Solution (source code)

= Solution

For the nonbiology fabrication objective, \b[reduce unwanted dipolar coupling while preserving a useful single-particle dynamic response]. Lithographically reduce magnetic <volume> or adjust aspect ratio to control $\mu\simeq M_sV$ and <magnetic anisotropy>. Reducing $V$ reduces the characteristic pair interaction approximately as $V^2/r^3$, but also changes $E_a$ and relaxation time.

A nonmagnetic spacer coating or stable surface layer can maintain minimum center-to-center separation after release and reduce aggregation. At a fixed magnetic <volume> fraction this geometric constraint has a real packing cost; separation cannot be increased without limit while claiming unchanged loading.

Tune particle <volume>, <magnetic anisotropy> and spacing together, then measure dynamic susceptibility/loop area at the specified <temperature> and <frequency>. In a simple single-relaxation model, useful phase lag occurs near $\omega\tau\sim1$; making particles so small that reversal is essentially instantaneous can reduce dissipative response. \b[Clinical treatment optimization remains user-deferred]; these are materials/fabrication controls, not a treatment recommendation.