal is nonuniform if the grain size is between LSDcoerc and LSDrem, so in this size range the SD state is less stable. To calculate the critical sizes, we use rigorous nucleation theory and obtain analytical expressions. The analytical form allows us to explore the effect of grain shape, stress, crystallographic orientation and titanium content in titanomagnetites. We adapt the theory to cubic anisotropy with K1 < 0, which allows us to apply the expressions to titanomagnetites. We find that the size range for SD coercivity is always small. The size range for SD remanence can vary enormously depending on the anisotropy. If the easy axes are oriented favorably, the SD state can occur in large x = 0.6 titanomagnetite grains. Ensembles of magnetite grains with aspect ratios greater than 5 have SD‐like remanence but low coercivity. However, most synthetic magnetite grains are nearly equant, and the predicted size range for SD remanence is small to nonexistent. This, rather than grain interactions, may be the reason they have properties such as saturation remanence that do not agree well with standard SD theory.