Fig. 3: Trace analysis of radius vector and temperature measurements for magnetic particles.

All experiments were conducted using 5 mg/mL FF, composed of 12.7 nm Co0.42Fe2.58O4@Co0.65Fe2.35O4 MNPs (overall composition is Co0.6Fe2.4O4, Keff = 168.1 kJ/m3) dispersed in hexane. a The 9-pixel average temperature profile of FF NPs activated at 104 kHz, fitted with the Box-Lucas function. b Comparison of the theoretical and experimental SAR values of FF. SARR denotes the calculated value based on the conventional model by Rosensweig, and SARN (Néel) and SARB (Brownian) are the calculated values from this work. Subsequently, logistic fitting was performed with the sigmoid function. Hth represents the value of H at which the fitted function reaches half of its maximum predicted value. c Plot of sin(α) as a function of the applied field amplitude, compared with the DC hysteresis value (black), illustrating the oscillation angle along the z-axis at 104 kHz. d The maximum rotary coefficient (kr,max) where ωϕ = ωext and the rotary coefficient deduced from a fitted logistic curve are represented.