Single-domain critical sizes for coercivity and remanence

It is usually assumed that magnetic parameters such as coercivity and satur ation 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 L-SD(coerc) for coercivity and L-SD(rem) for remanence. In general, L-SD(coerc) less than or equal to L-SD(rem). Up to L = L-SD(rem), the satur ation remanent state is single-domain. If a sufficiently large reverse fiel d is applied, a conventional SD state would reverse by uniform rotation. Ho wever, the mode of reversal is nonuniform if the grain size is between L-SD (coerc) and L-SD(rem), so in this size range the SD state is less stable. T o calculate the critical sizes, we use rigorous nucleation theory and obtai n analytical expressions, The analytical form allows us to explore the effe ct of grain shape, stress, crystallographic orientation and titanium conten t in titanomagnetites, We adapt the theory to cubic anisotropy with K-1 < 0 : which allows us to apply the expressions to titanomagnetites, We find tha t the size range for SD coercivity is always small. The size range for SD r emanence can vary enormously depending on the anisotropy, If the easy axes are oriented favorably, the SD state can occur in large x = 0.6 titanomagne tite grains. Ensembles of magnetite grains with aspect ratios greater than 5 have SD-like remanence but low coercivity. However, most synthetic magnet ite 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.