Magnetic nanoparticles provide a unique combination of small size and responsiveness to magnetic fields making them attractive for applications in electronics, biology, and medicine. When exposed to alternating magnetic fields, magnetic nanoparticles can generate heat through loss power mechanisms that continue to challenge a complete physical description. The influence of internal nanoparticle (intracore) magnetic domain structure on relaxation remains unexplored. Within the context of potential biomedical applications, this study focuses on the dramatic differences observed among the specific loss power of three magnetic iron oxide nanoparticle constructs having comparable size and chemical composition. Analysis of polarization analyzed small angle neutron scattering data reveals unexpected and complex coupling among magnetic domains within the nanoparticle cores that influences their interactions with external magnetic fields. These results challenge the prevailing concepts in hyperthermia which limit consideration to size and shape of magnetic single domain nanoparticles.