Table 1.

Summary of our findings.

Composition	Particle size (nm)	Adiabatic approach	Non-adiabatic approach		Non-adiabatic and radiating process
		SLP (W/g)	SLP (W/g)	$ϵ$ (W/K)	$\mathit{SLP}$ (W/g)	$ϵ$ (W/K)	$h_{\mathit{air}}$ (W/(m${}^2$K))
${\mathbf{Fe}}_3{\mathbf{O}}_{\mathbf{4}}$	$7.6\pm 0.2$	$0.67\pm 0.01$	$0.717\pm 0.002$	$0.00939\pm 0.00004$	$0.714\pm 0.002$	$0.00453\pm 0.00004$	$4.98\pm 0.06$
${\mathbf{Fe}}_3{\mathbf{O}}_{\mathbf{4}}$	$12.7\pm 0.2$	$1.60\pm 0.02$	$1.940\pm 0.003$	$0.01293\pm 0.00003$	$1.925\pm 0.003$	$0.00783\pm 0.00003$	$8.61\pm 0.06$
${\mathbf{MgFe}}_2{\mathbf{O}}_{\mathbf{4}}$	$13.4\pm 0.3$	$0.86\pm 0.01$	$0.891\pm 0.002$	$0.01171\pm 0.00004$	$0.887\pm 0.002$	$0.00683\pm 0.00004$	$7.51\pm 0.06$
${\mathbf{MgFe}}_2{\mathbf{O}}_{\mathbf{4}}$	$18.1\pm 0.2$	$1.07\pm 0.01$	$1.167\pm 0.002$	$0.01299\pm 0.00004$	$1.161\pm 0.002$	$0.00806\pm 0.00004$	$8.87\pm 0.07$
${\mathbf{MgFe}}_2{\mathbf{O}}_{\mathbf{4}}$	$24.2\pm 0.2$	$1.43\pm 0.01$	$1.704\pm 0.003$	$0.01425\pm 0.00003$	$1.693\pm 0.003$	$0.00923\pm 0.00003$	$10.15\pm 0.07$

The average particle size is estimated by TEM. The experimental thermal quantities for our magnetite and magnesium ferrite nanoparticles are estimated by fitting, using the theoretical approaches, from magnetic hyperthermia experiments performed with alternating magnetic field with frequency of 70.5 kHz and amplitude of 70 Oe. Specifically, we estimate SLP and $ϵ$, and consequently $h_{\mathit{air}}$ from Eq. (20), from our approach describing magnetic nanoparticles under AMF in a non-adiabatic and radiating process, as well as, for comparison, the SLP from the adiabatic model, and SLP and $ϵ$ from the approach considering non-adiabatic conditions.