The physical role of magnetically semi-hard Co-2(+) cation addition in enhancing the AC heat induction temperature (TAO) or specific loss power (SLP) of solid (CoxMn1-x)Fe-2O-4 superparamagnetic iron oxide nanoparticles (SPIONPs) was systematically investigated at the biologically safe and physiologically tolerable range of H-AC (H-AC,H-safe = 1.12 x 10(9) A m(-1) s(-1), f(appl) = 100 kHz, H-appl = 140 Oe (11.2 A m(-1))) to demonstrate which physical parameter would be the most critical and dominant in enhancing the T-AC (SLP) of SPIONPs. According to the experimentally and theoretically analyzed results, it was clearly demonstrated that the enhancement of magnetic anisotropy (K-u)-dependent AC magnetic softness including the Neel relaxation time constant T-N (approximate to tau(eff), effective relaxation time constant), and its dependent out-of-phase magnetic susceptibility (chi '') primarily caused by the Co2+ cation addition is the most dominant parameter to enhance the T-AC (SLP). This clarified result strongly suggests that the development of new design and synthesis methods enabling to significantly enhance the K-u by improving the crystalline anisotropy, shape anisotropy, stress (magnetoelastic) anisotropy, thermally-induced anisotropy, and exchange anisotropy is the most critical to enhance the T-AC (SLP) of SPIONPs at the H-AC,H-safe (particularly at the lower f(appl) < 120 kHz) for clinically safe magnetic nanoparticle hyperthermia.